A concave mirror has a 12 cm tall object placed 40 cm in front of it. An image forms 60 cm in front of the mirror. What is the size and orientation of the image?
A) 8.0 cm, inverted
B) 8.0 cm, upright
C) 18 cm, inverted
D) 18 cm, upright
E) 24 cm, upright

Question

Quizplus · Accepted Answer

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

Solving for focal length: 
1/f = 1/40 + 1/60 
1/f = 1/24 
f = 24 cm

Using the magnification equation: 
m = -di/do

Solving for image distance: 
m = hi/ho = -di/do 
-12/ho = -di/40 
di = -480/ho

Substituting the values: 
ho = 12 cm 
di = -480/12 = -40 cm

The negative sign indicates that the image is inverted.

Using the magnification equation again: 
m = hi/ho = -di/do 
hi/12 = -(-40)/40 
hi = 12 cm

Therefore, the size of the image is 18 cm (as it is inverted) and the orientation is inverted.

A Concave Mirror Has a 12 Cm Tall Object Placed