Module 5 : MODERN PHYSICS
Lecture 26 : Wave Nature of Particle - the de Broglie Hypothesis
  Exercise 7
 
Double Slit Interference with electrons
  We know that when a coherent source of light is incident on a Young's Double slit, an interference pattern is observed. The intensity when only the slit $ S_1$ is open is $ I_1$, while the intensity with $ S_2$ open is $ I_2$. When both slits are open, the expression for the intensity at any position $ P$ on the screen is given by
 
$\displaystyle I = I_1 + I_2+2\sqrt{I_1I_2}\cos\phi$
  where $ \phi$ is the phase difference between the waves arriving at $ P$ from $ S_1$ and $ S_2$. Points where the phase difference $ \phi = 2n\pi$, the intensity is a maximum
 
$\displaystyle I_{max}= (\sqrt{I_1} + \sqrt{I_2})^2$
  If the phase difference is an odd integral multiple of $ \pi/2$,
 
$\displaystyle I_{min}= (\sqrt{I_1} - \sqrt{I_2})^2$
   
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