A concave mirror has a focal length of 20 cm.What is the position (in cm)of the resulting image if the image is inverted and four times smaller than the object?
A)15
B)25
C)50
D)100
E)-15

Question

Quizplus · Accepted Answer

Using the mirror formula, 1/f = 1/u + 1/v where f is the focal length, u is the object distance and v is the image distance.
We know that f = 20 cm and the image is inverted, so v is negative.
Let the object distance be x.
Using the magnification formula, m = -v/u = 1/4
-4v = u
Putting this value of u in the mirror formula, we get:
1/20 = 1/x - 1/4v
1/20 = (4v-x)/4vx
v = 5x/3
Substituting this value of v in the magnification formula,
-1/4 = -5x/3u
u = 15x/4
Therefore, the object distance is 15x/4 and the image distance is 5x/3.
Since the image is inverted, the image distance is negative, giving us -5x/3.
So, the position of the resulting image is 25 cm behind the mirror. Therefore, the answer is B.

A Concave Mirror Has a Focal Length of 20 Cm