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(a) Write two characteristics features ...

(a) Write two characteristics features distinguishing the diffraction pattern from the interference fringes obtained in Young's double slit experiment.
(b) Two wavelengths of sodium light 590 nm and 596 nm are used , in turn, to study the diffraction taking place due to a single slit of aperture `1xx10^(-4)m`. The distance between the slit and the screen is 1.8m. Calculate the separation between the positions of the first maxima of the diffraction pattern obtained in the two cases.

Text Solution

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(a)

(b) Wavelength of the light beam, `lambda_(1) = 590 nm = 5.9 xx 10^(-7)m`
Wavelength of another light beam, `lambda_(2)= 596 nm =5.96 xx 10^(-7)m`
Distance of the slits from the screen `= D= 1.8m.`
Distance between the two slits `=1xx 10^(-4)m`
For the first secondary maxima, ` sin theta = (3 lambda_(1))/(2a)=(x_(1))/(D) rArr x_(1)=(3 lambda_(1)D)/(2a) and x_(2)=(3lambda_(2)D)/(2a)`
`therefore ` Spacing between the positions of first secondary maxima of two sodium lines
`=x_(1)-x_(2)=(3D)/(2a)(lambda_(2)-lambda_(1))=1.62 xx 10^(-4)m`
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