Question

A dentist uses a mirror in front of a decayed tooth at a distance of 4 cm from the tooth to get 4 times magnified the image. Use mirror formula to find the focal length and nature of mirror used. What is the nature of the image?

Answer 1

Object distance, u = -4 cm
Magnification, m= 4
We know, m = -v/u ⇒ v = -mu ⇒ v = -(4)(-4) = 16 cm
So image distance = 16 cm
Now, by mirror formula, 1/v + 1/u = 1/f
⇒ 1/16 + 1/-4 = 1/f
⇒ (1-4)/16 = 1/f
⇒ 1/f = -3/16
∴ focal length = -5.33 cm
Only a concave mirror can form magnified images. Since the image is formed behind the mirror, it is virtual and erect.