A woman stands 2.0 m in front of a convex mirror and notices that her image height is 1/4 of her actual height.Determine the radius of curvature of the mirror.
A)0.67 m
B)1.3 m
C)2.0 m
D)4.0 m
E)6.0 m

Question

Quizplus · Accepted Answer

From the mirror formula, 
1/f = 1/v + 1/u
where,
f = focal length
v = image distance
u = object distance

Since the image is formed behind the mirror, v is negative.

Given,
u = -2 m
v = -0.5 m (since the image height is 1/4 of the actual height, it means the magnification is 1/4. Therefore, v/u = -1/4)
magnification, m = -v/u = 1/4

Substituting these values in the mirror formula,

1/f = -1/0.5 - 1/(-2)
1/f = -3/2
f = -2/3 m

Since the mirror is convex, the radius of curvature is positive and given by R = 2f. Therefore,
R = 2 × (-2/3) = -4/3 m

However, since the question asks for the radius of curvature and not the focal length, we take the magnitude of R to get the final answer:
|R| = 4/3 m ≈ 1.3 m

Therefore, the best choice is B.

A Woman Stands 2