Question

A 2.0 centimeter tall object id placed 30.0 centimeters from a concave mirror. The focal length of the mirror is 10.0 centimeters. (a) where is thr image seen? (b) how tall is the image? 

Answer 1

Given:

$d_o=30.0\:\rm cm$

$h_o=2.0\:\rm cm$

$f=10.0\:\rm cm$

(a)

$$\frac{1}{d_0}+\frac{1}{d_i}=\frac{1}{f}$$

$$\frac{1}{d_i}=\frac{1}{f}-\frac{1}{d_0}=\frac{1}{10.0}-\frac{1}{30.0}$$

$$d_i=15.0\:\rm cm$$

(b)

$$\frac{h_i}{h_o}=-\frac{d_i}{d_0}$$

$$h_i=-\frac{d_i}{d_0}h_o=-\frac{15.0}{30.0}*2.0=-1.0\:\rm cm$$