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A diffraction grating has 1.26xx10^(4) r...

A diffraction grating has `1.26xx10^(4)` rulings uniformly spaced over width w=25.4 mm. It is illuminated at normal incidence by blue light of wavelength 450 nm At what angles to the central axis do the second order maxima occur

Text Solution

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The grafting spacing d is
`d=w/N=(25.4xx10^(-3))/(1.26xx10^(4))=20.16xx10^(-6)m=2016nm`
The second order maxima corresponds to `n=2`
For `lambda=450nm` we have
`d sin theta=2lambda rArr theta=sin^(-1)((2lambda)/d)`
`rArrtheta=sin^(-1)((2xx450xx10^(-9))/(2.016xx10^(-6)))`
`:.Angle theta approx 27^(@)`
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