Std 10 Science Part 1 · Chapter 6

6. Refraction of Light

Complete solutions to the Exercise, with ray diagrams, proofs and numericals. Maharashtra State Board (Balbharati), Std 10 Science and Technology Part 1.

Exercise

1Fill in the blanks and explain the completed sentences.

(a) Refractive index depends on the …… of light.

Refractive index depends on the velocity of light.

Explanation: The refractive index of medium 2 with respect to medium 1 is the ratio of the velocity of light in medium 1 to that in medium 2 (¹n₂ = v₁/v₂). Light travels with different velocities in different media, so their refractive indices are different.

(b) The change in …… of light rays while going from one medium to another is called refraction.

The change in direction of light rays while going from one medium to another is called refraction.

Explanation: Light changes its direction when it goes from one transparent medium to another, because its velocity changes. For example, a pencil dipped in water appears broken at the water surface.

2Prove the following statements.

(a) If the angle of incidence and angle of emergence of a light ray falling on a glass slab are i and e respectively, prove that i = e.

Refraction through a glass slab: AN is the incident ray, NM the refracted ray and MD the emergent ray. MD is parallel to AN (dashed line).

A ray AN enters the glass slab PQRS at N, travels along NM and comes out along MD. Let n be the refractive index of glass with respect to air.

At N (air to glass), by Snell’s law: sin isin r = n   …(1)
At M (glass to air): sin i₁sin e = 1n ⇒ sin esin i₁ = n   …(2)
Sides PQ and SR are parallel, so the normals at N and M are parallel. NM is a transversal, so r = i₁ (alternate angles)
Putting i₁ = r in (2): sin esin r = n   …(3)
From (1) and (3): sin isin r = sin esin r ⇒ sin i = sin e
∴ i = e

Hence proved. So the emergent ray MD is parallel to the incident ray AN, but slightly displaced sideways.

(b) A rainbow is the combined effect of the refraction, dispersion, and total internal reflection of light.

Light in a water droplet: refraction with dispersion, total internal reflection, and refraction again.

A rainbow is seen mainly after rainfall, when small water droplets are present in the air. Each droplet acts like a small prism.
Refraction and dispersion: When sunlight enters a droplet, it is refracted. White light splits into its seven colours, because the refractive index of water is different for different colours.
Total internal reflection: The coloured rays strike the back surface of the droplet and are reflected back inside it.
Refraction again: The rays are refracted once more while coming out of the droplet, and the colours spread further apart.
These three processes together produce the rainbow. Hence a rainbow is the combined effect of refraction, dispersion and total internal reflection of light.

3Mark the correct answer in the following questions.

(A) What is the reason for the twinkling of stars? (i) Explosions occurring in stars from time to time (ii) Absorption of light in the earth’s atmosphere (iii) Motion of stars (iv) Changing refractive index of the atmospheric gases

(iv) Changing refractive index of the atmospheric gases

The air keeps moving and its density and temperature keep changing, so its refractive index changes continuously. Hence the apparent position and brightness of a star keep changing, and it appears to twinkle.

(B) We can see the Sun even when it is little below the horizon because of (i) Reflection of light (ii) Refraction of light (iii) Dispersion of light (iv) Absorption of light

(ii) Refraction of light

Sunlight bends along a curved path as it passes through the layers of the earth’s atmosphere. So we see the Sun a little before sunrise and a little after sunset.

(C) If the refractive index of glass with respect to air is 3/2, what is the refractive index of air with respect to glass? (a) 1/2 (b) 3 (c) 1/3 (d) 2/3

^gn_a = 1^an_g = 13/2 = 23

(d) 2/3

4Solve the following examples.

(a) If the speed of light in a medium is 1.5 × 10⁸ m/s, what is the absolute refractive index of the medium?

Given: velocity of light in vacuum v₁ = 3 × 10⁸ m/s, velocity in the medium v₂ = 1.5 × 10⁸ m/s. To find: n

n = v₁v₂ = 3 × 10⁸1.5 × 10⁸ = 2

The absolute refractive index of the medium is 2.

(b) If the absolute refractive indices of glass and water are 3/2 and 4/3 respectively, what is the refractive index of glass with respect to water?

Given: n_g = 3/2, n_w = 4/3. To find: ^wn_g

^wn_g = n_gn_w = 3/24/3 = 32 × 34 = 98

The refractive index of glass with respect to water is 9/8.

★Project: Using a laser and soap water, study the refraction of light under the guidance of your teacher.

Fill a transparent rectangular glass tank or jar with water and add a few drops of liquid soap. Stir gently. The soap makes the path of the laser beam visible inside the water.
Darken the room. Shine a laser pointer from above so that the beam falls on the water surface at an angle.
Observe that the beam bends at the surface and goes towards the normal in water (rarer to denser medium).
Change the angle of incidence and note how the angle of refraction changes. A beam falling along the normal goes straight without bending.
Now shine the beam from below, through the side of the tank, towards the water surface. As the angle increases, the beam bends away from the normal, and beyond the critical angle it is totally reflected back into the water (total internal reflection).

Never look directly into a laser beam or point it at anyone’s eyes. Do this activity only under your teacher’s supervision.

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