Question

A concave mirror has a focal length of 30.6 cm. The distance between an object and its image is 56.8 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

object lies beyond the center of curvature,

real image will be formed and q < p

p - q = 56.8

and 1/f = 1/p + 1/q

1/30.6 = 1/p + 1/(p - 56.8)  

1/30.6 = (2 p - 56.8) / p(p - 56.8)

p^2 - 56.8 p = 61.2p - 1738.08

p^2 - 118p + 1738.08 = 0

p = 100.7 cm .....Ans(a) Object distance,

(b) image distance, q = p -56.8 = 43.9 cm .....Ans

(C) Now image will be virtual.

q will be negative.

p + q = 56.8

1/30.6 = 1/p - 1/q

1/30.6 = 1/p - 1/(56.8 - p) = 56.8 - 2p / (56.8p - p^2)

p^2 - 118p + 1738.08 = 0

p = 17.25 cm .....Ans(c)

(d) q = - 39.6 cm