In a single slit diffraction expriment, first minimum for red light `(660 nm)` coincide with first maximum of some other wavelength `lambda'`. Calculate `lambda'`.
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Here, `lambda_(r ) = 660 nm , lambda' = ?` For diffraction minima, `a sin theta = n lambda, sin theta = (n lambda)/(a)`, For first minima of red light, `sin theta = (1 lambda_(r ))/(a)` For diffraction maxima, `a sin theta = (2n + 1)(lambda)/(2)` `:.` for first maxima of `lambda'`, `a sin theta' = (3 lambda')/(2) , sin theta' = (3 lambda')/(2a)`, As the two coincide, therefore, `sin theta' = sin theta` `(3 lambda')/(2a) = (lambda_(r ))/(a) or lambda' = (2)/(3)lambda_(r )` or `lambda' = (2)/(3)(660) = 440 nm`
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