Question

The sun subtends an angle of $(1/2{)}^{th}$ on earth. The image of sun is obtained on the screen with the help of a convex lens of focal length $100$ cm the diameter of the image obtained on the screen will be.

• A. $18$ cm
• B. $1$ mm
• C. $50$ cm
• D. $8.73$ mm

Answer 1

Answer: (D)

$8.73$ mm

The sun subtends at an angle $(1/2{)}^0$,

The focal length of the convex lens, $f=100cm$

from the above figure,

$\theta$ in rad$=\frac{arc}{radius}=\frac{x}{f}$

as we know that, $\pi ={180}^0$

So, $\frac{\pi }{180}\times \frac{1}{2}=\frac{x}{100cm}$

$x=0.872cm=8.72mm$

The diameter of the image obtained on the screen is $8.72mm$

The correct option is D.