Powering the Future with Energy Forms

Light energy is a type of energy that moves in waves and helps us see the things around us.

In this topic, you will learn what light energy is, where it comes from, and how it behaves when it hits different objects. You will find out how light is used in our daily lives, like in seeing, taking pictures, using solar panels, and even sending messages through fibre optics.

You will also discover how tools like mirrors and lenses change the direction of light.

These tools help us form images in devices such as cameras, eyeglasses, telescopes, and microscopes.

KEY IDEAS

• Mirrors work by reflecting light rays that strike their surface, allowing us to see images of objects placed in front of them. Without light, mirrors cannot form any image, as there would be nothing to reflect.

• Light is a form of energy that travels in straight lines, can be reflected, refracted, or absorbed, and does not require a medium to move. Its properties help us see and understand the world around us.

• Light enables us to see, powers solar panels, helps plants grow through photosynthesis, and is essential for technologies like cameras and fibre-optic communication.

• Mirrors are used in devices such as periscopes and shaving mirrors, while lenses are vital in spectacles, cameras, microscopes, and telescopes to focus and form images.

• When light passes through a lens, it bends (refracts), causing the rays to converge or diverge.

This property of lenses is used to focus light and produce clear images in many optical instruments.

Lenses and Mirrors in Relation to Light Energy in Life Can you imagine a day when the sun will fail to rise? Of course, this happens in the polar regions of the Earth at certain times of year. However, those of us living near the equator do not have that experience. You can guess how difficult and costly it would be to live without the sun, which is the main source of light and warmth. Light is a very important form of energy which gives rise to other energy forms and phenomena, both natural and artificial.

Let us now delve into the concept of light.

Light and Its Properties

Light is a form of energy that is visible and enables us to see the world around us. It is one of the types of radiation in the electromagnetic spectrum and is made of basic particles called photons. The photons are capable of travelling through a vacuum, so light does not need any other medium to carry its particles along. The study of light, in relation to what it can do and the instruments that depend on it, is known as optics.

Properties of Light

₁. Rectilinear propagation: Light travel in a straight line in the same medium.

2. Reflection: Photons bounce off when they hit a surface which they cannot pass through.

3. Refraction: Photons increase their speed when they enter a less dense medium and decrease their speed when they enter a denser medium. This causes light to bend to follow a different path when they move from one medium into another.

4. Absorption: Photons may get trapped in materials on which they cannot bounce off or pass through. Materials with a dark surface absorb light more than those with light- coloured surfaces.

5. Finite speed: Speed of light in vacuum (or in air) is about 300,00km/s. This speed decreases in a medium which is denser than air, such as water or glass.

6. Colour: Visible Light is composed of the following colours: Red, Orange, Yellow, Green, Blue, Indigo and Violet (ROYGBIV). These colours can be seen as the rainbow when it appears in the sky.

Activity 5.1 To demonstrate that light travels in straight line Aim: To show that we see things when light travels, in straight lines, from those things into our eyes.

What you need

• Torch or candle as a source of light.

• Cardboard with a pinhole in each, in the middle.

• White screen or observer’s eye.

What to do

1. Place three cardboard pieces with holes in a straight line.

2. Light the torch or candle.

3. Place the lit torch or candle in front of the hole in the first cardboard and let it shine through the other holes towards a screen/observer’s eye..

4. Observe the light path.

5. Move one cardboard out of line and observe what happens.

Figure 5.1: Light travels in a straight line Safety precaution(s)

1. When using a candle, make sure there is no combustible material near you, to avoid setting the environment ablaze.

2. Place the source of light and cardboards on a levelled surface, for alignment.

MIRROR A mirror is an optical device that reflects light. It is usually made of glass, with its reflective surface coated with a thin layer of metal such as silver or aluminium. The other surface is painted to make it opaque. When light from an object hits a mirror and is reflected, the reflected light enters our eyes, enabling us to see the object.

Types of mirrors There are many types of mirrors. Three of these are

1. Plane mirror

2. Concave/converging mirror

3. Convex/diverging mirror Concave and convex mirrors are also known as curved or spherical mirrors.

Each type of mirror behaves differently with light and is used in various practical applications.

Figure 5.2: Types of mirrors A mirror is defined as a reflecting surface and can be explained by the laws of reflection which are detailed later in this section.

Terms related to mirrors on reflection of light

1. Incident ray: Is the ray of light that hits the mirror surface.

2. Reflected ray: Is the ray of light that bounces off after hitting the mirror surface.

3. Normal: Is an imaginary line that hits the mirror surface at 90° (perpendicular to the reflecting surface).

4. Angle of incidence: Is the angle between the incident ray and the normal with respect to which the incidence occurs.

5. Angle of reflection: Is angle between the reflected ray and the normal with respect to which the reflection occurs.

Figure 5.3: Reflection of light.

