Answer to Question #170568 in Optics for Innocent

Question

The image of an object in a convex mirror is 4cm from the mirror. If the mirror has a radius of curvature of 24cm,find the position of the object and the magnification

Answer 1

Write the equation for the convex mirror:

$$\frac{1}{d_0}-\frac{1}{d_i}=-\frac{1}{f},\\\space\\ d_0=\frac{d_if}{f-d_i}=\frac{d_iR/2}{R/2-d_i}=\frac{4·24/2}{24/2-4}=6\text{ cm}.$$

The magnification is

$$m=\frac{d_i}{d_o}=\frac{4}{6}=0.67.$$