Question

The nature of the image of a candle flame located 40cm from a concave mirror is real, inverted and magnified four times. The radius of curvature of the mirror will be

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

Answer 1

The correct option is B $64cm$

$m=-4u=-40cmm=-4=\frac{-v}{u}-4=\frac{-v}{-40},v=-160cm\text{By applying mirror formula}\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\frac{1}{f}=\frac{1}{-160}-\frac{1}{40}\frac{1}{f}=\frac{-1-4}{160}=\frac{-5}{160}f=\frac{-160}{5}=-32cm\text{Radius of curvature = 2f}=2\left(32\right)=64cm$