A circular coin is 33.3 cm from a concave spherical mirror.(Assume the coin is on the optical axis.)The image of the coin is produced 23.3 cm towards the mirror from its real position.Calculate the focal length of the mirror.
A)15.4 cm
B)7.69 cm
C)13.7 cm
D)27.4 cm
E)10.0 cm

Question

Quizplus · Accepted Answer

Using the mirror formula (1/f = 1/v + 1/u), where f is the focal length, v is the distance of the image from the mirror, and u is the distance of the object from the mirror, we have:

1/f = 1/v + 1/u
1/f = 1/23.3 + 1/33.3
1/f = (33.3 + 23.3)/(23.3 x 33.3)
1/f = 56.6/776.89
f = 13.7 cm

Therefore, the focal length of the mirror is 13.7 cm, which is option C.

A Circular Coin Is 33