Question

The refraction of light ray takes place from air to water, water to glass and again glass to air. The ray emerges parallel to incident ray. The correct relation is [\(n_a, n_w, n_g\) represent refractive indices of air, water and glass respectively]

• A. \( n_g^w = \dfrac{n_g^a}{n_w^a} \)
• B. \( n_g^w = n_g^a \times n_w^a \)
• C. \( n_w^g = \dfrac{n_w^a}{n_g^a} \)
• D. \( n_w^g = \dfrac{n_g^a}{n_w^a} \)

Hint:

Relative refractive index between two media is the ratio of their absolute refractive indices.

Answer 1

The Correct Option is D

Step 1: Condition for parallel emergence.
When a ray passes through multiple media and emerges parallel to the incident ray, the net angular deviation must be zero.
Step 2: Relation of refractive indices.
Using the law of refraction at successive interfaces, the refractive index between two media is given by the ratio of their absolute refractive indices.
Step 3: Deriving the relation.
\[ n_w^g = \frac{n_g}{n_w} = \frac{n_g^a}{n_w^a}. \]
Step 4: Conclusion.
Hence, the correct relation is \[ n_w^g = \dfrac{n_g^a}{n_w^a}. \]