Plane mirror It has a flat or plane reflecting surface. It is commonly used in everyday life, such as in barbering shops, cameras, periscopes, microscopes and for decorative purposes.

Figure 5.4: A plane mirror Reflection of Light in a Plane Mirror Reflection of light in a plane mirror is called regular or specular reflection. This means that when a number of rays of light are incident on the mirror surface at the same time, they are reflected in the same order and at the angle at which they arrived at the mirror. This process follows the laws of reflection of light which are stated below.

Laws of Reflection of Light

₁. The incident ray, reflected ray and normal at the point of incidence, all lie in the same plane.

2. The angle of incidence is equal to the angle of reflection.

These laws mean that when a set of light rays hits a plane mirror surface and bounces off, all three rays, i.e. the incident ray, reflected ray and the normal at the point of incidence, can all be found at the same point in the same plane of the mirror. Also, if a ray of light hits a plane mirror surface at an angle of ∠i, then it is reflected at an angle of ∠r such that ∠i = ∠r.

How true are the laws of reflection of light? Let us answer this question by performing the following activity. Do it in a group of four members.

Activity 5.2 Verifying the laws of reflection of light Aim: To explain the laws of reflection.

What we need

a. Plane mirror

b. Drawing board

c. White paper

d. Search pins (4)

e. Protractor

f. Ruler

g. Pencil

h. Small wooden block to hold the mirror upright.

What to do

a. Fix the white paper on the drawing board.

b. Draw a straight line (XY) across the paper and place the mirror strip vertically along this line, supported by the wooden block.

c. Draw a normal (ON) at any point O on XY.

d. Draw an incident ray (AO) at an angle to the normal (e.g., 30°). Fix two pins (P1 and P2) vertically on this line.

e. Looking at the reflection of P1 and P2 in the mirror, fix two more pins (P3 and P4) such that P3, P4, and the images of P1 and P2 are in a straight line.

f. Remove the mirror and the pins. Draw a line (OB) joining the pinpricks P3 and P4 and extend it to O. This is the reflected ray.

g. Measure the angle of incidence (∠AON) and the angle of reflection (∠BON).

h. Repeat for different angles of incidence (e.g., 45°, 60°).

i. Record your observation.

Precautions for accuracy

a. Fix the search pins firmly on the drawing board.

b. Place your eyes at the level of the pins.

c. Ensure there is no parallax between pins 1&2 and 3&4.

Key question

a. Write down your response in your notebook.

b. What other precautions would you adopt to ensure accuracy?

Image Formed at a Plane Mirror

A plane mirror forms the image of an object when light rays from the object reflect off the mirror surface according to the law of reflection, where the angle of incidence equals the angle of reflection. The reflected rays, if extended backward, appear to originate from a point behind the mirror where they intersect to locate the image formed. An example is illustrated below.

Figure 5.5: Image formed by plane mirror In the ray diagram above, the incident rays from the object are reflected off the plane mirror and hit our eye. Our brain projects the reflected rays behind the mirror, meaning the light rays do not actually reach the image. It is, therefore, a virtual image.

Now, study the following worked examples on the law of reflection of light.

Characteristics of image formed by a plane mirror ₁. It is virtual: Formed by backward extension of reflected rays (do not actually meet).

Such an image cannot be captured on a storage device.

2. It is erect/upright: Is oriented in the same direction as the object.

3. Same size: Size of the image formed is the same as size of the object. For instance, your height is the same as the height of your plane mirror image

4. Laterally inverted: The right side of the image corresponds with the left side of the object and vice versa. For instance, if you raise your right hand in front of a plane mirror, your image raises its left hand.

5. Same distance: Image is the same distance away from the mirror, behind it, as the object in front of it. If you stand one metre away from the mirror, your image also stands at one metre away from the mirror Worked examples (solutions in Annex 5.0 on page xxxxx) 5.1. A light ray strikes a plane mirror at an angle of incidence of 35°. What is the angle of reflection?

5.2. A ray strikes a mirror at an angle of incidence of 40°. What is the total angle between the incident ray and the reflected ray?

Uses of Plane Mirrors

Plane mirrors are used for variety of applications. The detailed applications of plane mirrors are mentioned below.

1. Periscope: Submarines use periscopes to see objects on the water’s surface. It is impossible to bend light rays since they move in straight directions, although they can be reflected. The plane mirrors of a periscope adjust the direction of light rays so that the item can be seen by the submarine’s viewer.

2. Telescope: A telescope is used to observe distant objects in the solar system, such as planets. Telescopes are classified into two types. A set of lenses is used in a refracting telescope. Plane mirrors are used in conjunction with spherical mirrors in reflecting telescopes.

3. Saloon: We can create unlimited images by installing plane mirrors parallel to each other. This allows the customer to view both the front and rear of a person.

