Optics formulas

Remember that: $\vec{a} = \mathbf{a}$, $\dot{a}= \frac{da}{dt}$ and $\Delta a = a_{final} - a_{initial} = a_{f} - a_{i} = a_{2} - a_{1}$. The $\propto$ symbol is read as "is proportional to". While $\hat{a} = \frac{\vec{a}}{\Vert \vec{a} \Vert}$ is the unit vector.

Symbols

Geometrical optics

Spherical mirror

Lenses

Physical optics

Two slit interference

name	equation
phase difference due to the difference in the optical path traveled	$$\delta = \frac{\Delta r}{\lambda} 2\pi = \frac{\Delta r}{\lambda} 360\ ^{\circ}\mathrm{C}$$
two-slit interference maxima	$$d \sin \theta_{\max} = m\lambda,\quad m = 0,1,2, \ldots$$
two-slit interference minima	$$d \sin \theta_{\min} = \left( m - \frac{1}{2} \right)\lambda,\quad m = 1,2,3, \ldots$$
two-slit phase difference	$$\frac{\delta}{2 \pi}= \frac{d \sin \theta}{\lambda}$$
distance on the screen to the m-th bright fringe	$$y_{m} = m \frac{\lambda L}{d}$$
intensity as a function of phase difference	$$I = 4 I_{0} \cos^{2} \frac{1}{2} \delta$$

One slit diffraction

name	equation
intensity null values	$$a\sin \theta = m \lambda, \qquad m = 1,2,3, \ldots$$
zero intensity minima	$$\tg \theta_{1} = \frac{y_{1}}{L}$$
diffraction intensity of a slit	$$I = I_{0} \left( \frac{\sin \frac{1}{2} \phi}{\frac{1}{2} \phi} \right)^{2}$$

Quantum optics