Question

When a plane wave front, of light, of wavelength 1, is incident on a narrow slit, an intensity distribution pattern, of the form shown is observed on a screen, suitable kept behind the slit. Name the phenomenon observed.

(i) Obtain the conditions for the formation of central maximum and secondary maxima and the minima. 

(ii) Why is there significant fall in intensity of the secondary maxima compared to the central maximum, where as in double slit experiment all the bright fringes are of the same intensity ? 

(iii) When the width of the slit is made double the original width, how is the size of the central band affected ?

Answer 1

The phenomenon observed is the phenomenon of diffraction

(i) At the central maxima. The contribution due to the secondary wavelets, from all parts of the wavefront (at the slit), arrive in phase at the central maxima θ = o

At the secondary maxima

It is only the contribution from (nearly) 1/3 (or 1/5, or 1/7,...) of the secondary maxima. These occur at points for which

At the minima

The contribution, from 'corresponding pairs', of the sub-parts of the incident wavefront, cancel each other and the net contribution, at the location of the minima, is zero. The minima occur at points for which 

(ii) There is a significant fall in intensity at the secondary maxima because the intensity there, is only due to the contribution.n o{ (nearly) (1/3  or 1/5 or 1/7,....) of the incident wavefronts.

(iii) The size of the central maxima would get halved when width of the slit is doubled.