4. SLR cameras: Single-lens reflex (SLR) cameras use plane mirrors to redirect light from the lens allowing photographers view exactly what is to be captured.

5. Microscopes: Plane mirrors are used to reflect light onto the specimen to brighten it.

6. Surveillance systems: Plane mirrors that are placed in a certain way can help people keep an eye on places that they cannot see directly. This can be useful in surveillance systems where people want to observe things without being noticed.

7. Education and science: Plane mirrors are educational tools in science classrooms, to demonstrate the principles of optics and light reflection to learners.

8. Navigation: In navigation tools such as sextants, plane mirrors aid in celestial navigation by reflecting light from celestial bodies, assisting sailors and navigators in determining their position relative to the horizon and celestial objects.

9. Decorative purposes: Plane mirrors are used in interior design to create illusions of space by reflecting light and enhancing the appearance of rooms.

Concave mirrors (converging mirrors) A concave mirror is a mirror whose reflecting surface curves inward, giving an impression of looking into a hollow or cave-like surface.

Properties of Concave Mirrors

₁. They bring light rays to a single point (focus) after reflection from the mirror. They are, therefore, called converging mirrors.

2. It can form real and virtual images, which may be smaller or larger than the object or have same size as object, depending on the distance of the object from it.

3. The closer an object gets to the mirror, the bigger is the image formed. The image gets smaller as the objects moves away from the mirror.

Figure 5.6: Reflection of light on concave mirror Uses of Concave Mirrors ₁. Shaving mirrors: When held close to the face, they produce a magnified and upright image, making it easier to see details.

2. Ophthalmoscopes: Used to construct ophthalmoscopes which are instruments that doctors use to examine the interior of the eye.

3. Astronomical telescopes: Used as objectives in astronomical telescopes to collect and focus light from distant celestial bodies. They must be large enough for this purpose (with a diameter of five metres (5m) or more).

4. Torchlights, headlights and searchlights: Used as reflectors to produce strong and focused parallel beams of light in car and aircraft headlights, torchlights and searchlights.

5. Solar furnaces and ovens: Large concave mirrors are used in solar heating devices to concentrate sunlight at a single focal point to generate intense heat. This heat is used for cooking, baking ceramic materials or melting substances such as metals.

Figure 5.7: Concave mirror for magnification

Figure 5.8: Ray diagram of a shaving mirror Convex mirror A convex mirror is a type of spherical mirror whose reflecting surface is curved outward, like the back of a spoon. It is also known as a diverging mirror because the light rays that strike its reflecting surface spread out (diverge) after reflection. The diverging rays then, appear to originate from a common point behind the mirror. The point where the diverging rays appear to originate is location of the image, formed of an object, by the mirror.

Characteristics of Convex Mirrors

₁. Spreading of light rays: They cause light rays to move apart (diverge), after reflection.

2. Virtual image: Form virtual images only. Images formed, therefore, cannot be projected on a screen.

3. Erect/upright image: Image formed is always erect/upright (has the same orientation as the object)

4. Diminished/smaller image: Always form images which is smaller than their objects.

These properties can be demonstrated by observing images of objects formed by the back of a spoon made of stainless (or another shiny metal). The spoon will be observed to be reflecting light falling on it to produce smaller, upright images of whatever objects that happen to be in front of it.

Figure 5.9: Convex mirror diverges light after reflection Uses of Convex Mirrors Uses of convex mirrors are based on their ability to capture a wider field of view (as a result of divergence of the reflected light) than other types of mirrors. Also, in addition to being virtual and erect, the images formed are diminished so that more images of objects can be accommodated in the view. These uses are:

1. Safety and monitoring: Convex mirrors are installed in sharp curves on highways, large offices, stores, hospitals, and other public buildings to monitor and boost safety by allowing people to see around corners, in hallways and corridors; and to help prevent collisions by providing visibility in blind spots.

2. Driving mirrors: Used in vehicles and motorcycles as rear-view and side mirrors to give a wider field of view, helping drivers see more of the road and traffic around them.

They also produce virtual, upright and reduced images, allowing more objects to be seen in a small mirror.

3. Magnifying glass: Used to make magnifying devices. In industrial applications, two convex mirrors can be placed back-to-back to enhance magnification effects.

4. Security and surveillance: Used for security purposes near ATMs, allowing users to see if they are being trailed. They are also widely used in shopping centres or parking areas to improve visibility or monitor suspicious activities.

5. Street light reflectors: Used in street lighting systems to help spread light over a wider area, improving coverage and illumination.

Figure 5.10: A convex mirror Important terms in concave and convex mirrors ₁. Pole (P): Is the midpoint of the mirror’s surface. Object distance, image distance and focal length are measured from the pole.

2. Aperture: Is the diameter of the reflecting surface of the mirror. It defines the size of the mirror and the area over which reflection of light occurs.

