Question

An unlit candle is $90cm$ from a concave mirror of radius $60cm$. Where must a flame be put from the mirror so that its image may be seen coming out of the candle?

• A. $45cm$
• B. $30cm$
• C. $20cm$
• D. $10cm$

Answer 1

The correct option is A $45cm$

Given

$R=60cm$ $\Rightarrow f=\frac{R}{2}=30m$ ($\because$ $f$ of concave mirrors is negative)

$v=-90cm$
Using mirror formula:

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

or, $\frac{1}{-90}+\frac{1}{u}=\frac{1}{-30}$

or, $\frac{1}{u}=\frac{-1}{30}+\frac{1}{90}$

$=\frac{-90+30}{2700}$

$=\frac{-6}{270}$ $=\frac{-1}{45}$

$\Rightarrow$ $u=-45cm.$