Aconcave mirror with a focal length of 32 cm produces an image whose distance from the mirror is one-third the object distance. (part a) find the object distance.
(part b) find the image distance.

part A ⇒ u = 1.28 m

part B ⇒v = 0.43 m

Explanation:

for u is the distance to the object from the mirror and v is the distance from the mirror to the image.

Part A:

the mirror equation is given by:

1/f = 1/v + 1/u

but we told that, v = 1/3u:

1/f = 3/v + 1/u = 4/u

1/f = 4/u

  f = u/4

 u = 4f

    = 4×(32×10^-2)

    = 1.28 m

Therefore the distance from the mirror to the object is 1.28 m.  

part B:

v = 1/3×u = 1/3×(1.28) = 0.43 m