Answer :

Distance of n^{th} fringe from central maxima, X_{n} = 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 3^{rd} from central maxima for wavelength 650 nm

n = 3

x_{3} = 3 × (650 nm) D/d

(b) The distance of n^{th} bright fringe from central maxima for two wavelengths, say λ_{1} and λ_{2}, are

X_{n} = nλ_{1}D/d

Y_{n} = nλ_{2}D/d

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

i.e., X_{n} = Y_{n}

n_{1}λ_{1}D/d = n_{2}λ_{2}D/d

n_{1}λ_{1} = n_{2}λ_{2}

n_{1}/n_{2} = λ_{2} /λ_{1}

= 520 / 650 = 8/10

Therefore, the bright fringe due to two wavelength coincide when n_{1} is integer multiple of 8 and n_{2} is integer multiple of 10.

Thus least distance for which they coincide,

S = n_{1} λ_{1}D/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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