Technology in Local Industries

In this section, we will discover the attractive science behind traditional textile production, such as tie-dye, batik, and Adire. These methods use a technique called resist dyeing, where certain parts of the fabric are protected from the dye using materials like wax, strings, or starch to create beautiful patterns. We will investigate the scientific principles at play, including how dye moves into fabric through processes like absorption and diffusion, how materials dissolve (solubility), and how colours are made permanent through chemical fixation. By understanding the role of heat and different types of dyes and fixatives, you will discover how these traditional art forms are deeply rooted in scientific principles.

KEY IDEAS

• Resist Dyeing Techniques: Adire, batik, and tie-dye use resist dyeing, where parts of fabric are covered with wax, string, or starch to block dye. When removed, they reveal patterned designs that reflect both creativity and an understanding of dye behaviour.

• Absorption and Diffusion: Dye spreads through diffusion, moving from concentrated areas into fabric fibres. The fabric’s absorption depends on fibre type—natural fibres like cotton absorb dyes better than synthetics.

• Solubility and Dye Preparation: Dyes must fully dissolve in water for even colouring.

Temperature, pH, and dye composition affect solubility and ensure smooth, lasting colour penetration.

• Chemical Fixation: Mordants or fixatives such as alum or soda ash bond dye molecules to fibres, making colours permanent and resistant to fading or washing.

• Role of Heat: Heat increases molecular movement, helping dyes bond faster and more evenly. In batik, hot wax controls dye spread and sets colour effectively.

• Eco-Relationships and Sustainability: Using natural dyes from plants, bark, and minerals reflects environmental awareness. These eco-friendly methods reduce pollution and support sustainable resource use.

• Integration of Art and Science: Indigenous textile making blends artistic skill with scientific principles. Through observation and practice, artisans apply chemistry and physics to create durable, beautiful fabrics.

Textile design, far beyond mere aesthetics, profoundly impacts the social, cultural, and economic well-being of individuals, communities, and nations. As a form of mobile cultural heritage, textiles serve as vital storehouses of identity, history, and belief systems, making their preservation, documentation, and study for future generations, research, and public education an imperative.

Defining Indigenous Ghanaian Textiles

In Ghana, indigenous textiles are more than just clothing; they are deeply woven into the fabric of society, representing the attire specific to various ethnic groups with strong historical and cultural roots. While elements like colour palettes, forms, and the yarns and fibre types used may have undergone some modifications across successive generations, the foundational ideas, underlying philosophies, intricate techniques, and rich histories embedded within these textiles have largely remained consistent.

Ghana is a vibrant hub for traditional African fabrics, showcasing a remarkable diversity of indigenous textiles. Examples of textiles found in Ghana include:

1. Bogolanfini: Hailing from Mali, its mud-dyed patterns reflect natural earth tones and abstract designs.

2. Adinkra cloth: A renowned Ghanaian fabric characterised by its stamped symbols, each carrying deep philosophical meanings and proverbs.

3. Kuba cloth: Originally from the Democratic Republic of Congo, known for its intricate geometric patterns created from raffia fibre.

4. Adire: A Yoruba resist-dyed textile from Nigeria, employing techniques like tying, stitching, or starch resist.

5. Kente: Perhaps the most iconic Ghanaian textile, woven from silk and cotton strips in vibrant, complex geometric patterns, each with specific names and meanings.

6. Akwete Cloth: A hand-woven fabric from Nigeria, similar to Kente, known for its bold patterns and vibrant colours.

7. Aso-Oke: A hand-loomed cloth from the Yoruba people of Nigeria, often used for special occasions.

These exquisite textiles are traditionally crafted from natural fibres like cotton, silk, and raffia, and dyed with pigments derived from plants, minerals, or insects. However, a critical challenge lies in their inherent susceptibility to degradation; the natural colours tend to fade over time, making these precious artefacts vulnerable to extinction if not actively preserved.

Indigenous textiles are far more than just handicrafts; they are living cultural artefacts that embody the very history, philosophies, and beliefs of a people. Their intricate designs, chosen colours, and production techniques symbolise a rich cultural history that must be safeguarded to uphold fundamental feelings of self, community, and belonging.

Groups of Indigenous Ghanaian Textiles

1. Traditional textiles made by hand (Kente) The complete history of kente cloth, one of Ghana’s most iconic textiles, is not definitively settled, with various accounts combining legend and historical evidence. Asante mythology attributes the origin of kente weaving to Ota Kraban and Ameyaw in Bonwire, who reputedly drew inspiration from a spider’s web, a narrative supported by the prevalence of woven lace and needlework during that era. However, historical accounts often trace kente’s roots to ancient weaving traditions in prosperous West African Kingdoms, flourishing between 300 and 1600 AD, pointing to archaeological findings of narrow-strip cloths from Mali, dating back to the 11th century AD.

Regardless of its exact genesis, weaving appears to have been established in West Africa long before the formal creation of kente as we know it. Evidence of early weaving, such as spindle whorls and loom weights, has been found in ancient empires like Meroe (500 BC to 300 AD). In Ghana, weaving reportedly began in the northern regions, initially using rough raffia and later local cotton provided by farmers. By the 17th century, weaving had become established in Bonwire, Ashanti.

Traditionally, women prepared the fibres by spinning cotton, while men handled the weaving process, setting the warp and went on a four-heddle loom. Early kente also incorporated local Okanantan spider silk, which was later supplemented or replaced by imported European silk, sometimes mixed with cotton yarns. The complex design and production methods, including the use of specific loom components, highlight kente’s profound historical and cultural significance as a mobile cultural heritage item essential for preservation, study, and public education.

Figure 10.1: Kente, a typical Ghanaian fabric.

2. Traditional textiles with handmade prints (Adinkra) Adinkra motifs serve as a powerful form of cultural expression, filled with deep symbolic meaning derived from both representational natural objects and abstract concepts. These designs, traditionally stamped onto fabric, communicate profound philosophical ideas and proverbs. For example, specific shapes like the oval convey concepts of holiness, femininity, and beauty, while a half-circle or crescent is associated with fertility. Other symbols carry equally significant messages: the cross embodies compassion, and the arrow signifies a new beginning. Beyond general cultural meaning, adinkra cloth was historically tailored to express a monarch’s personal philosophy. A king’s choice of aya (a fern-patterned) fabric, for instance, specifically communicated his fearlessness. Through this intricate visual language, adinkra textiles become wearable declarations of identity and wisdom.

Figure 10.2: Some adinkra symbols and their meaning.

Processes involved in the production of indigenous Adinkra textiles ₁. Fabric sourcing and preparation: The foundation of adinkra cloth is typically cotton fabric. Traditionally, this cotton would be woven locally. The fabric chosen can either be white (for a strong contrast with the dark stamp) or pre-dyed to a characteristic rusty brown colour. This brown hue is specifically known as kuntunkuni, a name derived from the tree whose bark provides the dye.

