Question

A vessel of depth d is half-filled with a liquid of refractive index ₁ and the upper half with a liquid of refractive index ₂. The apparent depth of the vessel seen perpendicularly is:

• A. d(₁₂)/(₁+₂)
• B. d((1)/(₁)+(1)/(₂))
• C. 2d((1)/(₁)+(1)/(₂))
• D. 2d((1)/(₁₂))

Hint:

For multiple media, add apparent depths layer-wise.

Answer 1

The Correct Option is B

Step 1: Apparent depth formula. Apparent depth = real depthμ
Step 2: Applying to two layers. dₐ = (d/2)/(₁) + (d/2)/(₂)
Step 3: Simplifying. dₐ = d((1)/(₁)+(1)/(₂))