Key Equations

Key Equations

16.1 Reflection

lens/mirror equation (reciprocal version)	$\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}$
lens/mirror equation (solved version)	$f=\frac{d_i{d}_o}{d_o+d_i}$
magnification equation	$m=\frac{h_i}{h_o}=\frac{-d_i}{d_o}$
radius/focal length equation	R = 2f

16.2 Refraction

index of Refraction	$n=\frac{c}{v}$
Snell’s law	$n_1\sin {\theta }_1=n_2\sin {\theta }_2\text{ or }\frac{n_1}{n_2}=\frac{\text{sin}{\theta }_2}{\text{sin}{\theta }_1}$
>Snell’s law in terms of speed	$\frac{\sin {\theta }_1}{\sin {\theta }_2}=\frac{v_1}{v_2}$
critical angle	${\theta }_c={\sin }^{\mathrm{-1}}(\frac{n_2}{n_1}\text{), for }{n}_1>n_2$

16.3 Lenses

power and focal length	$P=\frac{1}{f}$
mirror/lens (or thin-lens) equation	$\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}$
rearranged mirror/lens equation	$d_i=\frac{f{d}_o}{d_o-f}$
magnification equation	$m=\frac{h_i}{h_o}=-\frac{d_i}{d_o}$