2. Dye preparation: The distinctive dark dye used for stamping Adinkra motifs is prepared from the bark of a specific indigenous tree, the kuntunkuni tree (scientifically known as Bombax brevicuspe). The process involves boiling or steeping the bark for an extended period to extract its rich dark pigments. This extract is then reduced and prepared into a thick, dark, inky dye solution that is suitable for stamping. The quality and depth of this dye are crucial for the clarity and longevity of the adinkra symbols.

3. Motif stamp carving: Before stamping can begin, the adinkra motifs themselves must be prepared. These intricate symbols are traditionally carved onto small, durable pieces of calabash gourd or wood. The carving process creates a raised relief of the desired symbol.

Each specific adinkra symbol has a predefined meaning and shape, requiring precise carving skills to ensure accuracy and detail when transferred to the fabric. Each stamp usually has a handle for easy gripping.

4. Stamping process (Application): The chosen cotton fabric (white or kuntunkuni brown) is laid out smoothly, usually on a flat surface or a stretched frame. The carved adinkra stamp is then dipped into the prepared dark dye solution, ensuring an even coating of dye on the raised pattern. The dye-laden stamp is then physically pressed firmly and carefully onto the fabric. This action transfers the dark motif onto the cloth.

The artisan works systematically, repeating the stamping process across the entire fabric to create a coherent and often repetitive pattern, or to strategically place specific symbols.

5. Drying and finishing: After the stamping is complete, the fabric is traditionally laid out to dry in the sun. The heat of the sun aids in fixing the dye to the cotton fibres, making it more permanent. Once completely dry, the adinkra cloth may undergo a final rinsing to remove any excess dye or residue, which helps to further set the colour and ensures the patterns are crisp and clear.

Activity 10.1 Examining some indigenous textiles in Ghana Aim: To engage learners in massive research on some Ghanaian textiles and their significance.

What to do

1. In small groups of three or four, carry out research into various types of Ghanaian indigenous textiles.

2. In the same groups, discuss the textiles and highlight their cultural significance, traditional methods, and scientific principles involved in their production.

3. In the same groups, create visual aids like posters, diagrams, or digital presentations to illustrate key concepts and findings.

Discussions: Learners present their posters, diagrams and digital presentations for class discussion and display for a gallery walk.

Dye chemistry and pigment extraction ₐ. Biochemical extraction (Leaching): The characteristic dark, rusty-brown dye for adinkra is extracted from the bark of the kuntunkuni tree (Bombax brevicuspe).

This process typically involves boiling or prolonged steeping of the bark in water.

Scientifically, this is a form of leaching, where soluble organic compounds (the dye pigments, or chromophores) are extracted from the plant material into the hot water. The bark contains complex molecules, likely tannins (a class of polyphenols) and other natural organic pigments, which are responsible for the colour.

b. Dye solution formulation: The extracted liquid is then processed into a thicker, inky consistency suitable for stamping. The stability and viscosity of this dye

solution are critical for clear motif transfer.

c. Dye-metal interactions (Potential mordanting): While the provided text doesn’t explicitly mention a mordant for adinkra dye, many natural brown dyes, particularly those rich in tannins, form stable complexes with metal ions. If the dye pots are made of iron, or if the water used contains dissolved iron, a chelation reaction could occur, where the dye forms insoluble coordination complexes with iron ions (Fe³⁺), enhancing colour fixation and contributing to the characteristic “rusty brown” or dark brown/black hue. This type of reaction significantly improves the dye’s wash-fastness (measure of the dye’s resistance to fading when washed) and light-fastness (how well a fabric retains its colour when exposed to light).

Material science of fabric-dye Interaction ₐ. Cellulose fibre adsorption: Adinkra predominantly uses cotton fabric, which is composed primarily of cellulose fibres. Cellulose fibres are hydrophilic (water- loving) due to their hydroxyl (-OH) groups. The dye molecules adhere to these cellulose fibres through various intermolecular forces, including hydrogen bonding and van der Waals forces, which allow the dye to be physically adsorbed onto and within the fibre structure.

b. Capillary Action: it the ability of a liquid to flow in narrow spaces without the assistance of external forces. When the liquid dye is applied to the fabric, it spreads outward from the point of contact into the surrounding fibres through capillary action. This phenomenon, driven by the surface tension of the liquid and the adhesive forces between the liquid and the narrow inter-fibre spaces, dictates the sharpness or slight bleeding of the stamped motif’s edges.

Physical principles of stamping (Direct application) ₐ. Pressure and transfer: The act of physically pressing the carved adinkra stamp onto the fabric is governed by principles of pressure (force per unit area) and adhesion. The dye solution adheres to the raised surfaces of the stamp. When the stamp is pressed onto the fabric, the pressure ensures intimate contact, facilitating the direct transfer of dye from the stamp to the fabric.

b. Surface tension control: The viscosity and surface tension of the dye solution are carefully balanced through traditional preparation methods to ensure that the dye adheres well to the stamp without dripping excessively and transfers cleanly to the fabric without blurring the fine details of the motif.

Drying and dye fixation

a. Evaporation: After the motifs are stamped, the fabric is typically laid out to dry.

This process primarily involves the evaporation of the water molecules (solvent) from the dye solution, leaving the solid dye particles physically trapped within the fabric fibres.

b. Photochemical reactions (Sunlight): Exposure to sunlight during drying can also play a role. The heat from the sun can further assist in the drying process, while ultraviolet (UV) radiation can induce photochemical reactions in some natural dyes, contributing to the final colour development and enhancing the dye’s permanence and resistance to fading.

Processes involved in the production of indigenous tie-and-dye textile Tie-dye, a traditional textile art, boasts a rich history spanning centuries and continents, found in diverse cultures across Asia, Africa, and potentially Latin America. This marvellous technique involves using thread to bind bundles of fabric tightly before dyeing, creating intricate designs through the resist method. Across West Africa, from Senegal to Nigeria, including countries like Ghana, Mali, and Sierra Leone, tie-dye traditions like Gara and Adire are integral to the cultural landscape, utilizing either natural or synthetic dyes to produce their incredible patterns.

1. Fabric Preparation: The process typically begins with natural fibres, most commonly cotton, due to its absorbency and durability. Silk and rayon are also used in some traditions. The fabric is thoroughly washed to remove any impurities, sizing agents, or natural oils that might hinder dye absorption. It can then be left damp or dried, depending on the desired crispness or blending of the final pattern. For some Adire variations, the fabric might be pre-dyed to a base colour, such as the kuntunkuni brown.

