A projector lens is needed to form an image on a screen 10 times the size of its corresponding object.The screen is located 8.0 m from the lens.What is the required focal length of the lens?

Question

Quizplus · Accepted Answer

By using the formula for magnification, we have:
m = -di/do = 10
where di is the image distance and do is the object distance.
Since the image is formed on the screen, we have di = 8.0 m.
Thus, do = -di/m = -8.0/10 = -0.8 m (negative sign indicates that the object is located in front of the lens).
Using the thin lens equation, we have:
1/f = 1/do + 1/di
1/f = -1/0.8 + 1/8.0
f = 0.728 m ≈ 0.73 m (rounded to two significant figures)
Therefore, the required focal length of the lens is 0.73 m. The best choice is (C).

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