An object 15 cm high is placed 15 cm in front of a convex mirror with a focal length of −10 cm. What is the image height (in cm)?
A) 2
B) 4
C) 6
D) 8
E) 30

Question

Quizplus · Accepted Answer

Using the mirror equation: 
1/f = 1/do + 1/di 
where f is the focal length, do is the distance of the object from the mirror, and di is the distance of the image from the mirror.

Plugging in the values: 
1/-10 = 1/15 + 1/di

Solving for di: 
di = -30 cm

Since the image is virtual (due to negative di), it will be upright and the height will be magnified.

Using the magnification equation: 
m = hi/ho = -di/do

Plugging in the values: 
m = hi/15 = -(-30)/15 
m = 2

Solving for hi: 
hi = 2*ho = 2*15 = 30 cm

Therefore, the image height is 30 cm. The correct choice is C.

An Object 15 Cm High Is Placed 15 Cm in Front