Question

An object of 5cm tall is placed at a distance of 10cm from a concave mirror of radius of curvature 30cm
i) Find the nature, position and size of the image
ii) Draw the ray diagram to represent the above case.

Answer 1

Given: An object of 5cm tall is placed at a distance of 10cm from a concave mirror of radius of curvature 30cm

To find: the nature, position and size of the image and draw the ray diagram to represent the above case.

Solution:

According to the given criteria,

Let height of the image be $h_i$ and

Height of the object, $h_o=5cm$

Object distance, $u=-10cm$

Radius of curvature, $R=-30cm$

We know, focal length, $f=\frac{R}{2}=\frac{30}{2}=-15cm$

Now applying mirror formula, we get

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}⟹\frac{1}{v}=\frac{1}{f}-\frac{1}{u}⟹\frac{1}{v}=\frac{1}{-15}-\frac{1}{-10}⟹\frac{1}{v}=\frac{-10+15}{150}=\frac{5}{150}⟹v=30cm$

Position of the image is behind the mirror at the distance of 30 cm

Magnification, $m=-\frac{v}{u}=\frac{h_i}{h_o}⟹-\frac{30}{-10}=\frac{h_i}{5}⟹h_i=3\times 5=15cm$

Nature of the image formed: virtual, erect (as magnification is positive) and enlarged.

Ray diagram is as shown in above figure.