DeBroglie wavelength

λ=hp=hmv\lambda = \frac{h}{p} = \frac{h}{mv}

Speed of Light

c=1μ0ϵ0c = \frac{1}{\sqrt{\mu _0 \epsilon_0}}
v=cμrϵrv = \frac{c}{\sqrt{\mu _r \epsilon_r}}

Intensity EM-Wave

I=12ϵ0ϵrμ0μrE02, Bz=EyvI = \frac{1}{2} \sqrt{\frac{\epsilon_0 \epsilon_r}{\mu_0 \mu_r}} E_0^2 \,\,\,\,\\,\,\,\,\ B_z = \frac{E_y}{v}

Intensity when two waves are added

Itot=I1+I2+2I1I2<cosδ>I_{tot} = I_1 + I_2 + 2\sqrt{I_1I_2} <\cos \delta >

where

δ\delta

is the relative phase between the waves.

Refractive Index

ncv=μrϵrn \equiv \frac{c}{v} = \sqrt{\mu_r \epsilon_r}

Snell's Law

sinα1sinα2=λ1λ2=v1v2=n2n1\frac{\sin\alpha_1}{\sin\alpha_2} = \frac{\lambda_1}{\lambda_2} = \frac{v_1}{v_2} = \frac{n_2}{n_1}

Boundary Angle for Total Reflection

αg=arcsin(n2n1)\alpha_g = \arcsin \left( \frac{n_2}{n_1} \right)

Prism

sin(A+δ2)=nsin(A2)\sin\left( \frac{A + \delta}{2} \right) = n\cdot\sin \left(\frac{A}{2} \right)

Where

AA

is the prisms top angle and

δ\delta

the reflection angle.

Fiber Optics, Numerical Aperture

N.A.n0sinθmN.A. \equiv n_0 \sin \theta_m
N.A.=n12n22N.A. = \sqrt{n_1^2 - n_2^2}