JEE Main · 2024 · 27 Jan 2024 · Shift 1 · Geometrical Optics

Two immiscible liquids of refractive indices

\frac{8}{5}

and

\frac{3}{2}

respectively are put in a beaker as shown in the figure. The height of each column is 6 cm. A coin is placed at the bottom of the beaker. For near normal vision, the apparent depth of the coin is

\frac{α}{4} cm

. The value of

α

is ______.

Answer: 31

Solution

For two liquid layers of thickness

h

and refractive indices

μ_{1}, μ_{2}

, apparent depth

= \frac{h}{μ _{1}} + \frac{h}{μ _{2}}

h_{a pp} = \frac{6}{3/2} + \frac{6}{8/5} = 4 + 3.75 = 7.75 = \frac{31}{4} cm

Comparing with

α /4

α = 31

JEE Main · 2024 · 27 Jan 2024 · Shift 1 · Integer answer

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