Fichas
Optics starting constructive interference
Fichas del conjunto (10)
- 1Phase shift\[\delta\ = k\Delta\ x \]
Tip: light path difference \(\Delta\ x\) leads to phase shift \(\delta\) - 2Constructive and destructive double-slit interference in screenMaxima: \( d\sin\theta\ = m\lambda\ \)
Minima: \( d\sin\theta\ = (m+\frac{1}{2})\lambda\ \)
Tip: Note \( \theta=0 \) must be maximum because both ways travel same distance - 3Destructive single-slit interference in screenMinima: \[ a\sin\theta\ = m\lambda \ for \ m=1,2,3,...\]
Tip: Minima for single-slit diff. occur at maxima of double-slit diff. m can't be 0 - 4Optical path length\[\Delta\ x = nd \]
Tip: For n → ∞, the wave will be so slow that phase difference goes to infinity. - 5Thin films and phase shift\[ n_2 > n_1 : \ phase \ shift \ of \ \pi\ \ \\
2dn_2 = (m+\frac{1}{2})\lambda \ \\
n_2 < n_1 : \ no \ phase \ shift \ \\
2dn_2 = m\lambda \]
Tip: Additional phase shift of \( \pi \)
reverses conditions for constructive and
destructive interference - 6Circular aperture (Rayleigh criterion)Minimum: \[ D\sin \theta\ = 1.22\lambda \]
Tip: D = diameter of hole analogous to a in single-slit diffraction - 7Bragg diffractionConstructive interference:
\[2d \sin\ \theta\ = n\lambda\]
Tip: \(2d\sin\ \theta\ \) = extra distance traveled by X-ray scattering second layer and \(\theta\ \) = angle of incidence w.r.t plane - 8Sign conventions for s and s'+ distances (incoming for s, outgoing for s')
- distances - 9Rayleigh scattering\[ I \propto I_0 \dfrac{a^6}{\lambda^4}\ \ for \ \lambda >> a \]
Tip: Sky is blue because shorter wavelengths are scattered more strongly. - 10Doppler effect\[ f_{rec} = \dfrac{v_{med}+v_{rec}}{v_{med}-v_{sour}}\ f_{obs} \]
Tip: \( \frac{ + }{ - }\ \) if moving toward each other \( \frac{ - }{ + }\ \) if moving away from each other