2. Resist application (tying, folding, stitching, waxing or pasting): This is the defining stage of tie-dye, where specific areas of the fabric are physically prevented from absorbing dye. Artisans employ a variety of ingenious methods, which are:

a. Tying (e.g., Adire oniko, Gara): Sections of the fabric are tightly bound with raffia, thread, string, or rubber bands. Small objects like stones, seeds, or corn kernels might be tied inside the fabric to create distinct circular or oval patterns.

Folding the cloth into complex patterns (like a concertina or spiral) before tying creates geometric designs. The tightness and placement of the ties directly determine the pattern’s sharpness and size.

b. Stitching (e.g., Adire alabere): Fine stitches are sewn into the fabric along a desired pattern line, and the thread is then pulled taut to gather and compress the fabric. This creates linear, curved, or more elaborate stitched resist patterns.

c. Starch pasting (e.g., Adire eleko): A thick, viscous paste, traditionally made from cassava or maize flour, is hand-painted or stencilled onto the fabric. When this paste dries, it forms a physical barrier that the dye cannot penetrate.

d. Waxing (Batik): Melted wax is applied to the fabric using specialized tools (like a canting for fine lines or a cap for stamping). The hydrophobic wax solidifies and creates a barrier against the water-based dye.

3. Dye preparation

a. Natural dye extraction: Traditional tie-dye heavily relies on natural dyes.

Indigo: Leaves from the indigo plant (Lonchocarpus cyanescens or Indigofera tinctoria) are collected, often pounded, and then allowed to ferment in large earthenware dye pots, typically partially sunk into the ground. This fermentation process is a crucial chemical reduction, transforming the insoluble blue indigo into a soluble, yellowish-green “leuco-indigo” form. Wood ashes or caustic soda might be added to soften water and maintain alkalinity, vital for the dyeing process.

b. Kola nut: Kola nuts are finely crushed, usually with a mortar and pestle, and mixed with water and wood ashes (acting as a mordant/fixative) to produce a brown dye. This dye bath is labour-intensive to prepare and has a shorter usable life compared to indigo.

c. (Immersion and oxidation): The fabric, with its applied resists, is carefully immersed into the prepared dye bath. For indigo, the fabric is left in the soluble leuco-indigo solution to absorb the dye. Upon removal and exposure to air (oxygen), the leuco-indigo rapidly undergoes an oxidation reaction, reverting to its insoluble, vibrant blue form that is permanently trapped within the fabric fibres. The depth and richness of the blue hue are controlled by the number of times the fabric is dipped; the more immersions, the darker the indigo becomes.

For kola nut dye, the fabric absorbs the brown colour directly from the solution.

Sometimes, fabrics are over-dyed (e.g., dipped in kola nut dye first, then in indigo) to create complex multi-tonal effects like dark greens or greenish-blacks.

d. Removal of resist and finishing: Once the dyeing process is complete and the dye is fixed (often by drying), the resist materials are removed. For tied fabrics, the strings, raffia, or rubber bands are untied. For stitched fabrics, the threads are carefully cut and pulled out. For starch-resist Adire eleko, the dried cassava paste is scraped or washed off. For batik, the wax is typically removed by boiling the fabric in water, which melts the wax, allowing it to be skimmed off, followed by a thorough washing.

Scientific principles involved in tie-dye textile production

1. Physical principle of resist application

a. Mechanical barrier & pressure: The core of tie-dye involves physical manipulation of the fabric (tying, folding, twisting, knotting, stitching). These actions create a mechanical barrier by compressing and densifying the fabric in specific areas. The pressure exerted by the ties (e.g., raffia, string, rubber bands) physically blocks dye molecules from penetrating the tightly bound regions. This also reduces the pore space and hinders capillary action within those compressed areas.

b. Hydrophobicity (wax resist in batik/related methods): In techniques like Batik (which uses a similar resist principle), melted wax is applied. Wax is hydrophobic (water-repelling), creating an impermeable physical barrier against the aqueous dye solution.

c. Physical blockade (starch/clay resist): In some forms, a thick paste (e.g., cassava starch) is applied. This paste dries to form a physical solid layer that mechanically blocks dye penetration.

2. Fibre chemistry and dye adsorption/Binding

a. Cellulose fibre structure (Cotton): Most traditional tie and dye fabrics are made from cotton, which is composed primarily of cellulose (a polymer of glucose units). Cellulose fibres contain numerous hydroxyl (-OH) groups, making them hydrophilic (water-attracting) and capable of interacting with dye molecules.

b. Dye molecule properties (chromophores & auxochromes): Dyes contain chromophores (chemical groups responsible for colour by absorbing certain wavelengths of white light) and auxochromes (functional groups that enhance solubility and aid in binding to fibres).

c. Dye-fibre bonding: The permanence of the dye depends on the type of bond formed.

i. Covalent Bonding: Modern synthetic fibre-reactive dyes form strong, permanent covalent bonds with cellulose fibres under specific pH conditions (e.g., alkaline conditions created by soda ash). This is the most robust type of bonding, leading to high wash-fastness.

ii. Hydrogen bonding & van der Waals forces: Many natural dyes (like indigo or kola nut) and some synthetic dyes bind through weaker hydrogen bonds (between dye and cellulose hydroxyls) and van der Waals forces (general intermolecular attractions). These are less permanent than covalent bonds but still effective.

iii. Mordanting (chemical bridges): For many natural dyes (e.g., kola nut dye), a mordant (e.g., wood ashes containing metal salts like aluminium or iron compounds) is crucial. Mordants act as chemical bridges by binding to both the dye molecule and the fibre, forming a stable coordination complex. This enhances the dye’s adherence, lightfastness, and often modifies the final colour.

3. Dye bath chemistry (pH, reduction-oxidation for indigo)

a. pH control: The pH of the dye bath is often critical for optimal dye uptake and reaction. For example, fibre-reactive dyes require an alkaline environment (high pH) for their reaction with cellulose. Acid dyes (used for protein fibres like wool/ silk) require acidic conditions.

b. Redox reactions (indigo dyeing): Traditional indigo dyeing involves sophisticated reduction-oxidation (redox) chemistry.

i. Reduction: In its natural state, indigo (indigotin) is an insoluble blue. To be used, it must be chemically reduced (e.g., through fermentation of leaves or by adding reducing agents like sodium hydrosulphate) in an alkaline environment. This converts it into a soluble, yellowish-green form called leuco-indigo (or indigo white).

ii. Oxidation: The fabric is immersed in this soluble leuco-indigo solution.

Upon removal from the dye bath and exposure to air (oxygen), the leuco- indigo rapidly oxidises back to its insoluble blue form (indigotin), which then precipitates and becomes physically trapped within the fabric fibres, creating the permanent blue colour. This is why the colour develops upon exposure to air.

