Question

A monochromatic light wave is incident normally on a glass slab of thickness 𝑑, as shown in the figure.The refractive index of the slab increases linearly from 𝑛1 to 𝑛2 over the height ℎ. Which of the following statement(s) is(are) true about the light wave emerging out of the slab?

• A. It will deflect up by an angle tan−1$[\frac {(n_2^2 - n_1^2)d}{2h}]$.
• B. It will deflect up by an angle tan−1$[\frac {(n_2 - n_1)d}{h}]$.
• C. It will not deflect.
• D. The deflection angle depends only on (𝑛2 − 𝑛1) and not on the individual values of 𝑛1 and 𝑛2.

Answer 1

Answer: (D)

The deflection angle depends only on (𝑛2 − 𝑛1) and not on the individual values of 𝑛1 and 𝑛2.

Answer 2

The deflection angle indeed depends only on the difference between the refractive indices (n2 - n1) and is independent of the specific values of n1 and n2. As long as the refractive index increases linearly, the deflection angle will depend solely on the difference in refractive indices.
Therefore, option (4) is correct.