Question

A concave mirror has a focal length of 26.5 cm. The distance between an object and its image is 47.6 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

the object lies beyond the center of curvature s > 2f

the image is infront of the mirror

s - s' = 47.6 cm

s' = s - 47.6  

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

1/s + 1/(s - 47.6) = 1/26.5

s = 86.0 cm <<---------answer

(b)

image distane s' = 38.4 cm <<<---------answer

=================================

the object lies between the focal point and the mirror.s < f

the image is behind of the mirror and is virtual

s + s' = 47.6 cm

s' = 47.6 - s

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

1/s - 1/( 47.6 - s) = 1/26.5

s = 14.6 cm <<---------answer

(d)

image distane s' = 47.6 - 14.6 = 33 cm <<<---------answer