4. Physical processes during dyeing and finishing

a. Diffusion & capillary action: Dye molecules move from areas of high concentration (dye bath) into the fabric fibres (lower concentration) through diffusion. Within the fabric, dye solution spreads through the tiny spaces between fibres by capillary action.

b. Evaporation: During drying, water evaporates from the dyed fabric, leaving the dye solids embedded within the fibres.

i. Mechanical Fixation: Techniques like beating the cloth with a mallet (e.g., after indigo dyeing) can physically press dye particles deeper into the fibres and increase the fabric’s sheen by compacting the fibres.

ii. Heat transfer (wax removal): In wax-resist methods (like batik), removing the wax involves heat transfer (boiling water) to melt the wax, exploiting its lower density to separate it from the fabric.

Activity 10.2 A Visit to A Tie and Dye Textile Production Facility Objective: To help learners acquire firsthand information on the processes involved in tie-dye textile production.

What to do

1. Observation and documentation of key processes involved.

2. Hands-on interactions with equipment, materials, and production personnel (if permitted), to foster a deeper understanding of real-world applications of concepts and scientific principles involved in the production.

Discussions

1. In pairs, learners prepare a flowchart of the kente production process based on their interaction with the production facility.

2. Learners compare and discuss their flow charts in a class interaction.

3. Learners explain the scientific principles behind the processes observed and are made to offer suggestions on how to improve those processes for a better production process.

BATIK Batik fabric-making is a wax-resist dyeing technique done by hand, usually in homes and small workshops by families or small groups of dealers.100% cotton fibre is used. From cotton grown in the dry savannah climate of northern Ghana, the plain fabric is made in factories up there in northern Ghana. Either calico or grey baft is used, the former being softer. The fabric dyes are imported.

Steps In Batik Fabric-Making

₁. Pre-shrinking: The cloth is pre-shrunk, due to the dyeing, washing and re-dyeing process. Hand-dyed & hand-printed, they are suitable for a wide variety of projects.

Sometimes light damask fabric is used, and those have a slight shimmer to the finished product. They have strong, vibrant colours with abstract or Ghanaian designs.

2. Wax application: Melted wax is applied to the fabric in a design of the batik maker’s choice with a brush or pre-carved wooden block. Starting with a lighter colour, the cloth is dipped in the first dye and then dried. Wherever the wax has seeped through the fabric, the dye will not penetrate; the rest is the new colour. More wax is applied for the next set of designs, followed by dyeing and drying until the complete number of colours and designs has been achieved. (Often several colours are used, with a series of waxing and dyeing steps.)

3. Boiling: The fabric is boiled to remove the wax for re-use, and to reveal the deep, rich colours and the fine crinkle lines that give batik its character. The last stages involve a final drying and ironing for sale.

A few of them have two designs on the same piece, meant to complement each other. One fabric is an accent to the other.

Processes Involved In The Production Of

Indigenous Batik

₁. Fabric Preparation: The process typically begins with natural fabrics, most commonly cotton or sometimes silk, due to their absorbency and suitability for wax application.

The fabric is thoroughly washed to remove any impurities, starches, or sizing agents that could interfere with dye absorption or wax adherence. It is then often stretched taut on a frame to ensure a smooth, stable surface for intricate wax application.

2. Design, planning and transfer (optional but common): While some skilled artisans may apply wax freehand, designs are often sketched onto the fabric lightly with a pencil or charcoal. For complex or repetitive patterns, a pre-made design might be traced or stamped onto the fabric.

3. Wax preparation and application (The resist)

a. Wax melting: A blend of waxes (traditionally beeswax for flexibility and paraffin wax for its characteristic crackle effect) is melted in a wax pot over a heat source, maintaining it at a consistent, hot liquid state.

b. Wax application: The melted wax is then applied to the fabric using specialized tools.

i. Canting (Tjanting): A pen-like tool with a small copper reservoir and a fine spout, used for drawing intricate lines, dots, and detailed patterns by hand. This is known as batik tulis (written batik).

ii. Cap (Tjap): A copper stamp with a carved design, used for applying repetitive patterns more quickly and consistently over larger areas. This is known as batik cap (stamped batik).

iii. Brushes: Used for applying larger areas of wax or broader strokes.

4. Resist mechanism: The wax, being hydrophobic (water-repelling), solidifies upon contact with the fabric, forming an impermeable barrier. This ensures that when the fabric is dyed, the areas covered by wax resist the dye and retain their original colour.

5. Dyeing (Lightest colour first): Once the wax has hardened, the fabric is immersed in a dye bath. The dye molecules only penetrate and colour the unwaxed areas of the fabric. Dyeing proceeds as follows:

a. Colour progression: Batik dyeing typically proceeds from the lightest colours to the darkest. The first dye bath will be the lightest desired colour.

b. Fixation: Dyes are allowed to absorb, and for many synthetic dyes, a fixing agent (like soda ash) is used to create a permanent bond with the fabric fibres. Natural dyes (like indigo, kola nut) have their own specific preparation and fixation methods.

c. Drying: After dyeing, the fabric is carefully removed from the dye bath and hung to dry completely. Wringing or squeezing is avoided to prevent the wax from cracking prematurely, unless the crackle effect is desired at this stage.

6. Repeated waxing and dyeing (for multi-colour designs): For multi-coloured batik, the process of waxing and dyeing is repeated in layers. After the first dye colour has dried, additional wax is applied to areas that are to retain that first colour. The fabric is then dyed in a darker colour. This process can be repeated multiple times, applying new wax to protect previously dyed areas and progressively introducing darker shades.

The distinctive “crackle effect” often seen in batik is created by deliberately crinkling or manipulating the fabric after a layer of wax has hardened, causing the wax to crack.

When the fabric is then dyed, the dye seeps into these fine cracks, creating a network of fine lines of the new colour within the waxed areas.

7. De-waxing (wax removal): Once all the desired colours have been applied and dried, the wax resist must be removed. The most common traditional method is to immerse the fabric in boiling water. The heat causes the wax to melt and separate from the fabric. Since wax is less dense than water, it floats to the surface, where it can be skimmed off (and often reused). In some methods, ironing the fabric between layers of absorbent paper (like newspaper) can also remove wax, as the paper absorbs the melted wax.

8. Final washing and finishing: After de-waxing, the fabric is thoroughly rinsed in warm water with soap to remove any residual wax and unbound dye. It is then dried and may be pressed or ironed to smooth out wrinkles and achieve the final desired finish.

Figure 10.3: Some Ghanaian batik fabric.

Scientific Principles Involved In Batik Textile

Production

1. Physical principle of wax as a resist

a. Hydrophobicity: This is the core principle of batik. Wax is a hydrophobic (water-repelling) substance, meaning it does not mix with water. When applied to fabric, the melted wax solidifies and forms an impermeable physical barrier.