3. Principal/Main axis: Is an imaginary, straight, horizontal line that passes through the pole (P), principal focus (F) and centre of curvature (C). Measurement of angles and lengths are taken with respect to this axis.

4. Centre of curvature (C): Is the centre of the sphere from which the mirror surface is taken. It lies on the principal axis, outside the mirror surface. For a concave mirror, it is in front of the mirror; for a convex mirror, it is behind.

5. Principal focus/Focal point (F): Is the point on the principal axis where, in a concave mirror, parallel rays converge after reflection and in a convex mirror, where parallel rays appear to diverge from, after reflection.

6. Focal length (f): Is the distance from the pole to F.

7. Radius of curvature (R): Is the distance from the pole (P) to the centre of curvature (C). It is equal to twice the focal length, i.e., R = 2f .

Characteristics of images formed by a concave mirror The various locations of object, ray diagram, size and nature of image formed are shown in Table 5.1.

Table 5.1: Images formed by a concave mirror Image formed by a convex mirror There are two possible positions of the object in the case of a convex mirror. These are

1. When the object is at infinity.

2. When the object is between infinity and the pole of the mirror.

These are illustrated in Table 5.2 below.

Table 5.2: Image formed by a convex mirror Mirror Formula To solve numerical problems involving spherical mirrors (concave or convex), we use the mirror formula. This formula helps calculate important quantities. These are as follows:

1. Focal length (f)

2. Object distance (u)

3. Image distance (v)

4. Magnification (m) The mirror formula: 1 f = 1 v + 1 u Where:

f = focal length of the mirror.

v = image distance (from the pole).

u = object distance (from the pole).

Sign Convention (Based on the Cartesian System)

1. All distances are measured from the pole (P) of the mirror.

2. Distances measured to the right of the pole (along the direction of incident light) are positive.

3. Distances measured to the left of the pole (against the direction of incident light) are negative.

The focal length (f) is:

a. Negative for a concave mirror

b. Positive for a convex mirror

4. The object distance (u) is usually negative (as objects are generally placed in front of the mirror).

The image distance (v) is:

a. Positive if the image is formed behind the mirror (virtual).

b. Negative if the image is formed in front of the mirror (real).

Figure 5.11: New Cartesian convention.

Worked Example

5.3 An object is placed 30 cm in front of a concave mirror. The focal length of the mirror is 15 cm. Find the position and nature of the image.

Solution

By New Cartesian convention, object distance, u = –30 cm focal length, f = –15 cm image distance, v - ?

1 f = 1 v + 1 u 1

–15 = 1 v + 1

–30 1 v = 1 15 + 1 30 1 v = 2 + 1 30 + –1 30 v = –30 cm Result

• The image is formed 30 cm in front of the mirror.

• It is real and inverted (because v is negative).

• Same size as the object (since u = 2f ).

5.3. An object is placed 20 cm in front of a convex mirror. The focal length is 10 cm. Find the position and nature of the image. Find the solution in Annex 5.0!

Activity 5.3 Produce a Poster Demonstrating the Applications of Mirrors in Optics Create a single-sided A4 poster highlighting some of the applications of mirrors in various fields. Use pictures and diagrams to make your poster eye-catching. Try to include a brief summary of how mirrors are used in each context.

Some ideas for fields of optics are:

1. Photography

2. Periscopes

3. Microscopes

4. Driving mirrors

Activity 5.4 The Role of Mirrors in Manipulating Light Write a single paragraph response to the question ‘How are mirrors used to manipulate light and where do we encounter examples of this on a day-to-day basis?’

1. Dear learner, examine the picture below.

Figure 5.23: Using a periscope The man in Figure 5.23 above is using an optical instrument called a periscope.

Key questions Discuss and write down your response in your notebook.

a. Why is the man using the periscope?

b. How does a periscope work?

Now, let us build the prototype of a periscope and get an understanding of how it works.

Do this activity in your mixed-ability groups.

Activity 5.5 Building a prototype of a periscope Aim: To understand how two plane mirrors can be arranged to produce total internal reflection in a periscope that can see over or around obstacles.

What you need

• Two small plane mirrors (about 5 cm x 5 cm).

• A rectangular cardboard box or sturdy cardboard sheets (approximately 30 cm long).

• Ruler.

• Pencil.

• Cutter or scissors.

• Glue or tape.

• Protractor (for measuring 45° angles).

• Black paper (optional, to reduce light inside the periscope).

