Question

A small candle $2.5cm$ in size is placed $27cm$ in front of a concave mirror of radius of curvature $36cm$. At what distance from the mirror should a screen be placed in order to receive a sharp image? Describe the nature and size of the image.

Answer 1

Given: A small candle 2.5cm in size is placed 27cm in front of a concave mirror of radius of curvature 36cm.

To find the distance from the mirror should a screen be placed in order to receive a sharp image and the nature and size of the image.

Solution:

According to the given criteria,

Object height, $h_o=2.5cm$

Object distance, $u=-27cm$

Radius of the curvature,$R=-36cm$

Focal length of the mirror, $f=\frac{R}{2}=-\frac{36}{2}=-18cm$

Applying mirror formula, we get

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}⟹\frac{1}{-18}=\frac{1}{v}+\frac{1}{-27}⟹\frac{1}{v}=\frac{1}{-18}+\frac{1}{27}⟹\frac{1}{v}=\frac{-3+2}{54}⟹v=-54cm$

The negative sign indicates the image is formed in-front of the mirror. Thus the screen should be placed at a distance of 54 cm in front of the mirror on the same side as the object in order to receive a sharp image.

Magnification, $m=-\frac{v}{u}=\frac{h_o}{h_i}⟹-\frac{(-54)}{(-27)}=\frac{2.5}{h_i}⟹h_i=-\frac{2.5\times 27}{54}⟹h_i=-1.25cm$

The negative sign indicates the image is inverted and real

When the candle is moved closer to the mirror, the screen would have moved farther and farther. However, when the candle is closer than 18cm from the mirror, the image would be virtual and therefore cannot be collected on the screen.