Question

The sun's diameter is 1.4 x 10^9 m and its distance from the earth is 1.0*10^11 m. The diameter of its image, formed by a convex lens of focal length 1 m will be?

Answer 1

distance from earth of sun = object distance , u = 1 × 10¹¹ m
focal length of convex lens ,f = 1 m
here we can see that u >> f so, distance of object from lens taken as infinity.
hence, image will be formed as focus.

so, v = f = 1m ......(i)

now we know,
magnification , m = v/u = height of image/height of object.
1/(1 × 10¹¹ ) = height of image/(1.4 × 10^9)
height of image = (1.4 × 10^9)/(10¹¹) = 1.4 × 10^-2
height of image = 1.4 cm = 14 mm

hence, diameter of sun's image = 14mm

Answer 2

u = –1.5 x 1011 m ; f = +20 x10–2 m Since, f is very small compared to u, distance is taken as ∞  . So, image will be formed at focus. Read more on Sarthaks.com - https://www.sarthaks.com/42306/the-diameter-the-sun-and-its-distance-from-the-earth-is-x10-find-the-radius-the-image-the-sun