For the image of the overheard projector to be in focus, the distance from the projector lens to the image, d subscript i baseline, the projector lens focal length, f, and the distance from the transparency to the projector lens, d subscript o baseline, must satisfy the thin lens equation StartFraction 1 over f EndFraction equals StartFraction 1 over d subscript i baseline EndFraction plus StartFraction 1 over d subscript o baseline EndFraction. Which is the focal length of the projector lens if the transparency placed 4 inches from the projector lens is in focus on the screen, located 8 feet from the projector lens?

Question

For the image of the overheard projector to be in focus, the distance from the projector lens to the image, d subscript i baseline, the projector lens focal length, f, and the distance from the transparency to the projector lens, d subscript o baseline, must satisfy the thin lens equation StartFraction 1 over f EndFraction equals StartFraction 1 over d subscript i baseline EndFraction plus StartFraction 1 over d subscript o baseline EndFraction. Which is the focal length of the projector lens if the transparency placed 4 inches from the projector lens is in focus on the screen, located 8 feet from the projector lens?

Answer 1

First, we need to convert all units to the same denominator, let's convert feet to inches:

8 feet = 8 feet × 12 inches/foot = 96 inches

Now we can use the thin lens equation with the given distances:

1/f = 1/di + 1/do

Substitute di = 96 inches and do = 4 inches:

1/f = 1/96 + 1/4
1/f = 1/96 + 24/96
1/f = 25/96

To find f, take the reciprocal:

f = 96/25 = 3.84 inches

Therefore, the focal length of the projector lens is 3.84 inches.