Question

A concave mirror has a focal length of 29.6 cm. The distance between an object and its image is 46.4 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.

Answer 1

a)

v - u = 46.4

using mirror formula

1/f = 1/v + 1/u

- 1/29.6 = - 1/ (46.4 + u) - 1/u

( 46.4u + u^2) /29.6 = u + 46.4 + u

u^2 - 12.8 u - 1373.44 = 0

solving for

u = 44 cm

b)

v = 44 + 46.4 = 90.44 cm

c)

v + u = 46.4

again

using mirror formula

-1/29.6 = 1 / ( 46.4 - u) - 1/u

- (46.4 u - u^2) = 29.6* ( 2u - 46.4)

u^2 - 105.6 u + 1373.44 = 0

solving for u

u = 15.191 cm

d)

v = 46.4 - 15.191 = 31.209 cm

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