Question

A real image formed by a concave mirror is 4.5 times the size of the object. If the mirror is 20 cm from the object, its focal length is :

• A. $\frac{90}{11}$ cm
• B. $\frac{120}{11}$ cm
• C. $\frac{150}{11}$ cm
• D. $\frac{180}{11}$ cm

Answer 1

Answer: (D)

$\frac{180}{11}$ cm

Given: Magnification, $m=$$-4.5=\frac{-v}{u}$ $\Rightarrow -4.5\times u=-v$
Object distance, $u=-20cm$

$\Rightarrow -4.5\times (-20)=-v$

$\Rightarrow v=-90cm$

From mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{-90}+\frac{1}{-20}=\frac{1}{f}$

$\frac{1}{f}=-(\frac{1}{90}+\frac{1}{20})$ $=\frac{-110}{1800}$ $=\frac{-11}{180}$

$\Rightarrow$ $f=\frac{180}{11}cm$