What to do

a. Use a long cardboard box (like a cereal box) or create a rectangular tube using cardboard sheets.

b. Make sure the box is closed on all sides except for openings at both ends.

c. At the top and bottom ends of the box, mark two square holes on the front and back faces. These holes will allow light to enter and exit the periscope.

d. Carefully cut out the marked squares using a pair of scissors or any other cutter.

e. Inside the box, draw lines at 45° angles near both the top and bottom ends.

f. Use a protractor to ensure accuracy.

g. Place one mirror at the top, angled at 45°, facing the top opening.

h. Place the second mirror at the bottom, angled at 45°, facing the bottom opening.

i. Secure the mirrors with glue or tape.

j. Ensure the box is sealed except for the view holes.

k. Optionally, line the inside with black paper to minimise internal reflections.

l. Use your prototype to view over or around an obstacle.

Key question Discuss and write down your response in your notebook.

a. How convenient is your periscope, especially to those who are short?

b. In what other fields can periscopes be used?

What did you do to avoid injury and build a good prototype?

Write them down.

Figure 5.24: A simple periscope.

Dear learner, you are welcome to yet another exciting week in the study of light. We hope you enjoyed last week as you had fun learning about the properties of light and its reflection by mirrors, leading to the formation of images. That was quite interesting.

However, you also learnt that one of the properties of light is refraction or bending. Can you imagine how this happens? Just dip a straight stick in water and observe what happens to its ‘straightness’. This is what exactly happens to light. Let us now delve into the concept of refraction of light.

Refraction of light When you dip a straight stick into water, what do you observe of it? It appears bent just as it enters the water, isn’t it? This is what exactly happens to light as it passes from one medium into another.

When a ray of light travels from one medium (like air) into another medium of a different optical density (like water or glass), its speed changes. This change in speed causes the light ray to bend at the boundary between the two media. This bending is called refraction.

Figure 5.25: Demonstrating refraction of light.

Figure 5.26: Ray diagram of refraction of light.

Definition of Related Terms

₁. Incident ray: The incoming ray of light.

2. Refracted ray: The transmitted ray of light into another medium.

3. Medium of incidence: The medium in which light travels before it strikes the boundary.

4. Medium of refraction: The medium through which refracted ray travels.

5. Point of incidence: The intersection of the incident ray and the boundary.

6. Normal: An imaginary line drawn perpendicular to the boundary at the point of incidence.

7. Angle of incidence (i): The angle between the normal and the incident ray.

8. Angle of refraction (r): The angle between the normal and the refracted ray.

In order to understand the concept of refraction of light better, we need to perform an

activity.

Now, in groups of 3-5 people, perform Activity 5.3 to verify refraction of light.

Activity 5.3 Refraction of light Aim: To show the refraction of light between air and water.

What you need

• Glass of water

• Pencil/straw What to do

a. Fill the glass about two-thirds full with water.

b. Place the pencil or straw into the glass of water so that it is partially submerged.

c. Look at the pencil from the side, at the point where it enters the water.

Observation

a. How does the pencil appear at the air-water boundary?

b. Why does this happen?

c. Discuss your observation with your elbow friends.

Conclusion What conclusion can you draw from the activity?

Write it down in your jotter.

Precaution(s) taken for accuracy: What did you do to achieve the objective of the

activity? Give two examples.

The refractive index of a medium is a measure of how much the speed of light is reduced when it passes through that medium.

A higher refractive index means that light slows down more when travelling through the material compared to another medium.

It’s defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v).

Thus, n = c/v , Where n = refractive index of the medium, c = speed of light in vacuum and v = speed of light in the medium.

Table 5.3: Refractive Indices of Some Media

Material Index of Refraction

Air Very close to 1 (around 1.00029) Water (room temperature) 1.33 Ethyl Alcohol 1.36 Glass 1.50 Diamond 2.417 Vacuum 1 Effects of refractive index The higher the refractive index of a material is, the more light rays will bend and slow down as they enter that material. From Table 5.3 above, light rays will bend and slow down the most in diamond, while they bend and slow down the least in air. This significant bending of light by diamond creates intense internal reflections, which enhance its sparkling appearance.

Snell’s Law

This describes how light bends (refracts) when it passes from one medium to another, like from air into water or glass.

It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media.

Snell’s law formula n1sin⊖1= n2sin⊖2 What the symbols mean

1. n1 (Refractive Index of the first medium)

a. This tells us how much the medium slows down light compared to its speed in a vacuum.

b. Air has a refractive index close to 1.00 (because light barely slows down).

c. Water has a refractive index of about 1.33 (light slows down more).

d. Glass can have an index ranging from 1.5 to 1.9, depending on the type.

2. θ1 (Angle of Incidence)

a. This is the angle between the incoming light ray and the normal (an imaginary line perpendicular to the surface).

b. The larger the angle, the more dramatic the potential bending.

3. n2 (Refractive Index of the second medium)

a. If light enters a denser medium (higher refractive index) from a less dense medium, it slows down and bends towards the normal.

b. If light enters a less dense medium (lower refractive index) from a denser medium, it speeds up and bends away from the normal.