This barrier prevents the aqueous dye solution from penetrating the waxed areas, leaving them undyed.

b. Melting and solidification: Wax has a relatively low melting point. It is applied to the fabric in its liquid (molten) state, allowing for intricate drawing or stamping.

Upon cooling, it rapidly solidifies, creating a stable, physical mask on the fabric surface.

c. Viscosity and adhesion: The consistency (viscosity) of the melted wax (often a blend of beeswax for flexibility and paraffin for brittleness/crackle) is crucial.

It must be viscous enough to cling to the fabric without excessive spreading but fluid enough to flow smoothly from tools like canting (for fine lines) or tjap (for stamping). It adheres to the fabric fibres through various intermolecular forces.

2. Fabric chemistry and dye adsorption/Binding

a. Cellulose fibre (Cotton): Batik predominantly uses natural cellulose fibres like cotton. These fibres are hydrophilic (water-absorbing) and have numerous hydroxyl (-OH) groups that are receptive to dye molecules.

b. Dye-fibre interaction: The way dyes bind to the fabric is chemical. Dyes contain chromophores (colour-bearing groups) and auxochromes (groups aiding solubility and binding).

i. Covalent bonding: For synthetic fibre-reactive dyes often used today, the dye forms strong, permanent covalent bonds with the cellulose fibres, typically in an alkaline environment (e.g., pH adjusted by soda ash).

ii. Hydrogen bonding/Physical adsorption: Many natural dyes, and some synthetics, bind through weaker intermolecular forces like hydrogen bonds and van der Waals forces.

c. Capillary action: The dye solution is drawn into the unwaxed areas of the fabric through capillary action, filling the microscopic spaces between and within the fibres.

3. Dye chemistry (especially for traditional dyes like indigo)

a. Solubility and redox reactions (indigo): If traditional indigo dye is used, complex reduction-oxidation (redox) chemistry is involved. Natural indigo (indigotin) is insoluble in water. It must be chemically reduced (e.g., through fermentation in an alkaline vat) to a soluble, yellowish-green form (leuco-indigo). When the fabric is removed from the vat and exposed to oxygen in the air, the leuco-indigo rapidly oxidises back into its insoluble blue form, becoming permanently trapped within the fabric fibres.

b. Mordanting (for certain dyes): While not universally required for all batik dyes, some natural dyes need mordants (metal salts like alum or iron) to act as chemical “bridges” that help fix the dye permanently to the fabric, improving colour-fastness by forming stable coordination complexes.

Physical Processes During Dyeing And Layering

₁. Sequential dyeing (light to dark): The multi-colour effects in batik are achieved by a precise sequence of waxing and dyeing, typically moving from the lightest dye colours to the darkest. Each colour is applied only to the unwaxed areas, and then new wax is applied to protect those newly dyed areas before immersing the fabric in a darker dye bath.

2. Drying and evaporation: After each dyeing stage, the fabric is dried, allowing the water to evaporate and leaving the dye solids embedded in the fibres.

3. Wax removal (de-waxing) and finishing

a. Heat transfer and phase change: The wax resist is removed, usually by immersing the fabric in boiling water. This applies heat, causing the wax to undergo a phase change from solid to liquid.

b. Density difference: Since melted wax is less dense than water, it floats to the surface, allowing it to be skimmed off (and often recycled).

c. Solvent removal (alternative): In some modern methods, chemical solvents might be used to dissolve the wax, which also relies on solubility principles.

d. Final washing: A thorough wash with soap and hot water removes any residual wax and unbound dye particles, ensuring a clean, vibrant final product.

4. Crackling effect (physics of fracture): The distinctive “crackle” lines in some Batik designs are achieved by mechanically manipulating the fabric after the wax has been applied and hardened (e.g., crumpling or folding). This induces tiny fractures or cracks in the brittle wax layer. When the fabric is then dyed, the dye seeps into these fine cracks, creating the characteristic network of lines.

Adire are indigo-dyed cotton cloths decorated using a resist-dying technique to create striking patterns in blue and white. They were traditionally made and worn by women throughout Ghana and West Africa. The cloths were usually made up of two strips of factory-produced cotton, sewn together to form a shape that was roughly square, and worn as wraps around the body. Cloths were made up of two strips of factory-produced cotton shirting sewn together to form a shape that was roughly square. They were generally worn by women as wrappers. One of the most important factors in the popularity of adire during the 1960s was that a large number of cloths could be produced quickly and cheaply in response to changing customer demands. It has now however fallen out of favour.

Cloths were usually prepared and dyed, by women, and treated in a variety of ways to create patterns that would be revealed after dying. Raffia and starch were the two most common forms of resist used in the production of adire.

Adire techniques proceed as listed below.

1. The dyeing process The cloths are usually prepared, and always dyed, by women. Their bright colour comes from imported indigo grains or locally-grown indigo leaves, which are fermented and mixed with water softened with caustic soda to make a dye. The cloth is dipped into a large pot of dye, and then pulled out to allow it to oxidise, a process which can be repeated to make the colour darker. Sometimes after dyeing it, the cloth is beaten with a mallet to make it shine softly (give it sheen).

2. Creating pattern Before dyeing, the fabric is treated in a variety of ways to prevent certain parts of it from absorbing dye. This will create the patterns revealed after the dyeing process. Raffia and starch are the two most common forms of resist-dyeing used. Tying raffia around the cloth, a process known as àdìrẹ oniko, can produce a huge variety of patterns. For

example, tying small stones or seeds into the cloth will create small circles, or larger circles can be made by lifting a point of fabric and binding the fabric beneath it tightly.

A pattern formed of a specific combination of circles is given a name; the pattern name often varies from town to town or changes over time. One example made in Ibadan in the 1960s features five rows of large circles with small circles filling the rest of the cloth, a pattern known there as olosupaeleso, which means “moons and fruits”.

Figure 10.4: Adire fabric.

Adire, The Art Of Raffia Resist Dyeing

Adire represents a captivating facet of traditional textile production, where the humble raffia fibre is masterfully employed to create intricate resist-dyed patterns. This technique, a subcategory of the broader adire (tie-dye) tradition, is renowned for its versatility and the stunning array of designs it yields, often in vibrant indigo blue and contrasting white.

At its core, adire oniko is a mechanical resist dyeing method. This means that patterns are formed by physically binding or tying sections of the fabric very tightly with raffia (or sometimes thread) before the cloth is immersed in a dye bath. The tightly bound areas act as a physical barrier, preventing the dye solution from penetrating the fabric fibres underneath.

This creates sharp, undyed patterns against the dyed background.

Crafting Patterns With Raffia, Techniques And Variations

A remarkable variety of patterns can be produced by varying the way the raffia is applied as follows:

1. Creating circles

a. Smaller circles: Artisans often tie small stones or seeds directly into the cloth.

