Ray Optics Question 7
Question 7 - 2024 (29 Jan Shift 2)
If the distance between object and its two times magnified virtual image produced by a curved mirror is $15 \mathrm{~cm}$, the focal length of the mirror must be :
(1) $15 \mathrm{~cm}$
(2) $-12 \mathrm{~cm}$
(3) $-10 \mathrm{~cm}$
(4) $10 / 3 \mathrm{~cm}$
Show Answer
Answer: (3)
Solution:
$\mathrm{m}=2=\frac{-\mathrm{v}}{\mathrm{u}}$
$2=\frac{-(15-u)}{-u}$
$2 \mathrm{u}=15-\mathrm{u}$
$3 \mathrm{u}=15 \Rightarrow \mathrm{u}=5 \mathrm{~cm}$
$\mathrm{v}=15-\mathrm{u}=15-5=10 \mathrm{~cm}$
$\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}$
$=\frac{1}{10}+\frac{1}{(-5)}=\frac{1-2}{10}=\frac{-1}{10}$
$\mathrm{f}=-10 \mathrm{~cm}$
