Reflection and Mirrors

$f = \frac{R}{2}$

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \qquad \text{(Mirror Formula)}$

$m = -\frac{v}{u} = \frac{h_i}{h_o} \qquad \text{(Mirror Magnification)}$

Refraction

$n_1 \sin\theta_1 = n_2 \sin\theta_2 \qquad \text{(Snell's Law)}$

$n = \frac{c}{v}$

$\sin\theta_c = \frac{n_2}{n_1}, \quad n_1 > n_2 \qquad \text{(Critical Angle)}$

$\frac{n_1}{u} + \frac{n_2}{v} = \frac{n_2 - n_1}{R} \qquad \text{(Refraction at spherical surface)}$

Thin Lenses

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \qquad \text{(Lens Formula)}$

$m = \frac{v}{u} \qquad \text{(Lens Magnification — NO minus)}$

$\frac{1}{f} = (n-1)\!\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \qquad \text{(Lensmaker's Equation)}$

$P = \frac{1}{f} \text{ (f in m)}, \quad [P] = \text{D} = \text{m}^{-1}$

$P = P_1 + P_2 \qquad \text{(Combination in contact)}$

Prisms

$\delta = (i + e) - A$

$n = \frac{\sin\!\left(\dfrac{A + \delta_m}{2}\right)}{\sin\!\left(\dfrac{A}{2}\right)} \qquad \text{(Minimum Deviation)}$

$\delta = (n-1)A \qquad \text{(Thin prism, small A only)}$

$\omega = \frac{n_v - n_r}{n_y - 1} \qquad \text{(Dispersive Power)}$

Optical Instruments

$M = 1 + \frac{D}{f} \text{ (at D)}; \quad M = \frac{D}{f} \text{ (at } \infty\text{)} \qquad \text{(Simple Magnifier)}$

$M = -\frac{L}{f_o} \cdot \frac{D}{f_e} \qquad \text{(Compound Microscope at } \infty\text{)}$

$M = -\frac{f_o}{f_e}; \quad L = f_o + f_e \qquad \text{(Telescope, Normal Adjustment)}$

D = 25 cm = least distance of distinct vision for normal eye.