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?
(1 point)
Responses
0.375 in.
0.375 in.
6 in.
6 in.
0.167 in.
0.167 in.
3.84 in.
3.84 in.
To find the focal length of the projector lens, we need to use the thin lens equation:
1/f = 1/di + 1/do
Given that the transparency is placed 4 inches from the projector lens (do = 4 inches) and the screen is located 8 feet from the projector lens (di = 8 feet = 96 inches), we can substitute these values into the equation:
1/f = 1/96 + 1/4
Simplifying the equation:
1/f = 1/96 + 24/96
1/f = 25/96
To find f, we take the reciprocal of both sides:
f = 96/25 ≈ 3.84 inches
Therefore, the focal length of the projector lens is approximately 3.84 inches.