4. θ2 (Angle of refraction)

a. This is the angle between the refracted light ray and the normal inside the second medium.

b. It depends on the ratio of the refractive indices and the incident angle.

Figure 5.27: Snell’s law How Snell’s law works ₁. If light goes from a less dense medium to a denser medium (e.g., air to water), it bends toward the normal (line perpendicular to the surface).

2. If light goes from a denser to a less dense medium (e.g., water to air), it bends away from the normal

3. Snell’s Law explains why a pencil/straw looks bent in a glass of water and why lenses focus light in cameras and eyeglasses.

Worked examples 5.4. If the speed of light in a medium is 2.25×10⁸m/s, what is the refractive index of the medium? (Speed of light in vacuum c=3.00×10⁸m/s). The solution can be found in Annex 5.0.

5.5. If the refractive index of a medium is 2.0, what is the speed of light in the medium?

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

Solution to 5.5

The speed of light in a medium is calculated using, n = c/n where:

a. v = speed of light in the medium

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

c. n = refractive index of the medium (2.0) Substituting the values, v = 3.00 × 10⁸ 2.0 , v = 1.50 × 10⁸m/s 5.6. Light travels from air (refractive index = 1.00) into glass (refractive index = 1.50) at an angle of incidence of 30°. Find the angle of refraction. The solution can be found in 5.0.

5.7. Light passes from air (n1=1.00) into an unknown medium. The angle of incidence is θ1=60°, and the angle of refraction is θ2=30°.

Find the refractive index n2 of the medium.

Solution to 5.7

n₁× sinθ₁= n₂× sinθ₂ 1.00 × sin60° = n₂× sin30° 0.8660 = n₂× 0.6 n₂= 0.8660 0.5 n₂= 1.732 Applications of Snell’s law

1. Design of lenses Snell’s Law is crucial in designing optical lenses used in cameras, microscopes, and eyeglasses. By understanding how light refracts through different materials, manufacturers can create lenses that precisely focus light to improve image quality or correct vision.

2. Fiber optic communication In fibre optics, Snell’s Law helps engineers design the core and cladding of optical fibre to achieve total internal reflection. This principle ensures that light signals travel long distances with minimal loss, which is essential for high-speed internet and telecommunications.

3. Optical Instruments

Snell’s Law is used in the development of various optical instruments like telescopes, binoculars, and periscopes. It helps in calculating the necessary angles and materials for prisms and mirrors to correctly direct light and produce clear images.

4. Underwater Imaging

Snell’s Law explains how light bends when entering water from air, which is critical for designing underwater cameras and instruments. Understanding refraction helps correct distortions in underwater photography and videography.

5. Gemology/Study of gemstones In gemology, Snell’s law assists in cutting precious stones at angles that enhance their inherent brilliance. Proper cutting techniques that consider light refraction increase the sparkle and value of gemstones. It helps to determine real gemstones from fake ones

6. Meteorology Snell’s law helps meteorologists understand phenomena like mirages, where variations in the refractive index of air due to temperature gradients cause the bending of light rays from distant objects, creating optical illusions.

7. Medical imaging Some medical imaging techniques, such as optical coherence tomography, rely on understanding how light refracts through different tissues. Snell’s Law assists in interpreting the data to provide accurate images.

Real and Apparent depth When light passes from one medium to another, such as from water to air, it bends or refracts. This refraction causes objects submerged in water to appear shallower than they are. The difference between the actual depth (real depth) and the perceived depth (apparent depth) is an important concept in optics. Understanding real depth and apparent depth does not only help in physics but also has practical applications in fields such as underwater exploration, photography and fishing.

Real/Actual depth Real depth is the actual vertical distance between an object submerged in a medium and the surface of that medium. In other words, the distance from the surface to where the object really is in the medium Real depth is affected by the following factors:

1. Density of medium: This does not change the real depth itself but can affect the ease and method of measurement. In denser mediums, specialized instruments may be required to determine buoyancy or resistance.

2. Position of object: Real depth is directly determined by the object’s distance from the surface of the medium. This is a key factor in measuring any depth and forms the basis for calculating real depth.

3. Measurement tools: The accuracy of the type of tool used (such as a ruler, depth gauge, or sonar) influences how precisely the real depth is recorded. Faulty tools or human error can lead to inaccurate depth readings.

4. Variations of water surface: Changes in water level due to presence of tides, waves, or environmental factors may temporarily affect the measured depth. These changes must be considered in real-time depth assessments, especially in marine or hydrological studies.

Apparent depth This is the depth at which an object appears to be when submerged in a transparent medium, such as water or glass. The apparent depth of an object appears shallower than its actual depth due to refraction of light.

Factors which affect apparent depth are as follows:

1. Refractive Index of the medium: This determines how much light bends when it passes from one medium to another. A higher refractive index results in a greater difference between the real and apparent depth. For example: Light bends more in glass (higher refractive index) than in water.

