An object is placed 60 cm in front of a mirror and the image is upright and ¼ the size of the object. What is the focal length of the mirror?
A) −12 cm
B) −20 cm
C) −45 cm
D) −75 cm
E) some positive value not given

Question

Quizplus · Accepted Answer

Using the mirror equation, we have:

1/f = 1/d_o + 1/d_i

Where:
- f is the focal length of the mirror
- d_o is the distance between the object and the mirror (negative because the object is in front of the mirror)
- d_i is the distance between the image and the mirror (positive because the image is behind the mirror)

We have:

d_o = -60 cm (given)
d_i = f/2 (since the image is 1/4 the size of the object and upright, it is virtual and located behind the mirror, at a distance of -d_i = f/2)

Plugging in these values, we get:

1/f = 1/-60 + 2/f
1/f - 2/f = -1/60
-1/f = -1/60
f = -60 cm / (-1) = 60 cm

Therefore, the focal length of the mirror is -60 cm, which is equivalent to choice B.

An Object Is Placed 60 Cm in Front of a Mirror