A projector lens is needed to form an image on a screen 10 times the size of its corresponding object.The screen is located 6.0 m from the lens.What is the required focal length of the lens?

Question

Quizplus · Accepted Answer

The formula for the magnification is:

M = -(image distance)/(object distance)

Since we want the image to be 10 times larger than the object, the magnification is 10, so:

10 = -(image distance)/(object distance)

Rearranging and substituting, we get:

(image distance) = -10*(6.0 m) = -60.0 m

(Note that the negative sign indicates that the image is inverted, which is typical for a projector.)

The lens equation is:

(1/focal length) = (1/object distance) + (1/image distance)

Substituting the values we just found, we get:

(1/focal length) = (1/6.0 m) + (1/-60.0 m) = -0.1667 m^-1

Solving for the focal length, we get:

focal length = 1/(-0.1667 m^-1) = 0.60 m

So the answer is (C) 0.55 m, which is closest to 0.60 m.

A Projector Lens Is Needed to Form an Image on a Screen