Question

4) a shopper standing 3.00 m from a convex security mirror sees his image with a magnification of 0.250. (a) where is his image? (b) what is the focal length of the mirror? (c) what is its radius of curvature? explicitly show how you follow the steps in the problem-solving strategy for mirrors.

Answer 1

A. The image is located at a distance of -0.075 m

B. The focal length of the mirror is -0.077 m

C. The radius of curvature of the mirror is -0.154 m

How to calculate image distance, focal length and radius of curvature?

A. The image distance fro the image formed by the convex mirror is calculated as follow:

• Object distance (u) = 3.00 m
• Magnification (m) = -0.250 (For convex mirror)
• Image distance (v) =?

v = mu

v = -0.250 × 3

v = -0.075 m

B. The focal length of the mirror can be calculated as follow:

• Object distance (u) = 3.00 m
• Image distance (v) = -0.075 m
• Focal length (f) =?

`(1)/(f) = (1)/(v)\ +\ (1)/(u)\\\\(1)/(f) = (1)/(-0.075)\ +\ (1)/(3)\\\\(1)/(f) = -13\\\\f = -(1)/(13) \\\\f = -0.077\ m`

C. The radius of curvature of the mirror can be calculated as follow:

• Focal length (f) = -0.077 m
• Radius of curvature (r) =?

r = 2f

r = 2 × -0.077

r = -0.154 m