The tightness of the knot around the object creates a small, defined circular resist, resulting in crisp white dots against the dyed background.

b. Larger circles: For bigger circular motifs, a point of fabric is lifted, and the fabric directly beneath it is bound tightly with raffia. The size of the lifted and bound area determines the diameter of the resulting circle.

2. Achieving linear and geometric patterns:

a. Concertina folding (Accordion pleating): One highly effective technique involves meticulously folding the cloth from corner to corner like a concertina (an accordion-like pleat). Once folded, the entire length of the pleated cloth is then bound very tightly at various, evenly spaced points along its length. When this tightly bound, folded cloth is dyed, the dye only saturates the exposed areas between the bindings. The bound sections remain undyed.

Upon unfolding and unbinding the cloth, this method creates a striking diamond- shaped pattern with alternating blue and white stripes. The broadness of these stripes can be precisely controlled by adjusting the intervals at which the cloth is bound. Tighter, closer bindings produce finer stripes, while looser, more spaced bindings result in broader stripes.

b. Beyond simple shapes: The ingenuity of adire oniko extends to much more complex designs. Artisans might combine various tying methods, incorporate intricate knotting techniques, or strategically pleat and bind the fabric to achieve highly detailed geometric motifs, abstract compositions, or even figurative representations.

3. The dyeing process

a. Traditionally indigo: While modern adire may use synthetic dyes, the traditional and most revered adire oniko employs natural indigo dye. This involves a multi- step chemical process:

b. Preparation of the indigo vat: Natural indigo dye is insoluble in water in its vibrant blue form. It must be chemically reduced in an alkaline solution (traditionally through fermentation using ingredients like ash, local sweeteners, and bacteria) to a soluble, yellowish-green form called leuco-indigo.

c. Dyeing immersion: The raffia-bound cloth is carefully immersed in this leuco- indigo dye bath. The soluble dye penetrates the unwaxed/unbound fibres.

d. Oxidation: Upon removal from the dye bath, the leuco-indigo rapidly oxidizes when exposed to air (oxygen). This chemical reaction converts it back into its insoluble blue form, effectively trapping the colour within the fabric fibres.

e. Repeated dipping: To achieve deeper and richer shades of blue, the fabric is typically dipped multiple times, allowing it to oxidize between each dip, sometimes requiring dozens of immersions.

4. Unbinding and finishing: After the desired depth of colour is achieved and the fabric is fully oxidized and dried, the raffia bindings are carefully removed, revealing the intricate white patterns against the deep blue background. The cloth is then rinsed and washed to remove any excess dye.

The meticulous handwork involved in the tying and folding, combined with the transformative chemistry of the indigo vat, makes adire oniko a testament to the scientific and artistic heritage embedded in indigenous textile traditions. The popularity of specific designs, like the “cloth of the year” in 1964, further highlights the cultural significance and dynamic evolution of this ancient craft.

Stitch resist The term adire alabare is used when sewing has been used as a means to resist the dye. If the sewing has been done with raffia, then it would be a form of adire oniko. Both machine sewing and hand sewing could be used to produce patterns. Although adire cloths are usually made by women, those produced using sewing machine are made by men. When two pieces of dyed cloth are stitched together, it creates a diamond shaped pattern with alternating blue and white stripes. The broadness of the stripes can be varied by the intervals at which it is bound.

Adire Adire encompasses various resist-dyeing techniques primarily practiced by the Yoruba people of South-Western Nigeria. It traditionally uses natural indigo dye and different resist materials.

Types of Adire and their resist mechanisms ₁. Adire Oniko (Tying/Knotting): Involves tying raffia, thread, or individual corn kernels/pebbles tightly around sections of fabric. The fabric can also be twisted or folded and tied.

Scientific process: Similar to tie-dye, this is a mechanical resist. The physical compression and tight wrapping create a barrier that prevents dye penetration or allows only limited seepage, resulting in circular, striped, or irregular patterns.

2. Adire Alabere (Stitching) Resist: Patterns are created by stitching raffia or thread tightly into the fabric in a specific design (e.g., lines, curves, motifs). The fabric is then gathered tightly along these stitched lines.

Scientific process: This is also a mechanical resist based on physical tension and compression. The tightly stitched areas are inaccessible to the dye solution. After dyeing, the raffia/thread is removed, revealing the undyed pattern.

3. Adire Eleko (Starch paste resist): A paste made from cassava starch (or rice starch) and other ingredients (e.g., alum, copper sulphate) is painted onto the fabric. The paste hardens upon drying.

Scientific process: This is a physical barrier resist. The thick, dried starch paste creates an impermeable layer that physically blocks the dye from reaching the fabric fibres underneath. The paste acts as a non-reactive coating.

Dyeing process (Traditionally indigo): Traditional Adire uses natural indigo dye, typically extracted from plants like Lonchocarpus cyanescens. Indigo is a vat dye.

Reduction: Indigo dye is insoluble in water in its natural (oxidized) blue form. To be used, it must be chemically reduced in an alkaline solution (e.g., with natural reducing agents like fermentation by bacteria in a traditional indigo vat, or synthetic reducing agents like sodium hydrosulphite in modern use). This turns it into a soluble, yellowish-green form called leuco-indigo.

Dyeing: The fabric (with resist applied) is immersed in this leuco-indigo dye bath.

The leuco-indigo molecules penetrate the fibres.

Oxidation: When the fabric is removed from the dye bath and exposed to air (oxygen), the leuco-indigo rapidly oxidizes back to its insoluble blue form, becoming trapped within the fibres. This oxidation reaction is what “fixes” the blue colour.

Repeated dyeing: To achieve deeper shades of blue, the fabric is repeatedly dipped into the indigo vat and exposed to air for oxidation, sometimes 25 or more times for a deep blue-black.

Removal of resist: For adire eleko, the dried cassava paste is scraped or washed off after dyeing, revealing the undyed patterns.

Scientific principles involved in Adire textile production ₁. Physical principles of resist application: Adire employs various techniques to create patterns by physically preventing dye from reaching certain areas of the fabric.

a. Mechanical compression (Adire Oniko & Adire Alabere):

i. Principle: This relies on applying pressure and physical barriers to the fabric. In adire oniko (tying/knotting), sections of the fabric are tightly bound with raffia, thread, or string, often incorporating small objects like stones or seeds. In adire alabere (stitching), patterns are created by sewing intricate lines with raffia or thread, then pulling the threads taut to gather and compress the fabric.

ii. Mechanism: The tight binding or stitching physically compresses the fabric fibres, significantly reducing the pore space between threads and fibres. This high local pressure and reduced porosity physically block the larger dye molecules from penetrating the treated areas. Additionally, the compressed fabric has less surface area exposed to the dye solution, hindering dye uptake.

b. Physical barrier/Adsorption (Adire Eleko - Starch resist)

i. Principle: This method utilizes a thick paste, traditionally made from cassava starch, as a physical block.

ii. Mechanism: The starch paste is applied to the fabric, forming an impermeable, solid layer upon drying. Starch molecules (complex carbohydrates) form a dense network that physically obstructs the dye molecules from reaching the fabric fibres underneath. The paste adheres to the fabric but does not chemically react with it or the dye in a way that allows colour transfer.

