Question

A concave mirror has a focal length of 31.4 cm. The distance between an object and its image is 58.6 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

Given :-

f = 31.4 cm

u - v = 58.6 cm

v = u - 58.6

from lens law

1/f = 1/u + 1/v

1/31.4 = 1/u + 1/(u - 58.6)

1/31.4 = (u + u - 58.6) / u(u - 58.6)

1/31.4 = (2u - 58.6) / (u^2 - 58.6u)

31.4 = (u^2 - 58.6u) / (2u - 58.6)

31.4(2u - 58.6) = u^2 - 58.6u

62.8u - 1840.04 =  u^2 - 58.6u

u^2 - 121.4u + 1840.04 = 0

after solving quadratic equation,

u = 103.6 cm and u = 17.75 cm (not possible it is beyond 2f)

a)

u = 103.6 cm

b)

v = u - 58.6 cm

v = 103.6 - 58.6

v = 45 cm

c)

If object lies between mirror then,

u = 17.75 cm

v = 17.75 - 58.6 = -40.85 cm