Key Equations

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

index of Refraction	$n = \frac{c}{v}$
Snell’s law	$n_{1} \sin θ_{1} = n_{2} \sin θ_{2} or \frac{n_{1}}{n_{2}} = \frac{sin θ_{2}}{sin θ_{1}}$
Snell’s law in terms of speed	$\frac{\sin θ_{1}}{\sin θ_{2}} = \frac{v_{1}}{v_{2}}$
critical angle	$θ_{c} = \sin^{−1} (\frac{n_{2}}{n_{1}}), for n_{1} > n_{2}$

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	$m = \frac{h_{i}}{h_{o}} = - \frac{d_{i}}{d_{o}}$

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