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Light consisting of a plane waves of wavelength, lamda_(1)=8xx10^(-5)cmandlamda_(2)=6xx10^(-5)cm generates an interference pattern in Young's double slit experiment. If n_(1) denotes the n_(1) th dark fringe due to light of wavelength lamda_(1) which coincides with n_(2) th bright fringe due to light of wavelength lamda_(2), then |
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Answer» `n_(1)=3,n_(2)=1` `x_(n_(1))=(2n_(1)XX1)(Dlamda_(1))/(2d)` Position of `n_(2)^(th)` bright fringe due to light of wavelength `lamda_(2)` is given by `x_(n_(2))=-(n_(2)Dlamda_(2))/(d)` Since both the fringes are coincide to each other. Hence, `(2n_(1)+1)(Deltalamda_(1))/(2d)=(n_(2)Dlamda_(2))/(d)` `(2n_(1)+1)/(n_(2))=(2lamda_(2))/(lamda_(1))=(2xx6xx10^(-5))/(8xx10^(-5))` `(2n_(1)+1)/(n_(2))=(3)/(2)` `4n_(1)+2=3n_(2)` `4n_(1)-3n_(2)=-2` `4n_(1)-3n_(2)=-2""......(i)` when `n_(1)=1andn_(2)=2`, then Eq. (i) is SATISFIED. Hence, for `n_(1)=1andn_(2)=2` given fringes coincide to each other. |
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