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phy142kk:lectures:fr1 [2015/05/11 10:08]
kkumar [Anti reflective coating]
phy142kk:lectures:fr1 [2015/05/11 10:14] (current)
kkumar [Diffraction grating]
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 As the wavelength of light in a medium is given by $\lambda=\frac{\lambda_{0}}{n}$ where $n$ is the refractive index of the medium and $\lambda_{0}$ is the wavelength of the light in free space, the thickness of the coating should be $\frac{\lambda}{4n_{2}}$. As the wavelength of light in a medium is given by $\lambda=\frac{\lambda_{0}}{n}$ where $n$ is the refractive index of the medium and $\lambda_{0}$ is the wavelength of the light in free space, the thickness of the coating should be $\frac{\lambda}{4n_{2}}$.
  
 +
 +===== Intensity for double slit interference =====
 +
 +As we now have the intensity in terms of the phase difference $\delta$
 +
 +$I_{\theta}=I_{0}\cos^{2}\frac{\delta}{2}$
 +
 +we should return to our diagram to find the intensity in terms of $d$ and $\theta$
 +
 +{{twoslitphase.png}}
 +
 +We can see that 
 +
 +$\frac{\delta\lambda}{2\pi}=d \sin \theta$
 +
 +giving
 +
 +$\delta=\frac{2\pi}{\lambda}d\sin\theta$
 +
 +and the intensity is
 +
 +$I_{\theta}=I_{0}\cos^{2}(\frac{\pi d \sin \theta}{\lambda})$
 +
 +{{figure_34_14.jpg?​800}}
  
 ===== Intensity pattern for a single slit ===== ===== Intensity pattern for a single slit =====
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 but that the larger the number of slits from which diffraction occurs the sharper the maxima will be. but that the larger the number of slits from which diffraction occurs the sharper the maxima will be.
 +
 +===== n slits =====
 +
 +{{nslitgrating.png}}
 +
 +n=2 $\frac{I_{\theta}}{I_{0}}=\frac{(2+2\cos\delta)}{4}$
 +
 +n=3 $\frac{I_{\theta}}{I_{0}}=\frac{3+4\cos\delta+2\cos 2\delta}{9}$
 +
 +n=4 $\frac{I_{\theta}}{I_{0}}=\frac{4+6\cos\delta+4\cos 2\delta+2\cos 3\delta}{16}$
 +
 +For any $n$
 +
 +$\frac{I_{\theta}}{I_{0}}=\frac{n+\sum\limits_{k=1}^{n-1}2(n-k)\cos(k\delta)}{n^{2}}$
  
 ===== Polarizers ===== ===== Polarizers =====
phy142kk/lectures/fr1.1431353311.txt ยท Last modified: 2015/05/11 10:08 by kkumar
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