For the image of the overhead projector to be in focus, the distance from the projector lens to the image, d_(i) , the projector lens focal length, f, and the distance from the transparency to the projector lens, d_(o) , must satisfy the thin lens equation 1/f = d/_(i) + d_(o). 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)

Question

For the image of the overhead projector to be in focus, the distance from the projector lens to the image, d_(i) , the projector lens focal length, f, and the distance from the transparency to the projector lens, d_(o) , must satisfy the thin lens equation 1/f = d/_(i) + d_(o). 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)

Answer 1

First, convert all units to the same measurement. Since 1 foot is equal to 12 inches, 8 feet is equal to 96 inches.

Next, substitute the given values into the thin lens equation:

1/f = 8ft/96in + 4in

1/f = 1/12 + 4

1/f = 1/12 + 48/12

1/f = 49/12

Now, find the reciprocal of 49/12 to get the focal length:

f = 12/49 ≈ 0.244 feet

Therefore, the focal length of the projector lens is approximately 0.244 feet.