Question

the sun subtends an angle 1/2 degree at the pole of a concave mirror. what should be the radius of curvature of the mirror to produce an image of the sun on a screen where the diameter of the image is 2cm?​

Answer 1

Given :

The angle subtended by thesun at the pole = 1/2°

Diameter of the image = 2 cm

To Find :

The radius of curvature of the mirror

Solution :

• The angle substendes by the sun is given in degrees, the value should be changed to radians

• Angle subtended by the sun = 1/2° = (1/2)×π/180 rad

• We have the relation

                 $\theta=\frac{diameter\:of\:image}{focal\:length}$

                 $\theta=\frac{2}{\frac{R}{2} }$

                $R=45.97cm$

The radius of curvature of the mirror is 45.97 cm