Intensity when Diffraction

I=I0(sin⁡ββ)2        with        β=πλbsin⁡θI = I_0 \left( \frac{\sin \beta}{\beta} \right)^2 \,\,\,\,\,\,\,\ \textup{with} \,\,\,\,\,\,\,\ \beta =\frac{\pi}{\lambda}b\sin \theta

Diffraction minimun of slit

bsin⁡θ=mλ        where        m=±1,±2,±3,...b\sin\theta = m\lambda\,\,\,\,\,\,\,\ \textup{where} \,\,\,\,\,\,\,\ m=\pm 1, \pm 2, \pm 3, ...

Diffraction minimum of round opening

Dsin⁡θ=kλD\sin\theta = k\lambda
wherek=1,22       2,23       3,24       4,25       5,25...\textup{where} k=1,22\,\,\,\,\,\,\, 2,23\,\,\,\,\,\,\, 3,24 \,\,\,\,\,\,\, 4,25 \,\,\,\,\,\,\, 5,25 ...

Rayleigh's Resolution Criterion

Central top for the first point over the first min for the second point

Interference if Diffraction is neglected

I=I0(sin⁡Nγsin⁡γ)        da¨r        γ=πλdsin⁡θI = I_0 \left( \frac{\sin N\gamma}{\sin\gamma} \right)\,\,\,\,\,\,\,\ \textup{där} \,\,\,\,\,\,\,\ \gamma = \frac{\pi}{\lambda}d\sin\theta

Interference gives main max if

dsin⁡θ=mλ        da¨r        m=±1,±2,±3,...d\sin\theta=m\lambda \,\,\,\,\,\,\,\ \textup{där} \,\,\,\,\,\,\,\ m=\pm 1, \pm 2, \pm 3, ...

Visibility

V=Imax−IminImax+IminV=\frac{I_{max} - I_{min}}{I_{max} + I_{min}}

Grating, transmission or reflection

d(sin⁡α2+sin⁡α1)=mλd(\sin \alpha_2 + \sin \alpha_1) = m\lambda
d(sin⁡α2−sin⁡α1)=mλd(\sin \alpha_2 - \sin \alpha_1) = m\lambda

Max or min in case of interference in thin layers

2n2dcos⁡α2=mλ        da¨r        m=0,±1,±2,...2 n_2 d \cos \alpha_2 = m\lambda \,\,\,\,\,\,\,\ \textup{där} \,\,\,\,\,\,\,\ m=0, \pm 1, \pm 2, ...

Finesse in Fabry-Perot interferometer

F=Δfδf        where        Δf=c2dF=\frac{\Delta f}{\delta f} \,\,\,\,\,\,\,\ \textup{where} \,\,\,\,\,\,\,\ \Delta f = \frac{c}{2d}

Airy Function

T=11+[4r2(1−r2)2]sin⁡2(δ2)T = \frac{1}{1+\left[ \frac{4 r^2}{(1-r^2)^2}\right]\sin^2 \left(\frac{\delta}{2} \right)}