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 light is incident with angle qi from medium 1 and emerges in medium 2 with refraction angle θf with a lateral displacement ℓ. Which of the following statement(s) is(are) true ?

Engineering

Physics

Plane Surface Refraction

Question

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 light is incident with angle qi from medium 1 and emerges in medium 2 with refraction angle θ_f with a lateral displacement ℓ.

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

ℓ is independent of n₂

n₁ sin θ_i = n₂ sin θ_f

ℓ is dependent on n(z)

n₁ sin θ_i = (n₂ – n₁) sin θ_f

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By snell's law

$\Rightarrow \frac{\sin θ_{i}}{\sin θ_{F}} = \frac{n_{2}}{n_{1}}$

also ⇒ for refraction till the n (z),

⇒ here μ of this medium increases, simultaneosuly, the emergent ray is always depend on the refractive index of medium n (z) (here) also 'ℓ ' depends on the refractive index of the medium here n(z) and this ℓ is clearly independent of medium n₂.