Question

An object is lying at a distance of $90cm$ from a concave mirror of focal length $30cm$. The position and nature of image formed by it will be:

• A. $45cm$, of the size to object
• B. $95cm$, smaller than object
• C. $35cm$, bigger than object
• D. $-45cm$, smaller than object

Answer 1

The correct option is D $-45cm$, smaller than object

Given that,

Focal length $f=-30cm$

Object distance $u=-90cm$

Now, from the mirror formula

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

$\frac{1}{-30}+\frac{1}{90}=\frac{1}{v}$

$\frac{1}{v}=\frac{-2}{90}$

$v=-45cm$

Hence, the position and nature of image formed is -$45cm$ and smaller than object