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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.
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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