The size of the image of the Sun

[Akash47]

Homework Statement

The focal length of a concave mirror is f=20 cm. It is directed towards the sun and the sun makes an angle= 1° at the pole of the mirror. What is the size of the image of the sun?

Homework Equations

1/u +1/v =1/f ...(i) ,magnification= v/u= l₂/l₁ where l₁ =size of the sun,l₂ =size of image of the sun.

The Attempt at a Solution

Here,u=∞(as the light comes from a very large distance),so from (i),v= f =20 cm.So v/u= 20/∞ =0=l₂ /l₁,from that, l₂=0 or l₁=∞.But which is right?Also I can't make a relation with the given angle.This is all what I have done.Please point out the mistake in my approach and also give hints to carry it out.

 

[haruspex]

magnification= v/u

This is not useful here. Just as the distance to the sun is effectively infinite, so is its size, so the magnification in this sense is zero. You need instead to look at the ratio of the angles (angular magnification).
Instead of saying the sun is at infinity, just let u and l₁ be very large. In terms of those, what angle does the sun subtend on Earth?