Question

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]

(1) 0.04

(2) 0.40

(3) 0.1

(4) 0.01

Answer 1

Correct option is : (1) 0.04

When P = 2.5 D

\( \mathrm{F}=\frac{1}{\mathrm{P}}=\frac{1}{2.5}\) 

When P' = 2.6 D

\( \mathrm{F}^{\prime}=\frac{1}{\mathrm{P}^{\prime}}=\frac{1}{2.6}\)

Relative decrease in focal length

\( \frac{\mathrm{F}-\mathrm{F}^{\prime}}{\mathrm{F}}=\frac{\frac{2}{5}-\frac{5}{13}}{\frac{2}{5}}=1-\frac{25}{26}=\frac{1}{26}=0.04\)