Question

A dentist holds a concave mirror with radius of curvature 4 cm at a distance of 1.5 cm from a filling in a tooth. What is the magnification of the image of the filling?

Answer 1

Given :

Radius of curvature, R = 4 cm

Focal length, f = R/2 = 2 cm

Object distance, u = 1.5 cm

To find :

The magnification of the image of the filling

Solution :

• First, we'll use mirror formula to find image distance

That is given as,

1/v + 1/u = 1/f

1/v = 1/f - 1/u

= u - f / u×f

v = u×f/u-f

• According to sign convention,

u = -1.5 cm and f = -2 cm

• Substituting u and f values in above formula

v = (-1.5)×(-2)/(-1.5 - (-2))

v = 3 / (-1.5 + 2)

= 3 / 0.5

= 30/5

v = 6 cm

• We know the formula of magnification for mirror i.e m = -v/u

m = - [6 / (-1.5)]

= 6 / 1.5

= 60 / 15

m = 4

• Hence, the magnification of the image of filling is 4