Question

An object is placed $10\text{cm}$ in front of a concave mirror of radius of curvature $10\text{cm}$, magnification of the image is

• A. $-2$
• B. $-1$
• C. $1$
• D. $2$

Answer 1

The correct option is B $-1$


Object distance $u=-10\text{cm},v=?$
$f=\frac{R}{2}=\frac{-10}{2}=-5\text{cm}$
Now, using mirror equation
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\frac{1}{-10}=\frac{1}{-5}$
$\therefore \frac{1}{v}=\frac{-1}{5}+\frac{1}{10}=\frac{-2+1}{10}=-\frac{1}{10}$
$v=–10\text{cm}$
Magnification produced
$m=\frac{-v}{u}=-\frac{(-10)}{(-10)}=-1$