Answer to Question #218708 in Classical Mechanics for Amos

Question

An object is placed 10cm in front of a concave mirror whose radius of curvature is 12cm. calculate 

i. The position of the image 

ii. Magnification

Answer 1

$u = 10cm =0.1m$

$R = 12cm = 0.12m$

$\text{i.}$

$f = \frac{R}{2}=\frac{0.12}{2}=0.06m$

$u>f \text{ hence:}$

$\frac{1}{v}+\frac{1}{u}=\frac{2}{R}$

$\frac{1}{v}=\frac{2}{R}-\frac{1}{u}$

$v=\frac{uR}{2u-R}=\frac{0.1*0.12}{2*0.1-0.12}=0.15m$

$\text{ii.}$

$m = -\frac{v}{u}=-\frac{0.15}{0.1}= -1.5$

$\text{Answer: }v =0.15m;m=-1.5$