Question

A concave mirror of focal length 100 cm is used to obtain the image of the sun which subtends an angle of 30'. The diameter of the image of the sun will be

• A. 1.74 cm
• B. 0.87 cm
• C. 0.435 cm
• D. 100 cm

Answer 1

The correct option is B 0.87 cm.

Given,

The angle subtended by the image of the sun at the mirror = ${30}^{\prime }=(\frac{1}{2}{)}^o=\frac{\pi }{{360}^o}$

If x be the diameter of the image of the sun, then

$\frac{Arc}{Radius}=\frac{\pi }{{360}^o}$

$⟹\frac{x}{100}=\frac{\pi }{{360}^o}$

$⟹x=\frac{\pi }{{360}^o}\times 100$

$⟹x=0.87cm$.