Q. 63.9( 37 Votes )

A beam of light c

Answer :

Distance of nth fringe from central maxima, Xn = nλD/d


Where, λ is wavelength of light


D is distance from slits to screen


d is slit width


(a) We need to find distance of 3rd from central maxima for wavelength 650 nm


n = 3


x3 = 3 × (650 nm) D/d


(b) The distance of nth bright fringe from central maxima for two wavelengths, say λ1 and λ2, are


Xn = nλ1D/d


Yn = nλ2D/d


When bright fringe due to two wavelength coincide, their distance from central maxima is same


i.e., Xn = Yn


n1λ1D/d = n2λ2D/d


n1λ1 = n2λ2


n1/n2 = λ21


= 520 / 650 = 8/10


Therefore, the bright fringe due to two wavelength coincide when n1 is integer multiple of 8 and n2 is integer multiple of 10.


Thus least distance for which they coincide,


S = n1 λ1D/d


= 8 × (650 nm) D/d


[The question is not complete. This question cannot be answered completely without the values of d and D.]


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