A transparent slab of thickness d has a refractive index n(z) that increases with z. Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n₁ and n₂ (>n₁), as shown in the figure. A ray of the light incident with angle θ_i from medium 1 and emerges in medium 2 with refraction angle θ_f with lateral displacement l. Which of the following statement(s) is (are) true?

l is independent of n₂
n₁ sinθ_i = n₂sinθ_f
l is dependent on n(z)
n₁ sin θ_i = (n₂ – n₁) sinθ_f

Open in App

Solution

The correct option is C
l is dependent on n(z)

The explanation for correct options:
In case of option A:
The lateral displacement of light is independent of the refractive index of the outer medium of the slab.
The lateral displacement depends upon the refractive index of the medium through which it passes.
Hence l is independent of n₂, where l is the lateral displacement of light and n₂ is the refractive index of the outer medium.
In case of option B:
According to snell's law, The sine of the angle of incidence and the sine of angle refraction have a constant ratio.
$n_{1} \sin θ_{i} = n_{2} \sin θ_{f}$
Where, $n_{1}$ is the incident index, $n_{2}$ is the refractive index, $θ_{i}$ is the incident angle, and $θ_{f}$ is refracted angle.
Hence option B is correct.
In case of option C:
The lateral displacement of light is dependent on the refractive index of the medium through which it passes.
The more the refractive index, the more will be the value of lateral displacement of light.
l is dependent on n(z), where l is the lateral displacement of light and n(z) is the refractive index of medium inside the slab.
Explanation for incorrect options:
In case of option D:
According to snell's law, The sine of the angle of incidence and the sine of angle refraction have a constant ratio.
$n_{1} \sin θ_{i} = n_{2} \sin θ_{f}$
$n_{1} \sin θ_{i} = (n_{2} - n_{1}) \sin θ_{f}$ is the incorrect equation for snell's law.
Hence option D is incorrect.
Hence options A, B, and C are correct.

Suggest Corrections

Similar questions

Q. A transparent slab of thickness d has a refractive index n(z) that increases with z. Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices

n_{1}

and

n_{2}

(> n_{1})

, as shown in the figure. A ray of light incident with angle

θ_{i}

from medium 1 and emerges in medium 2 with refraction angle

θ_{f}

with lateral displacement

l

.
Which of the following statement(s) is (are) true?

Q. A ray of light travelling in a medium of refractive index

n_{1}

is incident on a medium of refractive index

n_{2} (< n_{1})

at an angle of incidence

θ

. The reflected and refracted rays make an angle of

120^{0}

with each other. Then the critical angle for the boundary separating the two media is

A ray of light is incident on a glass-slab from air at an angle . Thickness and refractive index of glass-slab are‘t’ and ‘ $μ_{a}$ ’ respectively, Find the lateral displacement of the emergent ray respective to incident ray.

Q. A rectangular glass slab ABCD of refractive index

n_{1}

, is immersed in water of refractive index

n_{2}

(

n_{1} > n_{2}

). A ray of light is incident at the surface AB of the slab as shown in the figure. The maximum value of angle of incidence

α_{m a x}

, such that the ray comes out only from the other surface CD, is given by

Q. AB & CD are 2 glass slabs with refractive indices 1.41 and 1.73. The medium between them has a refractive index 2. Find the minimum angle of incidence at Q, so that the ray is totally reflected by both the slabs.

Join BYJU'S Learning Program