An object with a height of 3.0-cm is placed 8.0 cm in front of a mirror.The virtual image is 4.0 cm further from the mirror when the mirror is concave than when it is planar.
-Determine the focal length of the concave mirror.
A)6.0 cm
B)12 cm
C)24 cm
D)48 cm
E)96 cm

Question

Quizplus · Accepted Answer

Using the mirror equation, 1/f = 1/di + 1/do, where f is the focal length, di is the image distance, and do is the object distance, we can solve for f. 
When the mirror is planar, the image distance is di = -do = -8.0 cm. 
Thus, 1/f = -1/8 + (-1/-8 - 1/3) 
Simplifying and solving for f, we get f = -24 cm. Since the mirror is concave, the focal length is positive, so f = 24 cm. 
Therefore, the best choice is (C) 24 cm.

An Object with a Height of 3