Question

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

Answer 1

Given;

Magnification (m) = 4; 

Object distance (u) = -4cm; 

Image distance = v; 

Magnification (m) = - \(\frac{v}{u}\)

⇒ 4 = - \(\frac{v}{-4}\)

⇒ v = 4 × 4 = 16cm

Image distance = 16cm.

By mirror formula; \(\frac{1}{v}\,+\,\frac{1}{u}\,=\frac{1}{f}\)

⇒\(\frac{1}{16}\,+\,\frac{1}{4}\,=\frac{1}{f}\)

⇒\(\frac{1-4}{16}\,=\frac{1}{f}\)

⇒ - \(\frac{3}{16}\,=\frac{1}{f}\)

⇒ f = - \(\frac{16}{3}\) = -5.33 cm

Hence the focal length is -5.33cm. Since the focal length is negative therefore the mirror is concave.