JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Geometrical Optics

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A container contains a liquid with refractive index of 1.2 up to a height of 60 cm and another liquid having refractive index 1.6 is added to height H above first liquid. If viewed from above, the apparent shift in the position of bottom of container is 40 cm. The value of H is ____ cm.
(Consider liquids are immisible)

Answer: 80

Solution

Viewed from above, each liquid layer raises the apparent position of the bottom by

t (1 - \frac{1}{μ})

, and the two shifts add. The lower layer (

t = 60

cm,

μ = 1.2

) gives

60 (1 - \frac{1}{1.2}) = 60 \times \frac{1}{6} = 10 cm,

and the upper layer of height

H

(

μ = 1.6

) gives

H (1 - \frac{1}{1.6}) = 0.375 H

. Setting the total shift to

40

cm,

10 + 0.375 H = 40 \Rightarrow 0.375 H = 30.

Solving gives

H = 80

cm.

JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Integer answer

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