2. Angle of observation: The apparent depth depends on the angle at which the observer views the object. When viewed normally (perpendicularly), the effect of refraction is minimal. When viewed at an angle other than perpendicularly the bending of light increases, making the object appear even shallower.

3. Real depth of the object: A greater real depth increases the difference between the actual and apparent positions. Objects closer to the surface show less noticeable displacement.

4. Optical properties of the medium: Different materials such as air, water and glass have different optical densities and refractive indices. The change in perception of depth depends on the difference between the refractive indices of the two media.

5. Curvature of surface: If the surface of the medium is curved (like in a lens or rippling water), it causes light to bend differently at different points. This results in non-uniform apparent depth, which is often observed in curved containers or lenses.

6. Temperature of medium: Temperature can slightly affect the refractive index of a medium. For example, warm water has a lower refractive index than cold water. This alters apparent depth slightly.

Figure 5.28: Real and apparent depth Real and Apparent Depth Formula This can be used to calculate the refractive index of the medium in which an object is viewed. Thus, Refractive index = Real depth apparent depth Worked examples 5.8. A coin is placed at the bottom of a beaker filled with water. The real depth of the coin is measured to be 12 cm. If the refractive index of water is 1.33, calculate the apparent depth of the coin as observed from directly above the beaker.

Solution

Apparent depth = Real depth Refractive index Given, Real depth = 12 cm, refractive index of water = 1.33 Substituting values, Apparent depth = 12 cm 1.33 = 9.02 cm 5.1.1. An object appears to be at a depth of 10 cm when viewed from directly above a tank filled with water. If the refractive index of water is 1.33, calculate the real depth of the object. The solution can be found in Annex 5.0.

Dear learners, let us perform another activity (Activity 5.4), which involves the use of real depth and apparent depth to find the refractive index of named liquids. Do this in groups of 3-5 people.

Activity 5.4 Finding the refractive index of liquids Aim: To use real depth and apparent depth to find the refractive index of some liquids.

What you need

• A transparent container (glass or plastic).

• Water, coconut oil.

• A coin or small object.

• A ruler or measuring tape.

• A piece of cardboard.

What to do

1. Place the coin at the bottom of the container.

2. Fill the container with water to a certain depth.

3. Measure the total depth of the water in the container (from the surface to the coin) – this is the real depth.

4. Observe the coin from above, at an angle (around 45 degrees is suggested). The coin will appear to be raised due to refraction. Use a piece of cardboard to block the view of the coin, then slowly add water until the coin comes back into view.

Measure its location from the surface of the water as the apparent depth.

5. Calculate the refractive index (n) of water, using the formula: n = real depth / apparent depth.

6. Repeat the process using coconut oil.

7. Compare your calculated values to theoretical values.

Observations

a. How do your calculated values compare with theoretical values?

b. Share your thoughts with your elbow friends.

Conclusion

a. What conclusion can you draw from the activity?

b. Write it down for a class discussion.

Now, imagine you are walking alone down a tarred road on a hot sunny day. Suddenly, you notice something ahead; it looks like a pool of water on the road, with people seemingly walking through it. You keep walking, expecting to reach it… but strangely, no matter how far you go, it never gets closer. Why? This is not real water at all; it is a mirage, an optical illusion created by the phenomenon of total internal reflection. Let’s explore how this fascinating effect happens.

Figure 5.29: Mirage, an optical illusion Total Internal Reflection (TIR) This is an optical phenomenon that occurs when light traveling from a medium with a higher refractive index (optically denser), such as water, to a medium with a lower refractive index (optically less dense), such as air, strikes the interface between the two media at an angle of incidence greater than a specific angle called the critical angle. (Critical angle is the specific angle of incidence at which light travels from a denser to a less dense medium that results in an angle of refraction of exactly 90°).

In the process, the incident light is completely reflected back into the denser medium on hitting the boundary of the two media. For total internal reflection to take place, some conditions must be satisfied. These are stated below.

Conditions necessary for TIR

1. The light must travel from an optically denser medium towards an optically less dense medium. Eg: From water to air, glass to water.

2. The angle of incidence must be greater than a certain critical angle, c, i.e. i > c.

Under these conditions, instead of the incident light refracting into the less dense medium, all of it is reflected back into the denser medium.

How Total Internal Reflection occurs ₁. As light moves from a denser to a less dense medium, it speeds up and bends away from the normal. For angles less than the critical angle, the incident light ray undergoes refraction and a weak internal reflection. As the angle of incidence increases, the angle of refraction gets closer to 90 degrees.

2. At the critical angle, the incident light ray is refracted at 90º along the boundary of the two media. It is described as grazing the boundary and is referred to as a grazing ray.

