Question

The moon's diameter is 3.48 106 m, and its mean distance from the earth is 3.85 108 m. The moon is being photographed by a camera whose lens has a focal length of 48.5 mm.

(a) Find the diameter of the moon's image on the slide film.

(b) When the slide is projected onto a screen that is 15.1 m from the lens of the projector (f = 103.4 mm), what is the diameter of the moon's image on the screen?

I got part a to be 4.38e-4 m but have no idea how to do b

Answer 1

(a)
1/do+1/di =1/F
1/di=1/F-1/do=1/48.5•10⁻³- 1/3.85•10⁸.
di≃48.5•10⁻³m
x/di=D/do
x=D•di/do =3.48•10⁶•48.5•10⁻³/3.85•10⁸.=
=4.38•10⁻⁴ m
(b)
1/do₁+1/di₁ =1/f
1/do₁=1/f- 1/di₁ =
=1/103.4•10⁻³-1/15.1 ≃ 9.6
do₁=0.1404 m
x/do₁=Y/di₁
Y=di₁•x/do₁=15.1•4.38•10⁻⁴/0.104 = 0.0636 m