Key Equations

Image distance in a plane mirror	$d_{o} = − d_{i}$
Focal length for a spherical mirror	$f = \frac{R}{2}$
Mirror equation	$\frac{1}{d_{o}} + \frac{1}{d_{i}} = \frac{1}{f}$
Magnification of a spherical mirror	$m = \frac{h_{i}}{h_{o}} = − \frac{d_{i}}{d_{o}}$
Sign convention for mirrors
Focal length f	$\begin{matrix} + for concave mirror \\ - for convex mirror \end{matrix}$
Object distance d_o	$\begin{matrix} + for real object \\ - for virtual object \end{matrix}$
Image distance d_i	$\begin{matrix} + for real image \\ - for virtual image \end{matrix}$
Magnification m	$\begin{matrix} + for upright image \\ - for inverted image \end{matrix}$
Apparent depth equation	$h_{i} = (\frac{n_{2}}{n_{1}}) h_{o}$
Spherical interface equation	$\frac{n_{1}}{d_{o}} + \frac{n_{2}}{d_{i}} = \frac{n_{2} - n_{1}}{R}$
The thin-lens equation	$\frac{1}{d_{o}} + \frac{1}{d_{i}} = \frac{1}{f}$
The lens maker’s equation	$\frac{1}{f} = (\frac{n_{2}}{n_{1}} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$
The magnification m of an object	$m \equiv \frac{h_{i}}{h_{o}} = − \frac{d_{i}}{d_{o}}$
Optical power	$P = \frac{1}{f}$
Optical power of thin, closely spaced lenses	$P_{total} = P_{lens 1} + P_{lens 2} + P_{lens 3} + ⋯$
Angular magnification M of a simple magnifier	$M = \frac{θ_{image}}{θ_{object}}$
Angular magnification of an object a distance L from the eye for a convex lens of focal length f held a distance ℓ from the eye	$M = (\frac{25 cm}{L}) (1 + \frac{L - ℓ}{f})$
Range of angular magnification for a given lens for a person with a near point of 25 cm	$\frac{25 cm}{f} \leq M \leq 1 + \frac{25 cm}{f}$
Net magnification of compound microscope	$M_{net} = m^{obj} M^{eye} = − \frac{d_{i}^{obj} (f^{eye} + 25 cm)}{f^{obj} f^{eye}}$