Question

An object of length $30$ cm is placed on principal axis of a concave mirror of focal length $30$cm. Its one end at a distance of $45$cm as shown. If length of image is $10$x(in cm) find the value of x.

Answer 1

Given focal length $f=30cm$ object length =30 cm and object distance $u$= 45 cm.

Thus from mirror formula we get ,

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

Here both focal length and object distance lies in front of the mirror so consider them negative,hence the above equation can written as

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

$\frac{1}{v}=\frac{u-f}{uf}$

$v=\frac{uf}{u-f}$

$v=-90$

Also we know magnification $m=\frac{-v}{u}=\frac{h_i}{h_o}$

$10x=2\times 30$

$x=6cm$