Question

(a) Describe briefly how a diffraction pattern is obtained on a screen due to a single narrow slit illuminated by a monochromatic source of light. Hence obtain the conditions for the angular width of secondary maxima and secondary minima. 

(b) Two wavelengths of sodium light of 590 nm and 596 nm are used in turn to study the diffraction taking place at a single slit of aperture 2 x 10^-6 m. The distance between the slit and the screen is 1.5 m. Calculate the separation between the positions of first maxima of the diffraction pattern obtained in the two cases.

Answer 1

(a)

The path difference (NP-LP), between the  two edges of the slit, is given by

We, therefore, get maxima and minima, at different points of the screen, depending on the path difference between the contributions from the wavelets, emanating from different points of the slit. This results in a diffraction pattern on the screen. Y, 

The path difference between two points M1 and M₂ in the slit plane, separated by a distance y, is yθ.

At the central point, θ is zero.

All parts of the slit contribute in phase. Hence C is a maximum.

This is because of a net (almost) zero contribution of the whole slit at these points.

(b) Angular width of the secondary maxima