Question

11.Sun light is incident on a concave mirror, parallel to its principal axis. the image is formed at a distance of 12 cm from the pole. find the radius of curvature of mirror.

(3 Points)

3cm

6cm

12cm

24cm​

Answer 1

Answer :

The radius of curvature is 24cm

Given :

• Sun light is incident on a concave mirror , parallel to its principal axis
• The image is formed 12cm from the pole

To Find :

• The radius of curvature of the mirror

Formula to be used :

Mirror formula

$\sf \star \: \: \dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}$

Solution :

Given , sun light is incident on the mirror and is parallel to its principal axis , thus

$\sf Object \: \: distance , \: u = - \infty$

And , the image distance , v = -12cm

From mirror formula we have

$\sf \implies \dfrac{1}{-12}+\dfrac{1}{-\infty}=\dfrac{1}{f}\\\\ \sf \implies \dfrac{1}{-12} - \dfrac{1}{\infty} =\dfrac{1}{f}\\\\ \sf \implies \dfrac{1}{f}= -\dfrac{1}{12}-0 \\\\ \sf \implies f = -12cm$

Thus the focal length is 12cm

We know that,

Radius of Curvature = 2 focal length

$\sf \implies R = 2\times f \\\\ \sf \implies R =2 \times (-12cm) \\\\ \sf \implies R = -24cm$

Thus the radius of curvature is 24cm