# Refraction of Light Class 10 Science Notes Maharashtra Board

## Refraction of Light Class 10 Science Notes Maharashtra State Board

We have seen that, generally light travels in a straight line. Because of this, if an opaque object lies in its path, a shadow of the object is formed. We have also seen in previous classes how these shadows change due to the change in relative positions of the source of light and the object. But light can bend under some special circumstances as we will see below.

Refraction of Light
Material: Glass, 5 rupee coin, Pencil, metallic vessel, etc.

Activity 1:
1. Take a transparent glass and fill it with water.
2. Dip some portion of a pencil vertically in water and observe the thickness of the portion of the pencil, in water.
3. Now keep the pencil inclined to the water surface and observe its thickness.

Activity 2:
1. keep a 5 rupee coin in a metallic vessel.
2. Slowly go away from the vessel.
3. Stop at the place where the coin disappears.
4. Keep looking in the direction of the coin.
5. Ask a friend to slowly fill water in the vessel.
You will be able to see the coin once the level of water reaches a certain height. Why does it happen? In both cases, the portion of the pencil inside water appears to be thicker than the portion above water. In the second case, the pencil appears to be broken near the surface of the water. Why does it happen?

In both the above activities the observed effects are created due to the change in the direction of light while coming out of water. Light changes its direction when going from one transparent medium to another transparent medium. This is called the refraction of light.

Activity 3:
1. Keep a glass slab on blank paper and draw its outline PQRS as shown in the figure.
2. Draw an inclined straight line on the side of PQ so that it intersects PQ at N. Pierce two pins vertically at two points A and B along the line.
3. Look at the pins A and B from the opposite side of the slab and pierce pins C and D vertically so that the images of A and B are in line with C and D.
4. Now remove the chip and the pins and draw a straight line going through points C and D so that it intersects SR at M.
5. Join points M and N. Observe the incident ray AN and emergent ray MD.

The first refraction occurs when a light ray enters the glass from the air at N on the side PQ. The second refraction occurs when light enters the air through the glass at point M on the side SR. For the first refraction, the angle of incidence is i while for the second it is i1. The angle of refraction at N is r. Note that i1 = r. In the second refraction, the angle of refraction is e which is equal to i. On both parallel sides PQ and RS of the glass slab, the change in direction of light ray is equal but in opposite directions. Thus, the light ray MD emerging from the glass slab is parallel to the incident ray AN on the side PQ of the slab. However, the emergent ray is somewhat displaced concerning the incident ray.

Laws of Refraction
Let us study the light ray entering a glass slab from air as shown in the figure. Here AN is the incident ray and NB is the refracted ray.

• Incident ray and refracted ray at the point of incidence N are on the opposite sides of the normal to the surface of the slab at that point i.e. CD, and the three, incident ray, refracted ray and the normal, are in the same plane.
• For a given pair of media, here air and glass, the ratio of sin i to sin r is a constant. Here, i is the angle of incidence and r is the angle of refraction.

Refractive Index
The change in the direction of a light ray while entering different media is different. It is related to the refractive index of the medium. The value of the refractive index is different for different media and also for the light of different colours for the same medium. The refractive indices of some substances concerning vacuum are given in the table. The refractive index of a medium concerning vacuum is called its absolute refractive index. The refractive index depends on the velocity of light in the medium.
$$\frac{\sin \mathrm{i}}{\sin \mathrm{r}}$$ = constant = n
n is called the refractive index of the second medium concerning the first medium. This second law is also called Snell’s law. A ray incident along the normal (i = 0) goes forward in the same direction (r = 0).

Absolute Refractive Indices of Some Media

 Substance Refractive Index Air 1.0003 Ice 1.31 Water 1.33 Alcohol 1.36 Kerosin 1.39 Fused Quartz 1.46 Turpentine Oil 1.47 Benzene 1.50 Crown Glass 1.52 Rock Salt 1.54 Carbon disulphide 1.63 Dense Flint Glass 1.66 Ruby 1.76 Sapphire 1.76 Diamond 2.42

Let the velocity of light in medium 1 be v1 and in medium 2 be v2 as shown in the figure. The refractive index of the second medium concerning the first medium, 2n1 is equal to the ratio of the velocity of light in medium 1 to that in medium 2.

Similarly, the refractive index of medium 1 with respect to medium 2 is $${ }_1 \mathrm{n}_2=\frac{\mathrm{v}_2}{\mathrm{v}_1}$$
If the first medium is vacuum then the refractive index of medium 2 is called absolute refractive index and it is written as n.

• When a light ray passes from a rarer medium to a denser medium, it bends towards the normal.
• When a light ray passes from a denser medium to a rarer medium, it bends away from the normal.
• When a light ray is incident normally at the boundary between two media, it does not change its direction and hence does not get refracted.

Twinkling of Stars
Local atmospheric conditions affect the refraction of light to some extent. In both the examples above, the air near the hot road or desert surface and the Holi flames is hot and hence rarer than the air above it. The refractive index of air keeps increasing as we go to increasing heights. In the first case above, the direction of light rays, coming from a distance, keeps changing according to the laws of refraction.

The light rays coming from a distant object appear to be coming from the image of the object inside the ground as shown in the figure. This is called a mirage. In the second example, the direction of light rays coming from objects beyond the Holi fire changes due to the changing refractive index above the fire. Thus, the objects appear to be moving.

