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  • When a parallel beam of monochromatic source of light of wavelength  is incident on a single slit of a width a, show how the diffraction pattern is formed at t

When a parallel beam of monochromatic source of light of wavelength \lambda is incident on a single slit of a width a, show how the diffraction pattern is formed at the screen by the interference of the wavelets from the slit.

Show that, besides the central maximum at \theta = 0, secondary maxima are observed at \theta =\left ( n+\frac{1}{2} \right )\frac{\lambda}{a} and the minima at \theta =\frac{n\lambda}{a}.

Why do secondary maxima get weaker in intensity n? Explain.

 

 

 

 
 
 
 
 

Answers (1)

The diffraction pattern formed can be understood by adding the contribution from various wavelets of the incident wavefront.

At the central point, the slit is divided into two halves. The contribution of wavelets from those two halves are in phase. So maxima is obtained at centre.

Maxima is obtained when \theta =\left ( n+\frac{1}{2} \right )\frac{\lambda}{a} and destructive interference (minima) is obtained when \theta =\frac{n\lambda}{a} , n =\pm 1, \pm 2...

Diffraction patterns on the screen is made up of points of maxima and minima

The secondary maxima get weaker in intensity with the increase of n because

  • for first secondary maxima only \frac{1}{3}rd of incident wavefront contributes
  • for second secondary maxima only \frac{1}{5}th of incident wavefront on the slit contributes and so on.
Posted by

Safeer PP

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