Question

A concave mirror of radius of curvature $20cm$ forms image of the sun. The diameter of the sun subtends an angle $1^o$ on the earth. Then the diameter of the image is (in cm):

• A. $\frac{2\pi }{9}$
• B. $\frac{\pi }{9}$
• C. 20
• D. $\frac{\pi }{18}$

Answer 1

Answer: (D)

$\frac{\pi }{18}$

Given: A concave mirror of radius of curvature 20cm forms image of the sun. The diameter of the sun subtends an angle $1^o$ on the earth.

To find the diameter of the image

Solution:

As sun is more far from the earth,

Then we take u = infinite

Radius of curvature, $R=-20cm$

Focal length, $f=\frac{R}{2}=\frac{-20}{2}=-10cm$

From the mirror formula

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}⟹\frac{1}{(-10)}=\frac{1}{v}+\frac{1}{\infty }⟹v=-10cm$

And we also know that

Angle = $1^o=\frac{\pi }{{180}^{\circ }}$

We know,

$\theta =\frac{d}{f}$, where $\theta$ is the angle subtended on the earth, $d$ is the diameter of the image and $f$ is the focal length of the concave mirror.

$d=\theta \times f⟹d=\frac{\pi }{{180}^{\circ }}\times 10⟹d=\frac{\pi }{18}cm$

is the diameter of the image