Formula Quick Reference¶
A single-page cheat-sheet of every governing equation used across the 18 experiments, grouped the same way as the main Contents. Use this page while doing calculations so you don't have to open each experiment page individually — click the linked experiment name if you need the full derivation or context.
Wave Optics¶
\[
\Delta = \dfrac{d\,y}{D} \qquad \Delta = n\lambda \;(\text{bright}) \qquad \Delta = \left(n+\tfrac12\right)\lambda \;(\text{dark}) \qquad \beta = \dfrac{\lambda D}{d}
\]
\[
a\sin\theta = m\lambda \qquad (a+b)\sin\theta = n\lambda \qquad R = \dfrac{\lambda}{\Delta\lambda} = nN
\]
\[
I(\theta) = I_0\cos^2\theta
\]
\[
n(\lambda) = A + \dfrac{B}{\lambda^2} \qquad \delta \approx (n-1)A_{\text{apex}} \qquad \omega = \dfrac{n_v - n_r}{n_y - 1}
\]
\[
\text{OPD} = 2\,\Delta L \qquad \Delta m = \dfrac{2\,\Delta L}{\lambda} \qquad \Delta L = \dfrac{\Delta m\,\lambda}{2}
\]
Geometrical Optics¶
\[
N_f = \dfrac{f}{D} \qquad r_{\text{Airy}} \approx 1.22\,\dfrac{\lambda f}{D}
\]
\[
\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f} \qquad m_i = -\dfrac{v_i}{u_i} \qquad m_{\text{total}} = m_1 \times m_2
\]
Particle Nature of Light¶
\[
E = h\nu = \dfrac{hc}{\lambda} \qquad KE_{\max} = h\nu - \phi \qquad V_0 = \dfrac{h\nu - \phi}{e}
\]
\[
\Delta\lambda = \lambda_C(1-\cos\theta) \qquad \lambda_C = \dfrac{h}{m_e c} = 2.426\ \text{pm} \qquad \lambda' = \lambda + \Delta\lambda
\]
\[
P(y) \propto \cos^2\!\left(\dfrac{\pi d y}{\lambda D}\right)
\]
Laser Light Concepts¶
\[
\tau_c \approx \dfrac{1}{\Delta\nu} \qquad L_c = c\,\tau_c
\]
12. Directionality & Beam Quality
\[
D_{\text{spot}}(L) \approx D_0 + \theta_{\text{div}}\,L
\]
13. Monochromaticity & Spectral Purity
\[
\text{Purity} = \dfrac{\Delta\lambda}{\lambda}
\]
\[
I = |E_{\text{obj}} + E_{\text{ref}}|^2 = |E_{\text{obj}}|^2 + |E_{\text{ref}}|^2 + 2\,\text{Re}\!\left(E_{\text{obj}}E_{\text{ref}}^{*}\right)
\]
Explore & Stay Safe¶
15. Red → UV Wavelength & Photon-Energy Explorer
\[
\nu = \dfrac{c}{\lambda} \qquad E = h\nu = \dfrac{hc}{\lambda}
\]
Practical Applications¶
\[
f_D = \dfrac{2v\cos\theta}{\lambda} \qquad v_{max} = A\omega
\]
17. Optical Fiber NA & Attenuation
\[
\text{NA} = \sqrt{n_1^{2}-n_2^{2}} \qquad P_{out} = P_{in}\times 10^{-\alpha L/10}
\]
\[
s \approx 1.22\dfrac{\lambda z}{D} \qquad C \approx 1-\exp\!\left[-\left(\dfrac{2\pi\sigma}{\lambda}\right)^{2}\right]
\]
Physical Constants Used Throughout¶
| Constant | Symbol | Value |
|---|---|---|
| Speed of light | c | 3 × 10⁸ m/s |
| Planck's constant | h | 6.626 × 10⁻³⁴ J·s (= 4.1357 × 10⁻¹⁵ eV·s) |
| Electron charge | e | 1.602 × 10⁻¹⁹ C |
| Electron rest mass | mₑ | 9.109 × 10⁻³¹ kg |
| Compton wavelength | λ_C = h/(mₑc) | 2.426 pm |
| Thermal voltage (300 K) | V_T = kT/e | 25.85 mV |