JEE Main · 2024 · 29 Jan 2024 · Shift 1 · Geometrical Optics

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A biconvex lens of refractive index 1.5 has a focal length of 20 cm in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:

(A)-16 cm
(B)-160 cm✓ Correct
(C)+160 cm
(D)+16 cm

Answer: (B)

Solution

Using

\frac{1}{f} = (μ_{r e l} - 1) \frac{2}{R}

, where

μ_{r e l}

is the refractive index of the lens material relative to the surrounding medium.

In air:

μ_{r e l} = 1.5

f = 20 cm

\frac{1}{20} = (0.5) \frac{2}{R} ⟹ \frac{2}{R} = \frac{1}{10}

In the liquid (

n = 1.6

μ_{r e l} = \frac{1.5}{1.6} = 0.9375

\frac{1}{f ^{'}} = (0.9375 - 1) (\frac{1}{10}) = - 0.00625 ⟹ f^{'} = - 160 cm

Key confirmed: B.

JEE Main · 2024 · 29 Jan 2024 · Shift 1 · Single correct option

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