Question

You are standing 5.0 mm from a convex security mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the radius of curvature of the mirror. Follow the sign conventions. Express your answer to one significant figure and include the appropriate units.

Answer 1

PLEASE check your question again and see that you should be standing at a distance of 5.0 m from the mirror, it is not possible to stand at a distance of 5.0 mm, So I'm solving it using 5.0 m, Let me know if you want to solve it with 5.0 mm, which is not possible.

We know that mirror equation is given by:

1/f = 1/u + 1/v

f = focal length of mirror = ?

u = object distance = 5.0 m

v = image distance = ?

Magnification of image is given by:

M = -v/u = hi/ho

given that height of your image to be half of your actual height, So

hi/ho = 1/2, So

-v/u = 1/2

v = image distance = -u/2 = -5.0/2

v = -2.5 m

Now Using mirror equation:

1/f = 1/u + 1/v = 1/5.0 - 1/2.5

1/f = -1/5.0

f = focal length of convex mirror = -5.0 m

Radius of curvature will be:

R = 2*f = 2*focal length = 2*(-5.0)

R = -10 m

Use Negative sign as per conventions.

Let me know if you've any query.