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.
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.
1 answer