A concave mirror has a focal length of 281 cm The distance b

A concave mirror has a focal length of 28.1 cm. The distance between an object and its image is 45.4 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.

Solution

a )

u - v = 45.4

v = u - 45.4

1 / 28.1 = 1 / u + 1 / u - 45.4

1 / 28.1 = u - 45.4 + u / ( u² - 45.4 u )

( u² - 45.4 u ) / ( 2 u - 45.4 ) = 28.1

u² - 45.4 u = 56.2 u - 1275.7

u² - 101.6 u + 1275.7 = 0

u = 86.92 , 14.67 cm

u = 86.92 cm

b )

v = u - 45.4

v = 86.92 - 45.4

v = 41.52 cm

c )

u = 14.67 cm

d )

u = 14.67 cm

v = u - 45.4

v = 14.67 - 45.4

v = - 30.73 cm