Question

the sun subtends an angle of 1/2 degree at the surface of the earth . a converging lens of focal length 100 cm is used to obtain an image on the screen . calcutate the diameter of the image formed.

Answer 1

Sun is at a huge distance in comparison with the focal length of the lens.
Hence, the objective distance can be considered at infinity.
Hence the image will be formed at its focus.
Consider the following situation:

Understand the angle subtended by the common tangents with Sun and its image are vertically opposite angles. Hence they are equal to each other and is equal to 0.5 degrees.
Thus the angle BOA = 0.5 degrees.
Also the distance OA=OB=100 cm
Hence the distance AB is
AB=x260(2πr)r=100 cmx=0.5∘AB=0.5360(2×227×100)AB=0.873 cm