Question

A concave mirror of focal length $10\text{cm}$ produces an image which can be obtained on the screen. If the image size is four times the size of the object, the distance of object from the pole of the mirror is

• A. $10.5\text{cm}$
• B. $12.5\text{cm}$
• C. $11.5\text{cm}$
• D. $13.5\text{cm}$

Answer 1

The correct option is B $12.5\text{cm}$

Since image can be obtained on the screen, it is a real image.
Given:
Focal length, $f=-10\text{cm}$
$[$concave mirror$]$
$m=-4$
$[$real image$]$
So, $m=\frac{-v}{u}=-4$
$\Rightarrow v=4u$
Applying mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{4u}+\frac{1}{u}=\frac{-1}{10}$
$\Rightarrow \frac{5}{4u}=\frac{-1}{10}$
$\Rightarrow u=-12.5\text{cm}$
​​​​​​​Hence, the distance of the object from the pole of the mirror is $12.5\text{cm}$.