JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Geometrical Optics

A vessel of depth 'd' is half filled with oil of refractive index

n_{1}

and the other half is filled with water of refractive index

n_{2}

. The apparent depth of this vessel when viewed from above will be-

Answer: (B)

Solution

The apparent depth for a layered medium is the sum of apparent depths of individual layers. Each layer has thickness

d /2

.

For the oil layer:

d_{a pp, 1} = \frac{d /2}{n _{1}}

For the water layer:

d_{a pp, 2} = \frac{d /2}{n _{2}}

Total apparent depth:

d_{a pp} = \frac{d}{2 n _{1}} + \frac{d}{2 n _{2}} = \frac{d}{2} (\frac{1}{n _{1}} + \frac{1}{n _{2}}) = \frac{d}{2} \cdot \frac{n _{1} + n _{2}}{n _{1} n _{2}} = \frac{d ( n _{1} + n _{2} )}{2 n _{1} n _{2}}

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Single correct option