A slit of width `d` is illuminated by white light. For what value of `d` is the first minimum for red light of `lambda = 650 nm`, located at point `P` at `30^(@)`. For what value of the wavelength of light will the first diffraction maxima also fall at `P` ?
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Here, `lambda = 650nm, d = ?` For first minimum, `n = 1, theta = 30^(@)` `d sin theta = n lambda` `d = (n lambda)/(sin theta) = (1 xx 650)/(sin 30^(@)) = 1300 nm` For first maximum to lie at `P`, we have `d sin theta = (2n + 1)(lambda')/(2) = (3 lambda')/(2)` `lambda' = (2)/(3)d sin theta = (2)/(3) xx 1300 xx (1)/(2) = 433.3 nm`
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