Question

A concave mirror has a focal length of 42.2 cm. The distance between an object and its image is 78.8 cm. Find (a) the object and (b) image distances, assuming that the object lies beyond the center of curvature and (c) the object and (d) image distances, assuming that the object lies between the focal point and the mirror.

Answer 1

Given that,

focal length f = 42.2 cm

distance between an object and its image, u - v = 78.8 cm

so, v = u - 78.8

From mirror equation,

1 / f = 1 / v + 1 / u

1 / 42.2 = 1 / (u - 78.8) + 1 / u

u (u - 78.8) = 42.2*(2u - 78.8)

u^2 - 163.2u + 3325.36 = 0

By solving the quadratic equation,

u = 139.33 cm

or u = 23.86 cm

(a)

lf  object lies beyond the center of curvature,

object distance, u = 139.33 cm

(b)

lmage distance,

v = 139.33 - 78.8

v = 60.53 cm

(c)

lf  object lies between the focal point and the mirror,

u = 23.86 cm

(d)

v = 23.86 - 78.8

v = -54.94 cm