Question

A$4.5cm$ needle is placed $12cm$ away from a convex mirror of focal length $15cm$. Give the location of the image and the magnification.

Answer 1

Given: A 4.5cm needle is placed 12cm away from a convex mirror of focal length 15cm.

To find the location of the image and the magnification.

Solution:

According to the given criteria,

Object height, $h_o=4.5cm$

Object distance, $u=-12cm$

Focal length of the mirror, $f=15cm$

Applying mirror formula, we get

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}⟹\frac{1}{15}=\frac{1}{v}+\frac{1}{-12}⟹\frac{1}{v}=\frac{1}{15}+\frac{1}{12}⟹\frac{1}{v}=\frac{4+5}{60}⟹v=6.6cm$

Hence, the image is at a distance of 6.6 cm,

Magnification, $m=-\frac{v}{u}=\frac{h_o}{h_i}⟹-\frac{6.6}{-12}=\frac{4.5}{h_i}⟹h_i=\frac{4.5\times 12}{6.6}⟹h_i=+8.2cm$

The image is diminished and erect.

So magnification, $m=-\frac{v}{u}=-\frac{6.6}{-12}=0.55$

Is the magnification.