Aconcave mirror has a focal length of 30.0 cm. the distance between an object and its image is 45.0 cm. find the object and image dis- tances, assuming that (a) the object lies beyond the center of curvature and (b) the object lies between the focal point and the mirror.

object and image distances when object lies beyond center of curvature is 90 cm

object and image distances when object lies between focal point and mirror is 15 cm

Explanation:

given data

focal length f = 30.0 cm

distance between object and image = 45.0 cm

to find out

object and image distances

solution

we will apply here lens formula that is

(1/v) + (1/u) = (1/f)   1

and here v - u = 45

so v = 45 + u       2

so from equation 1

(1/(45+u)) + (1/u) = (1/30)

solve it we get u

u = 45 cm or -30 cm

so from equation 2

v = 45 + u

v = 45 + 45

v = 90 cm

object and image distances when object lies beyond center of curvature is 90 cm

and

v = 45 -30

v = 15 cm

object and image distances when object lies between focal point and mirror is 15 cm