What is the relative decrease in focal length of a lens for an increase in optical power by 0.1 D from 2.5D…

What is the relative decrease in focal length of a lens for an increase in optical power by 0.1 D from 2.5D ? ['D' stands for dioptre]
  1. $0.01$
  2. $0.04$
  3. $0.40$
  4. $0.1$

Solution

Initial optical power, \(P_1=2.5 \mathrm{D}\)
Final optical power, \(P_2=2.5 D+0.1 D=2.6 D\)
Step 1: Relation Between Focal Length and Power
The focal length \(f\) (in meters) of a lens is related to its optical power \(P\) by:
\(P=\frac{1}{f}\)
So,
\(\begin{gathered}
f_1=\frac{1}{P_1}=\frac{1}{2.5}=0.4 \mathrm{~m} \\
f_2=\frac{1}{P_2}=\frac{1}{2.6} \approx 0.3846 \mathrm{~m}
\end{gathered}\)
Step 2: Relative Decrease in Focal Length
The relative decrease in focal length is given by:
\(\frac{\Delta f}{f_1}=\frac{f_1-f_2}{f_1}\)
Substituting the values:
\(\begin{aligned}
\frac{\Delta f}{f_1} & =\frac{0.4-0.3846}{0.4} \\
& =\frac{0.0154}{0.4}
\end{aligned}\)
\(=0.0385\) which is approx 0.04
Final Answer: 0.04

Asked in: JEE Main 2025 (24 Jan Shift 1)

Practice more Ray Optics questions on Aicharya