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)
A) 0.375 in
B) 6 in
C) 0.167 in
D) 3.84 in
To solve this problem, we need to convert all the distances to the same unit. Let's convert feet to inches:
1 foot = 12 inches
Distance from the transparency to the projector lens, d_(o) = 8 feet * 12 inches/foot = 96 inches
Now, we can use the thin lens equation to find the focal length of the projector lens:
1/f = 1/d_i + 1/d_o
Substitute the given values:
1/f = 1/4 + 1/96
1/f = 24/96 + 1/96
1/f = 25/96
f = 96/25 = 3.84 inches
Therefore, the focal length of the projector lens is 3.84 inches. The correct option is:
D) 3.84 inches