Question

A ray of light travels from air to water to glass and again from glass to air. Refractive index of water with respect to air is \( x \), glass with respect to water is \( y \) and air with respect to glass is \( z \). Which one of the following is correct?

• A. \( xz = y \)
• B. \( yz = x \)
• C. \( xyz = 1 \)
• D. \( xy = z \)

Hint:

Product of refractive indices around a closed path is always equal to 1.

Answer 1

The Correct Option is C

Step 1: Use definition of refractive index.
Refractive index of medium A with respect to medium B is given by \[ n_{AB} = \frac{n_A}{n_B} \]
Step 2: Write given refractive indices.
\[ x = \frac{n_w}{n_a}, \quad y = \frac{n_g}{n_w}, \quad z = \frac{n_a}{n_g} \]
Step 3: Multiply all three.
\[ xyz = \frac{n_w}{n_a} \cdot \frac{n_g}{n_w} \cdot \frac{n_a}{n_g} = 1 \]
Step 4: Conclusion.
The correct relation is \( xyz = 1 \).