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09 Wave Phenomena (Interference (Diffraction grating (Increase in slit…

- - - - Primary maxima
        
        Increased intensity
        
        Thinner width
      - Secondary maxima
        
        More maxima (\(N-2\))
        
        Less bright
    - - Increase in d
        
        Decrease in \(\sin\theta\)
        
        Maxima are closer together
    - - When expressed as rulings per mm
        \(d=\frac{1}{N}\times10^{-3}m\)
    - - Interference pattern modulated by single-slit diffraction envelope
        
        Intensity further from maxima decreases
  - - - Linear Separation
        between maxima
        
        \(s_n=D\tan\theta\)
        
        \(s_n=D\sin\theta\)
        
        \(s_n=\frac{Dn\lambda}{d}\)
        
        \(d\sin\theta=n\lambda\)
        
        Inductive Process
        \(s=\frac{D\lambda}{d}\)
        
        NOT IN FORMULA BOOKLET
        
        \(\tan\theta\approx\sin\theta\)
    - - interference of light from two slits
      - Interference of light from single slit
  - - - Similar to reflection of
        pulse at fixed end
    - - Similar to reflection of
        pulse at free end
    - - \(\textrm{Path Difference}=2d\)
        
        Destructive Interference
        
        Opposite
        
        Constructive Interference
        
        One phase change
        
        \(2dn=(m+\frac{1}{2})\lambda_{oil}\)
        
        \(2dn=(m+\frac{1}{2})\lambda\)
        
        \(\lambda_{oil}=\frac{\lambda}{n}\)
        
        No / Two phase change
        
        \(2dn=m\lambda\)
  - - - Different light rays have constant phase difference
    - - Of a single wavelength
- - - - \(f'=f(\frac{v}{v+u_s})\)
    - - \(f'=f(\frac{v}{v-u_s})\)
  - - - \(f'=f(\frac{v+u_o}{v})\)
    - - \(f'=f(\frac{v-u_o}{v})\)
  - - - :two:
        
        Object is moving
        away from observer
        :car::camera:
        
        Incident waves strike observer :car: moving away from source :camera:
        
        Reflected waves come from source :car: that is moving away from observer :camera:
        
        Object is moving
        towards observer
        :camera::car:
        
        Incident waves strike observer :car: moving towards source :camera:
        
        Reflected waves come from source :car: that is moving towards observer :camera:
        
        :three:
        
        Decrease in
        frequency
        
        Increase in
        frequency
- - - - \(\lambda ≥ b\)
    - - \(\lambda\ll b\)
  - - - Angle of first minimum
        
        Since its FIRST minimum
        
        \(P.D.=\frac{n\lambda}{2}\)
        n=1
        
        \(\frac{d}{2}\sin\theta=\frac{\lambda}{2}\)
        
        \(d\sin\theta=\lambda\)
        
        \(\theta\ (rads)=\frac{\lambda}{d}\)
        
        1 more item...
      - Every light ray on top corresponds to a ray below with path difference x
      - Length L
        
        \(\tan\theta=\frac{y}{L}\)
        
        \(\theta=\frac{y}{L}\)
- - - - \(\Delta\lambda=\frac{\lambda_{avg}}{mN}\)
    - - \(N=\frac{\lambda}{m\Delta\lambda}\)
        
        Beam width\(=\frac{N}{N_0}\times mm\)
  - - - Angle of 1st Minima \(\theta_D\)
        
        Single Slit
        
        \(\theta=\frac{\lambda}{b}\)
        
        Circular Slit
        
        \(\theta=1.22\frac{\lambda}{b}\)
      - Separation angle \(\theta_s\)
        
        \(\theta\ (rads)=\frac{s}{d}\)
      - \(\frac{s}{d}=1.22\frac{\lambda}{b}\)
        
        \(s=1.22\frac{d\lambda}{b}\)
      - \(\frac{s}{d}=\frac{\lambda}{b}\)
        
        \(s=\frac{d\lambda}{b}\)