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 $\theta_{i}$ from medium 1 and emerges in medium 2 with refraction angle $\theta_{f}$ with a lateral displacement λ. Which of the following statement(s) is(are) true?
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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 $\theta_{i}$ from medium 1 and emerges in medium 2 with refraction angle $\theta_{f}$ with a lateral displacement λ. Which of the following statement(s) is(are) true?

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G1 Physics · Accepted Answer

Derived solution: Step 1: Use Snell’s law at each plane interface. For paraxial viewing through a plane surface, apparent depth = real depth × n(observer)/n(object medium). Step 2: Test each statement independently using these relations and the data/figure. Step 3: The statements that satisfy the required optical conditions are A: λ is independent of n₂; B: λ is dependent on n(z); D: n1sin θi = n₂ sin θf. Hence the correct answer is A,B,D.