The effect of atmospheric conditions on the refraction of light can be seen in the twinkling of the stars. Stars are self-luminous and can be seen at night in the absence of sunlight. They appear to be point sources because of their being at a very large distance from us. As the density of air increases with lowering height above the surface of the earth, the refractive index also increases. Starlight coming towards us travels from rarer medium to denser medium and constantly bends towards the normal. This makes the star appear to be higher in the sky as compared to its actual position as shown in the figure.

The apparent position of the star keeps changing a bit. This is because of the motion of atmospheric air and changing air density and temperature. Because of this, the refractive index of air keeps changing continuously. Because of this change, the position and brightness of the star keep changing continuously and the star appears to be twinkling.

We do not see the twinkling of planets. This is because planets are much closer to us as compared to stars. They, therefore, do not appear as point sources but appear as a collection of point sources. Because of changes in atmospheric refractive index, the position as well as the brightness of individual point sources change but the average position and total average brightness remain unchanged and planets do not twinkle. By Sunrise we mean the appearance of the Sun above the horizon. But when the Sun is somewhat below the horizon, its light rays can reach us along a curved path due to their refraction through Earth’s atmosphere as shown in the figure. Thus, we see the Sun even before it emerges above the horizon. The same thing happens at the time of Sunset and we keep seeing the Sun for a short while even after it goes below the horizon.

Dispersion of Light
Hold the plastic scale in your compass in front of your eyes and see through it while turning it slowly. You will see light rays divided into different colours. These colours appear in the following order: violet, indigo, blue, green, yellow, orange and red. You know that light is electromagnetic radiation. Wavelength is an important property of radiation. The wavelength of radiation to which our eyes are sensitive is between 400 and 700 nm. In this interval, radiation of different wavelengths appears to have different colours mentioned above. Red light has the maximum wavelength i.e. close to 700 nm while violet light has the smallest wavelength, close to 400 nm. Remember that 1 nm = 10-9 m.

In a vacuum, the velocity of light rays of all frequencies is the same. But the velocity of light in a medium depends on the frequency of light and thus different colours travel with different velocities. Therefore, the refractive index of a medium is different for different colours. Thus, even when white light enters a single medium like glass, the angles of refraction are different for different colours. So when the white light coming from the Sun through the air, enters any refracting medium, it emerges as a spectrum of seven colours.

The process of separation of light into its component colours while passing through a medium is called the dispersion of light. Sir Issac Newton was the first person to use a glass prism to obtain the Sun’s spectrum. When white light is incident on the prism, different colours bend through different angles. Among the seven colours, red bends the least while violet bends the most. Thus, as shown in the figure, the seven colours emerge along different paths and get separated and we get a spectrum of seven colours.

Partial and Total Internal Reflection
When light enters a rarer medium from a denser medium, it gets partially reflected i.e. part of the light gets reflected and comes back into the denser medium as per laws of reflection. This is called partial reflection. The rest of the light gets refracted and goes into the rarer medium. As light goes from denser to rarer medium, it bends away from the normal i.e. the angle of incidence i, is smaller than the angle of reflection r. This is shown on the left side of the figure. If we increase i, r will also increase according to Snell’s law as the refractive index is a constant.

For a particular value of i, the value of r becomes equal to 90°. This value of i is called the critical angle. For angles of incidence larger than the critical angle, the angle of refraction is larger than 90°. Such rays return to the denser medium as shown towards the right in the figure. Thus, all the light gets reflected into the dense medium. This is called total internal reflection. We can determine the value of the critical angle as follows.
$${ }_1 \mathrm{n}_2=\frac{\sin \mathrm{i}}{\sin \mathrm{r}}$$
For total internal reflection,
i = critical angle, r = 90°
$${ }_1 \mathrm{n}_2=\frac{\sin \mathrm{i}}{\sin 90^{\circ}}$$ = sin i (∵ sin 90° = 1)

Rainbow is a beautiful natural phenomenon. It is the combined effect of several natural processes. It is the combined effect of dispersion, refraction, and total internal reflection of light. It can be seen mainly after rainfall. Small droplets of water act as small prisms. When light rays from the Sun enter these droplets, they get refracted and dispersed. Then there is internal reflection as shown in the figure, and after that once again the light gets refracted while coming out of the droplet. All these three processes together produce the rainbow.

Solved Examples

Example 1.
The absolute refractive index of water is 1.36. What is the velocity of light in water?
(velocity of light in vacuum 3 × 108 m/s)
Given:
V1 = 3 × 108 m/s
n = 1.36
n = $$\frac{V_1}{V_2}$$
1.36 = $$\frac{3 \times 10^8}{V_2}$$
V2 = $$\frac{3 \times 10^8}{1.36}$$ = 2.21 × 108 m/s

Example 2.
Light travels with a velocity of 1.5 × 108 m/s in a medium. On entering the second medium its velocity becomes 0.75 × 108 m/s. What is the refractive index of the second medium concerning the first medium?
Given:
V1 = 1.5 × 108 m/s
V2 = 0.75 × 108 m/s
$${ }_2 \mathrm{n}_1=\frac{1.5 \times 10^8}{0.75 \times 10^8}$$ = 2

Maharashtra State Board Class 10 Science Notes Refraction of Light can be used for revisiting and reinforcing previously learned content.