Chapter 23, Problem 13P

You are standing 3.4 m 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.

To determine

The radius of curvature of the mirror.

Answer to Problem 13P

Solution:

Radius of curvature is 6.4 cm

Explanation of Solution

Formula used:

Radius of curvature, $r=2f$

$1/u+1/v=1/f$

Here, v and f are image and focal length.

Magnification, $m=h_i/h_o=-v/u$

Calculation:

The image distance from the magnification,

$\begin{array}{l}m=+0.5=h_i/h_o=-v/u\\ =-v/3.4\\ v=-1.7\text{cm}\\ \end{array}$

Now from mirror formula,

$\begin{array}{l}1/f=1/u+1/v=1/3.4+1/-1.7\\ f=-3.4\text{cm}\\ \end{array}$

Therefore, radius of curvature

$r=2f=-2\times 3.4=6.4\text{cm}$