Question

To an observer viewing the sun, the angle subtended by the sun is $30$ minutes. A convex lens of focal length $60$ cm if used to form the image of sun, then the diameter of the image of the solar disc is?

Answer 1

As sun is at a very large distance, the object distance $u$ will be $\infty$

From lens formula we get ,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$; where f=focal length of the lens; v=image distance

Now as the object is at infinity its image will produce at a distance equal to its focal length and will be real and inverted also highly diminished.

Thus $v=-f$

Now as the angel subtended by the sun with respect to the observer =30 minutes=30$\times$0.01667=${0.5}^0$

Also we know $\theta =\frac{d}{f}$ where d= diameter of the image and f=focal length

Thus $d=\theta \times f$=0.5$\times$ 60 cm =30 cm