Refraction

Q1

During refraction of light, which of the following quantities does not change : velocity, wavelength, frequency and amplitude ?The atmospheric pressure is 80 cm of Hg. Express it in N m^–2 Use: density of Hg = 13.6 g cm^–3, g = 9.8 m s^–2?

Sol:

The frequency of light does not change on refraction.

Q2

A ray of light falls normally on a glass slab. What is the angle of refraction?

Sol:

For normal incidence, angle of incidence i	=	0°
∴ angle of refraction r	=	0°

Q3

Refractive index of water is 4/3. Calculate the speed of light in water. Speed of light in vacuum is 3 × 10⁸ m s^–1 ?

Sol:

∴ Refractive index of water	=	(Speed of light in vacuum) / (Speed of light in water)
4/3	=	((3 × 10⁸) ms^–1)/(Speed of light in water)
or Speed of light in water	=	(3/4) × 3 × 10⁸ ms^–1
	=	2.25 × 10⁸ ms^{– 1}

Q4

A ray of light strikes a glass slab 7 cm thick, making an angle of incidence equal to 30^o. Construct the ray diagram showing the refracted ray and the emergent ray through the glass block. The refractive index of glass is 1.5. Also calculate the lateral displacement of the ray?

Sol:

The ray diagram is given in below.

Given, μ = 1.5, i = 30°

From Snell's law, (sin i)/(sin r) = μ

∴ sin r	=	(sin i)/μ
	=	(sin 30°)/1.5
	=	(1/2)/1.5
	=	1/3
or r	=	19.5°

Lateral displacement = 1cm nearly (on proper scale)^×

Q5

The diagram below shows a glass block suspended in a liquid. A beam of light of single colour is incident from liquid on one side of the block.

(i) Draw diagrams to show how light bends when it travels from liquid to glass and then to liquid if (a) the light slows down in glass, (b) the light speeds up in glass.

(ii) State two conditions under which the light ray moving from liquid to glass passes straight without bending. Will the glass be visible then?

Sol:

(i) (a) If light slows down in going from liquid to glass (i.e.,μ_glass > μ_liquid).

It will bend towards the normal at the point of incidence in passing from liquid to glass at the first surface while it will bend away from the normal at the second surface in passing from glass to liquid. The ray diagram is shown in below figure.

Light ray passing from liquid to glass block

(i) (b) If light speeds up in going from liquid to glass (i.e., μ_glass > μ_liquid), it will bend away from tne normal at the point of incidence on the first surface in passing from liquid to glass, while it will bend towards the normal at the second surface in passing from glass to liquid. The ray diagram is shown in below figure.

Light ray passing from liquid medium to glass medium

Note that in both the cases, the emergent ray is parallel to the incident ray.

(ii) A light ray moving from liquid to glass passes straight without bending under the following two conditions :

(a) When light ray falls normally on glass from the liquid (i.e.,

i = 0°, then

r = 0°).

(b) When refractive index of liquid is the same as that of glass.

The glass will not be visible then.

Q6

The diagram below shows the section of a semi–circular glass block having centre at O. A, B, and C are monochromatic rays of light of the same colour. On the diagram, mark the critical angle by i_c. Draw the paths of rays A and C after they strike the edge XY. Name the phenomena which the paths of rays A and C (into and out of the block) exhibit?

Sol:

The completed diagram is shown in below figure.

The critical angle has been marked as ic.

The ray A suffers refraction from glass to air.

The ray C suffers total internal reflection.

semi-circular glass block critical angle