JEE Main · 2025 · 24 Jan 2025 · Shift 1 · Geometrical Optics

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What is the relative decrease in focal length of a lens for an increase in optical power by 0.1 D from 2.5 D ? ['D' stands for dioptre]

(A)0.04✓ Correct
(B)0.40
(C)0.1
(D)0.01

Answer: (A)

Solution

Power and focal length are related by

P = \frac{1}{f}

(with

f

in metres).

Initial:

P_{1} = 2.5

\Rightarrow f_{1} = \frac{1}{2.5} = 0.4

m

Final:

P_{2} = 2.5 + 0.1 = 2.6

\Rightarrow f_{2} = \frac{1}{2.6}

m

Relative decrease in focal length:

\frac{f _{1} - f _{2}}{f _{1}} = 1 - \frac{f _{2}}{f _{1}} = 1 - \frac{P _{1}}{P _{2}} = 1 - \frac{2.5}{2.6} = 1 - \frac{25}{26} = \frac{1}{26} \approx 0.04

JEE Main · 2025 · 24 Jan 2025 · Shift 1 · Single correct option

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