After dyeing, the dry paste is brittle and can be scraped off or washed away, revealing the undyed pattern.

c. Dye chemistry (Primarily traditional indigo vat dyeing): Traditional adire is renowned for its use of natural indigo dye, which involves a complex and fascinating series of chemical reactions.

d. Biochemical reduction (Fermentation): Natural indigo (indigotin), extracted from plants like Lonchocarpus cyanescens (Yoruba: elu) or Indigofera tinctoria, is insoluble in water in its vibrant blue form. To make it usable for dyeing, it must undergo a chemical reduction process. Traditionally, this is achieved through fermentation in a deep earthenware dye vat. Microorganisms (bacteria) consume sugars and other organic matter in the vat, creating an anaerobic (oxygen- free), alkaline environment (often maintained with wood ash or caustic soda) and producing reducing agents. These agents chemically reduce the insoluble blue indigotin to a soluble, yellowish-green form called leuco-indigo (or indigo white).

e. Alkalinity: The alkaline (high pH) environment of the indigo vat is crucial for both the reduction process and for keeping the leuco-indigo soluble and stable until it is absorbed by the fabric.

f. Oxidation for colour fixation: When the fabric is removed from the dye bath, the soluble leuco-indigo molecules that have penetrated the fibres are exposed to oxygen in the air. This triggers a rapid oxidation reaction, where the leuco- indigo is chemically converted back into its insoluble blue indigotin form. This insoluble pigment precipitates and becomes physically trapped within the fabric fibres, permanently colouring the cloth blue. The intensity of the blue colour is directly proportional to the number of times the fabric is dipped and air-dried.

g. Dye-fibre interaction: The leuco-indigo molecules interact with the cellulose fibres of the cotton through various intermolecular forces while in the vat. Once oxidised, the insoluble indigotin is mechanically entrapped within the fibre matrix, making it highly wash-fast.

2. Material Science (Fabric properties) Cellulose fibre structure (Cotton): As with other natural fibre textiles, the cellulose structure of cotton fabric, with its numerous hydroxyl groups, plays a vital role in adsorbing the leuco-indigo solution. The porous nature of the woven fabric allows for efficient penetration of the dye into the unwaxed areas.

3. Physical processes in application and finishing

a. Diffusion and capillary action: The dye solution spreads into the unwaxed portions of the fabric through diffusion (movement from high to low concentration region) and capillary action (the wicking of liquid into the narrow spaces of the fabric).

b. Evaporation: After dyeing, the fabric is dried, a process of evaporation that removes the water solvent, leaving the dye solids fixed.

c. Mechanical compaction: For some indigo-dyed fabrics, beating the cloth with a mallet after drying can help compact the fibres, enhance the dye’s adherence, and impart a sheen (soft lustre).

Activity 10.3 Research Factors Involved in Textile Production

Produce a single-page summary (mind-map or short essay) about the following in relation to textile production in Ghana

1. Sustainable practices

2. Safety regulations

3. Market trends

4. Community impacts

Activity 10.4 Diamond Nine Task on Indigenous Texture Production Instructions: Below are nine statements about the economic importance of indigenous textile production. Arrange them in a diamond nine formation.

• 1 at the top (most important)

• 2 below

• 3 in the middle

• 2 below that

• 1 at the bottom (least important).

Be ready to explain why you ranked them in that order.

Statements to Rank

1. Provides a source of income and employment for local artisans and families.

2. Supports cultural tourism and attracts visitors seeking authentic heritage products.

3. Encourages sustainable, small-scale production with low environmental impact.

4. Strengthens national identity and pride, adding value to local economies.

5. Offers export opportunities, boosting foreign exchange earnings.

6. Reduces dependency on imported textiles and promotes self-reliance.

7. Preserves traditional skills that can be passed down to future generations.

8. Provides affordable, locally produced clothing for rural and urban communities.

9. Stimulates related industries such as natural dye farming, weaving tool production, and local markets.

1. List and explain the processes involved in adinkra production.

2. Discuss the steps involved in batik fabric making.

3. How do scientific principles apply to adire textile production?

Activity 1.1

Observation: When the glass is placed over the burning candle, the flame gradually becomes dim and goes out. At the same time, the water level inside the glass rises slightly above the level in the dish.

Explanation: The candle goes out because it uses up the oxygen inside the glass.

Since oxygen makes up about 21% of air, once it is depleted, the flame cannot continue burning. The rise in water level occurs because the used-up oxygen reduces the air pressure inside the glass, allowing water from the dish to be pushed in by the greater air pressure outside.

Activity 1.2

Observation: Learners will notice that water does not enter the glass fully.

Conclusion and explanation: This is because air inside the glass prevents water from filling it, showing that air occupies space.

Activity 1.3

Observation: If carbon dioxide is present, the limewater will turn milky or cloudy.

Explanation: This happens because CO2 reacts with calcium hydroxide to form calcium carbonate (CaCO3), which is insoluble and makes the solution appear cloudy.

Activity 1.4

Environmental impact of changes in the percentages of components of air.

Air component % in air Role If increased If decreased Nitrogen (N2) 78% • Provides inert balance

• Dilutes oxygen

• Supports nitrogen fixation

• Further dilutes oxygen, affects respiration

• Reduces combustion

• Minor climate/ health impact

• Increases oxygen levels, fire risk

• Disrupts the nitrogen cycle

• Affects soil fertility Oxygen (O2) 21% • Essential for respiration

• Supports combustion

• Higher fire risk

• Increased metabolism, oxidative stress

• May help breathing temporarily

• Breathing difficulties, fatigue

• Risk of death at <15%

• Collapse of aerobic life Carbon dioxide (CO2) 0.04% • Needed for photosynthesis,

• Greenhouse gas

• Global warming

• Ocean acidification

• Disrupts ecosystems

• Reduced photosynthesis and plant growth

• Global cooling Argon (Ag) 0.93% • Inert gas

• Stabilises the atmosphere No significant effect (inert) No significant effect (inert) Water vapour 0-4% (Variable)

• Affects climate

• Part of the water cycle

• Increased rainfall and clouds

• Traps heat (greenhouse effect)

• Floods and extreme weather

• Dry conditions

• Reduced plant growth

• Drought risk Ozone/Oxone (O3) Trace • Absorbs UV rays

• Protects life

• Ground-level ozone causes smog

• Respiratory problems

• More UV exposure

• Skin cancer, cataracts

• Harm to plankton and crops

Activity 1.6

Observations

1. Vigorous bubbling when baking soda meets vinegar

2. Balloon inflates.

3. The flame is extinguished by the suspected CO2.

Conclusion: Bubbling and inflation indicate the release of a gas (CO2).

