Question

A concave mirror has a focal length of 36.4 cm. The distance between an object and its image is 52.6 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

focal length f = 36.4 cm

If object is beyond center of curvature

the image is real

s - s' = 52.6 cm

s = object distance

s' = image distance

s' = s - 52.6

part(a)

from mirror equation

1/s + 1/s' = 1/f

1/s + 1/(s-52.6) = 1/36.4

object distance s = 107.6 cm

part (b)

image distance s' = s - 52.6

image distance s' = 107.6 - 52.6 = 55 cm

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part (c)

If object is between focal point and mirror

the image is virtual

image distance distance is negative

s + s' = 52.6 cm

s = object distance

s' = image distance

s' = 52.6 - s

part(c)

from mirror equation

1/s + 1/s' = 1/f

1/s - 1/(52.6 - s) = 1/36.4

object distance s = 17.8 cm

part (d)

image distance s' = 52.6 - 17.8

image distance s' = 34.8 cm