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Question
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 1 × 10−4 m. The distance between the slit and the screen is 1.8 m. Calculate the separation between the positions of the first maxima of the diffraction pattern obtained in the two cases.
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Solution
Given that:
Wavelength of the light beam, λ1 = 590 nm = 5.9 ×10-7 m
Wavelength of another light beam, λ2 = 596 nm = 5.96 ×10-7 m
Distance of the slits from the screen = D = 1.8 m
Distance between the two slits = a = 1 ×10-4 m
For the first secondary maxima, `sin theta =(3lambda_1)/(2a) = x_1/D`
` x_1 = (3lambda_1D)/(2a) and x_2 = (3lambda_2D)/(2a)`
∴ 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^-4m`
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