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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