Question

Write an expression of refractive index of a liquid relative to air in terms of velocity of light in liquid and in air. Derive the formula of apparent depth of an object placed in liquid.

Hint:

The refractive index determines how light slows down when passing through different mediums, affecting the apparent depth of objects.

Answer 1

Step 1: Expression for Refractive Index.
The refractive index \( n \) of a medium is the ratio of the velocity of light in a vacuum (or air) to the velocity of light in that medium. For a liquid relative to air, the refractive index is given by: \[ n_{\text{liquid/air}} = \frac{c}{v} \] Where:
- \( c \) is the speed of light in air,
- \( v \) is the speed of light in the liquid.
Step 2: Apparent Depth Formula.
When an object is placed in a liquid, its apparent depth is different from the actual depth due to the refraction of light. The formula for the apparent depth \( d_{\text{apparent}} \) is given by: \[ d_{\text{apparent}} = \frac{d}{n} \] Where: - \( d \) is the actual depth, - \( n \) is the refractive index of the liquid relative to air.
Final Answer:
The refractive index of the liquid relative to air is \( n_{\text{liquid/air}} = \frac{c}{v} \), and the formula for the apparent depth of an object placed in a liquid is \( d_{\text{apparent}} = \frac{d}{n} \).