An object 10.0 cm in height is placed 37.0 cm in front of a concave mirror of focal length 18.5 cm. What is the height of the image?
A) -2.5 cm
B) -5.0 cm
C) -7.5 cm
D) -20.0 cm
E) -10.0 cm

Question

Quizplus · Accepted Answer

The magnification equation for concave mirrors is: 
m = -di/do = f/do - 1,
where di is the image distance, do is the object distance, and f is the focal length.

We are given:
h_o = 10.0 cm (height of the object)
do = -37.0 cm (object distance: negative because it is in front of the mirror)
f = -18.5 cm (focal length: negative for concave mirrors)

Solving for the image distance:
m = -hi/h_o = f/do - 1
-hi/10.0 = -18.5/(-37.0) - 1
-hi/10.0 = 0.5
hi = -5.0 cm (height of the image)

The negative sign indicates that the image is inverted.

An Object 10