Question

A spherical mirror having focal length $f=-25\text{cm}$ is used to obtain an image which is of the same size as that of the object. What should be the object distance $\left(u\right)$ as per sign convention?

• A. $u=+25\text{cm}$
• B. $u=-30\text{cm}$
• C. $u=-25\text{cm}$
• D. $u=-50\text{cm}$

Answer 1

The correct option is D $u=-50\text{cm}$

Given that, $f=-25\text{cm}$
Focal length of concave mirror is always negative, because focal length is measured opposite to the direction of incident ray.

In the case of a concave mirror, same size of image is obtained when the object placed at the centre of curvature.
so, $u=R=2f=-50\text{cm}$
$\therefore u=-50\text{cm}$

Concept involved:-
(1) Focal length of a concave mirror is always negative.
(2) When an object placed at centre of curvature,
Image height = Object height