Question

A vessel of depth 2d cm is half-filled with a liquid of refractive index \( \mu_1 \) and the upper half with a liquid of refractive index \( \mu_2 \). The apparent depth of the vessel seen perpendicularly is

• A. \( \frac{\mu_1 + \mu_2}{\mu_1 + \mu_2} \, d \)
• B. \( \frac{1}{\mu_1 + \mu_2} \, d \)
• C. \( \frac{1}{\mu_1 + \mu_2} \, 2d \)
• D. \( \frac{1}{\mu_1 + \mu_2} \, d \)

Hint:

For a vessel with liquids of different refractive indices, the apparent depth is calculated by considering the refractive indices of both liquids and the depth.

Answer 1

The Correct Option is C

Step 1: Formula for apparent depth.
When the light passes through two different media, the apparent depth is given by: \[ d_{\text{apparent}} = \frac{d}{\mu} \] where \( \mu \) is the refractive index of the medium.
Step 2: Combine the effects of both liquids.
Since the vessel is half-filled with two liquids, the apparent depth is influenced by both refractive indices. The formula for the apparent depth is: \[ d_{\text{apparent}} = \frac{1}{\mu_1 + \mu_2} \, 2d \]
Final Answer: \[ \boxed{\frac{1}{\mu_1 + \mu_2} \, 2d} \]