A concave mirror has a focal length of 30.6 cm. The distance between an object a

Question

A concave mirror has a focal length of 30.6 cm. The distance between an object and its image is 61.0 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.

A concave mirror has a focal length of 30.6 cm. The distance between an object and its image is 61.0 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.

Explanation / Answer

f = -30.6 cm
1/u + 1/v = 1/f
but (u - v) = -61
u = -61 + v
1/(-61 + v) + 1/v = -1/30.6
(2v-61)*30.6 = -v^2 + 61v
v^2 + 0.2v - 1927.6 = 0
v = (-122.2 +-(87.8))/2
v = -17.1954 cm
u = -78.19 cm

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