Answer to Question #71357 in Optics for sofia Espulgar

Question

A darkened room has a tiny aperture in the roof through which sunlight enters when the sun is directly overhead. What is the size of the sun's image on the floor 12 ft below the aperture? the sun is 93 million miles away, and its diameter is 865,000 miles.

Answer 1

Distance between floor and aperture - d_1=12 ft
The size of the sun’s image - S_1
Distance between sun and aperture - d_2=93,000,000 miles
The size of the sun - S_2=865,000 miles
For this system:
S_1/d_1 =S_2/d_2 =>S_1=(S_2*d_1)/d_2 ≈0.112 ft
Answer: S_1≈0.112 ft