Question

A small candle $2.5\text{cm}$ in size is placed $27\text{cm}$ in front of a concave mirror of radius of curvature $36\text{cm.}$ At what distance in cm from the mirror should a screen be placed in order to receive sharp image?

• A. 54.0
• B. 54
• C. 54.00

Answer 1

Answer: (A), (B), (C)

Here$u=-27\text{cm},f=\frac{R}{2}=-\frac{36}{2}=-18\text{cm}$
Putting values in expression
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
We get
$\frac{1}{-18}=\frac{1}{v}+\frac{1}{-27}$
or
$\frac{1}{v}=\frac{-1}{18}+\frac{1}{27}=-\frac{1}{54}$
or $v=-54\text{cm}$

Hence the screen should be placed at 54 cm from the mirror on the same side as the object.

Why this question? Note: According to the sign convention, the direction of incident light rays is taken as positive.