Question

An object OA is placed in front of the concave mirror as given in the image. The point F is the focal length of the mirror and P is the pole. Determine the distance of the image from the pole of the concave mirror.

• A. $66.66cm$
• B. $66.66cm$
• C. $33.33cm$
• D. $33.33cm$

Answer 1

The correct option is C $33.33cm$

Given, object distance $u=-50cm$ (Using sign convention)
Let the image distance be $v$.
Focal length, $f=-20cm$

Using the mirror formula
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\frac{1}{v}+\frac{1}{-50}=\frac{1}{-20}\frac{1}{v}=\frac{1}{-20}-\frac{1}{-50}\frac{1}{v}=\frac{1}{-20}+\frac{1}{50}\frac{1}{v}=\frac{1}{-20}\times \frac{5}{5}+\frac{1}{50}\times \frac{2}{2}\frac{1}{v}=\frac{-5}{100}+\frac{2}{100}\frac{1}{v}=\frac{2-5}{100}\frac{1}{v}=\frac{-3}{100}v=\frac{-100}{3}v=-33.33cm$
(Negative sign indicates that the image is formed in front of the mirror)