Question

A concave mirror has a focal length of 43.8 cm. The distance between an object and its image is 76.6 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

f = -43.8 cm (focal length is negative for concave mirror)

If the object lies beyond the center of curvature image is formed between the center and focus in front of the mirror

let the object distance be x and image distance be y

x - y = 76.6 cm

x = y + 76.6

object distance u = -x (negative as the object is in front of the mirror)

image distance v = -y  (negative as the image is in front of the mirror)

f = -43.8 cm

using mirror equation we have

Solving quadratic equation we get

y = 63.7 cm (we reject the other negative root)

x = y +76.6 = 63.7 +76.6 = 140.3 cm

c) In this case

x +y = 76.6

y = 76.6 - x

u = -x  (negative as the object is in front of the mirror)

v =+y (positive as the image is formed behind the mirror)

f = -43.8 cm

using mirror equation we have

x = 140.3 , 23.8 cm

x is object distance and it is between focus and pole so it must be less than focal length so we take

x = 23.8 cm (object distance)

y = 76.6 - x = 52.8 cm (image distance)