3. If the angle of incidence is increased further, there’s no angle of refraction greater than 90º possible according to Snell’s Law. Instead, the energy of the light wave is entirely reflected back into the original medium (without any refraction).

Figure 5.30: Total internal reflection

• Key question: How do organisms living below water receive light for their life

activities?

Figure 5.31: Light under water by TIR Applications of Total Internal Reflection TIR is a crucial phenomenon with numerous important applications as follows:

1. Optical Fibres: This is perhaps the most significant application. Optical fibres are thin strands of glass or plastic that transmit data as pulses of light. The light signals are guided along the fibre by repeated total internal reflection at the interface between the high refractive index core and the lower refractive index cladding. This allows for high-speed, long-distance communication with minimal signal loss.

Figure 5.32: Optical fibre

2. LASER is an acronym for Light Amplification by Stimulated Emission of Radiation.

LASERS produce a narrow, focused beam of light, unlike regular light sources such as bulbs. This focused beam is used in a variety of technologies and instruments and is often used as the light source in fibre optics.

Figure 5.33: LASER beams.

3. Prisms in optical instruments: Prisms are used in binoculars, telescopes, and single- lens reflex (SLR) cameras to reflect light and change its path. Using TIR within a prism provides a highly efficient reflection with minimal light loss, often superior to using mirrors.

4. Medical endoscopes: Endoscopes use bundles of optical fibres to transmit images from inside the human body to a viewing screen. Light is shone into the body through some fibres, and the reflected light carrying the image is transmitted back through other fibres, all relying on TIR.

5. Sensors: TIR-based sensors can be used to measure various physical quantities or detect the presence of specific substances by detecting changes in the conditions required for TIR at an interface.

6. Gemstones: The brilliance and sparkle of gemstones like diamonds are partly due to their high refractive index and the occurrence of total internal reflection within the cut facets, trapping and reflecting light back to the observer.

7. Mirages: This is an optical illusion. Mirages are a natural example of TIR occurring in the atmosphere. Light travelling down from higher atmosphere passes from cold to warm to hot air (from denser to less dense medium) near the ground. In so doing, it bends gradually away from the ground (away from the normal) until it re-enters the atmosphere. This creates a virtual image of the blue sky on the ground, viewed as a pool of water by an observer. It is normally viewed on a hot road (usually tarred ones) or desert.

Figure 5.34: Formation of mirage Learners, we learnt earlier that one of the uses of total internal reflection is the use of optical fibres to carry information Let us perform the following activity to demonstrate how that basically happens.

Perform Activity 5.5 in small groups of 3-5 people.

Activity 5.5 Demonstration of fibre optics Aim: To show how light carries information through a fibre using total internal reflection.

What you need

• A large transparent plastic bottle.

• Water.

• Laser pointer or flashlight.

• Tape or cork with a small hole.

What to do

1. Fill the bottle with water and make a small hole on its side near the bottom.

2. Shine the laser through the back of the bottle and straight out of the hole you have made while water flows out of the hole.

Observation

a. Carefully examines how the light bends and follows the stream of water.

b. Why do you think this happens? Discuss your observation with your elbow friends.

Conclusion: What conclusion can you draw from the activity?

Safety measures: What safety measures must you adopt when using a LASER beam?

Why must you adopt such measures? Write your responses down.

Activity 5.6 Produce a Poster Demonstrating the Applications of Lenses in Optics

1. Create a single-sided A4 poster highlighting some of the applications of lenses in various fields.

2. Use pictures and diagrams to make your poster eye-catching.

3. Try to include a summary of how mirrors are used in each context.

Some ideas for fields of optics are:

a. Spectacles

b. Telescopes

c. Fibre-optics

Activity 5.7 The Role of Lenses in Manipulating Light Write a single paragraph response to the question ‘How are lenses used to manipulate light and where do we encounter examples of this on a day-to-day basis?’

Activity 5.8 Concept Map

Produce a concept map discussing some of the concepts of light energy that we have made so far, including

a. Reflection

b. Types of mirrors and their effect on light

c. Refraction

d. Snell’s Law

e. Applications of refraction

f. Total Internal Reflection

g. Applications of TIR

1. Explain how light allows us to see things and discuss how different sources of light are used in places like homes, schools, and hospitals. Give real-life examples to support your answer.

2. Light travels at a speed of 3 × 10⁸m/s. If the distance between the Sun and Earth is 1.5 × 10¹¹ metres;

a. Calculate how long it takes sunlight to reach Earth in minutes.

b. Evaluate the importance of this natural light in human activities.

3. Explain why a straw appears bent when placed in a glass of water, using the concept of refraction.

4. In a group of 5 members, design and construct a functional optical device (such as a periscope, magnifier, projector, or simple microscope, pin) using locally available materials. Demonstrate how your model works and explain the scientific principles of reflection or refraction used. Justify how this device could solve a problem in your community or daily life.