A concave mirror f 57 cm produces an image whose distance f

A concave mirror (f = 57 cm) produces an image whose distance from the mirror is one-third the object distance. Determine (a) the object distance and (b) the (positive) image distance.

Solution

f = 57 cm

d_i = 1/3 d_o

from mirror equation 1/d_o + 1/d_i = f

1/d_o + 1/[1/3 d_o] = f

d_o = 4 f = 4 * 57 = 228 cm

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image distance d_i = 1/3 d_o

= 1/3 * 228 = 76 cm