Question

The nature of the image of a candle flame located $40cm$ from a concave mirror is real, inverted and magnitude four times. Then the radius of curvature of the mirror is:

• A. $32cm$
• B. $64cm$
• C. $48cm$
• D. $80cm$

Answer 1

Answer: (B)

$64cm$

$\text{Image is inverted so magnification is negative.}$

(since $=\frac{r_1}{r_2})$

so magnification $=-4$

$\begin{array}{cc}-\frac{V}{u}& =-4\\ \frac{V}{U}& =4\\ V& =44\end{array}$

Distance between object and mirror $=u=-40cm$

$v=4(-40)=-160$

$\begin{array}{c}\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\\ \frac{2}{R}=\frac{1}{-160}+\frac{1}{-40}(-f=\frac{2}{2})\\ \frac{8}{R}=\frac{-1}{160}+\frac{-4}{160}\end{array}$

$\frac{R}{2}=-\frac{160}{5}$

$R=-64cm$

so option $B$ is correct.