Activity 1.9

Observation: The glowing splint rekindles (light-up) Conclusion: Oxygen support for burning ANNEX 2.0

Activity 2.0

In the cold separation step, the lighter colours (such as green for petrol) separated and rose to the top first, while the heavier colours (such as red for heavy fuel oil) remained at the bottom. This showed that lighter fractions of oil separate more easily at low temperatures.

When the mixture was warmed in hot water, the layers mixed more at first, but as it settled, the heavier fractions (red and blue for heavy fuel oil and diesel) stayed at the bottom while the lighter ones (green and yellow for petrol and kerosene) moved upward. This showed that higher temperatures are needed to separate heavier fractions in refining.

In the density tower, the liquids settled in distinct layers: the coloured water (heaviest) stayed at the bottom, the oil mixture (diesel/kerosene) floated in the middle, and the light oil (petrol) rose to the top. This demonstrated that oil products separate based on density, just like in real fractional distillation.

Activity 2.2

Example flow chart Flowchart of crude oil refinery processes.

ANNEX 3.0 Answer to the trial question on page xxxx

a. Role of the autonomic nervous system (ANS): The autonomic nervous system controls automatic body functions like heartbeat, breathing, and sweating. In Emmanuel’s case, the ANS helped his body adjust to stress before the speech (by making his heart beat faster, his hands sweaty, and breathing quick) and then helped his body calm down afterwards (by slowing his heartbeat and breathing and making him feel relaxed).

b. Sympathetic and parasympathetic nervous systems:

i. The sympathetic nervous system prepared Emmanuel’s body to face the stressful situation before the speech. It increased his heartbeat, made him breathe faster, and caused sweating. This is called the “fight or flight” response.

ii. The parasympathetic nervous system helped Emmanuel’s body return to normal once he saw the audience smiling. It slowed his heartbeat, calmed his breathing, and made him feel relaxed. This is called the “rest and digest” response.

Note: When the cup almost slipped from his hand, his nervous system reacted quickly through a reflex action, allowing him to grab the cup without thinking.

Activity 3.7

Observation and Conclusion

Observation: The leg moves involuntarily after the tendon is tapped, demonstrating the reflex arc’s function.

Conclusion: The knee-jerk response is a spinal reflex that bypasses the brain, highlighting the speed and efficiency of reflex actions.

ANNEX 4.0

Activity 4.7

Part of the body Name of the joint found there

1. Between vertebrae Cartilaginous joint (symphysis)

2. Wrist, ankle, or spine Gliding/Planar joint

3. Shoulder or hip Ball-and-socket joint

4. Between cranial bones Fibrous joint (suture)

5. Knee or elbow Hinge joint

6. In phalanges Hinge joint

7. Between radius and ulna Pivot joint

8. Neck (between C1 and C2 vertebrae) or elbow Pivot joint ANNEX 5.0

Activity 5.1

Observations

1. With all the holes aligned, the observer could see the source of light.

2. With one hole out of the line, the observer could not see the source of light again.

Conclusion: Light travels in a straight line.

Activity 5.2

Observation: The angle of incidence and angle of reflection must be equal for all angles of incidence chosen.

Conclusion: The laws of reflection of light hold true.

Worked example 5.1

According to the law of reflection:

Angle of incidence = Angle of reflection So, angle of reflection=35°Worked example 5.2 Θr = θi = 40° Total angle between the rays=θi + θr = 40°+ 40°= 80°Worked example 5.4 By the New Cartesian convention, Object distance, u = –20 cm Focal length, f = +10 cm (convex mirror → positive) Image distance, v = ?

1 f = 1 v + 1 u 1 10 = 1 v + 1

–20 1 v = 1 10 + 1 20 1 v = 2 + 1 20 + 3 20 v = +6.67 cm Result

• The image is formed 6.67 cm behind the mirror.

• It is virtual and erect (because v is positive).

• It is diminished in size.

Worked example 5.5

Refractive index = n = c/v Where:

• n = refractive index

• c = speed of light in vacuum (3.00×10⁸m/s)

• v = speed of light in the medium (2.25×10⁸m/s) Substituting the values, n = 3.00 × 10⁸ 2.25 × 10⁸n = 1.33

Worked example 5.7

Using Snell’s law, n1 sinθ₁= n₂sinθ₂ n1=1.00, n2 = 1.50, θ₁= 30° Substituting values, 1.00 × sin30° = 1.50 × sin₂ 0.5 = 1.50 × sinθ₂ sinθ₂= 0.5 1.50 = 0.333 θ₂= sinθ⁻¹(0.333) θ₂= 19.5° So, the light bends at approximately 19.5° in the glass.

Worked example 5.11

Real depth = Apparent depth × Refractive indes Given, Apparent depth = 10 cm, refractive index = 1.33 Substituting values, Real depth = 10 × 1.33 = 13.3 cm ANNEX 6.0

Activity 6.5

Observation: The number of marbles that move on the opposite end should equal the number that hits from one side, demonstrating momentum transfer.

Worked example 6.2

a. Momentum of the first car: 1.2 kg * 2 m/s = 2.4 kg m/s

b. Momentum of the second car: 1.4 kg * 0 m/s = 0 kg m/s

c. Total momentum before collision: 2.4 kg m/s + 0 kg m/s = 2.4 kg m/s

d. Their total momentum after the collision must be 2.4 kg m/s, since momentum is conserved.

Worked example 6.3

Initial momentum of both cars: (1000kg x 20m/s) + (1500kg x 10m/s) = 35000kgm/s Since the cars stick together after a collision, they have a common velocity. Let this be v.

Final momentum: (1000kg + 1500kg) v = (2500kg) v.

By the principle of conservation of momentum, 35000kgm/s = (2500kg) v.

This implies v = 35000kgm/s / 2500kg = 14m/s.

When a super ball is dropped on the floor, it bounces back up, but not to the original height. Explain why this is an inelastic collision.

Explanation

a. Collision: The ball collides with the floor.

b. Energy loss: Some of the ball’s kinetic energy is converted into heat, sound, and deformation of the ball and the floor. This is why it doesn’t bounce back to the same height.

c. Momentum is still conserved: Even though kinetic energy is not conserved, the total momentum of the ball and the Earth is conserved. However, the Earth’s mass is so large that its change in velocity is negligible.