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Question

(a) In what way is different from each slit related to the interference pattern in a double slit experiment
(b) Two wavelength of sodium light 590 nm and 596 nm are used in turn to study the diffraction taking place at a single slit of aperture 2×104m, The distance between the slit and the screen is 1.5m, Calculate the separation between the positions of the first maxima of the diffraction pattern obtained in the two cases.

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Solution

(a) If the width of each slit is comparable to the wavelength of light used, the interference pattern thus obtained in the double-slit experiment is modified by diffraction from each of the two slit.
(b) Give that Wavelength of the light beam, λ1=590nm=5.9×107m
Wavelength of the light beam, λ2=596nm=5.96×107m
Distance of the slit from the screen =D+1.5m
Distance between the two slits, a=2×104m
For the first secondary maxima, sinθ=3λ12a=xiD
X1=3λ1D2aandX2=3λ2D2a
X1=3×590×109×152×2×104,X2=3×596×109×1.52×2×104
X1=663.75×105,X2=670.50×105
Spacing between the position of first secondary maxima of two sodium lines
X2X1=6.75×105m=0.0675mm

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