Question

An object of $5cm$ high is placed at a distance $60cm$ in front of a concave mirror of focal length $10cm$. The size of the image is:

• A. $1cm$
• B. $2.5cm$
• C. $5cm$
• D. $10cm$

Answer 1

The correct option is A $1cm$

Given,

Size of object $h_o=5cm$

Size of the image $h_i=?$

Focal length, $f=-10cm$

Object distance $u=-60cm$

Image distance $v=?$

Using mirror formula,

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

$\frac{1}{-10}=\frac{1}{v}+\frac{1}{-60}$

$\frac{1}{v}=\frac{-6+1}{60}$

$v=-12cm$

Hence, the position of the object is at 12 cm in front of the mirror.

Magnification (M)$=\frac{h_i}{h_o}=\frac{-v}{u}=\frac{12}{-60}=-0.2$

$h_i=-0.2\times h_o$

$h_i=-0.2\times 5=-1cm$

Height of inverted image is $1cm$.