(a) Explain how the intensity of diffraction pattern changes as the order (n) of the diffraction band varies.
(b) Two wavelengths of sodium light 590 nm and 596 nm are used in turn to study the diffraction at a single slit of size 4mm. The distance between the slit and screen is 2m. Calculate the separation between the positions of the first maximum of the diffraction pattern obtained in the two cases.

Explanation

(a) Intensity of first secondary maximum `(m =1)` is due to the wavelets from only `1//3^(rd)` part of the slit because first two parts of the slit send wavelets in opposite phase and hence contribution to the intensity of light due to these first two parts is zero. Intensity of second secondary maximum `(m=2)` is due to the wavelets from only one-fifth part of the slit because the first four parts send wavleets in opposite phase and so on. Hence, intensity of secondary maxima decreases with increase in the order (m) of maxima
(b) `y_(lamda) = (2n +1) (lamdaD)/(2d) " " lamda_(1) = 590 nm " " D = 2m`
`y_(1 lamda_(1)) = (2xx 1 + 1) lamda_(1) (D)/(2d) " " lamda_(2) = 596nm " " d = 4 xx 10^(-3)`
`y_(1 lamda_(2))= 3lamda_(2) (D)/(2d) " " :. y_(1) lamda_(2) gt y_(1) lamda_(1)`
`:.` Distance between the first brightness of two `y_(1 lamda_(2)) - y_(1 lamda_(1))`
`= (3D)/(2d) (lamda_(2) - lamda_(1)) = (3)/(2) xx (2)/(4_(2) xx 10^(-3)) xx 6^(3) xx 10^(-9) = 4.5 xx 10^(-6) m = 4.5 mm`