A beam of light c

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

x₃ = 3 × (650 nm) D/d

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

X_n = nλ₁D/d

Y_n = nλ₂D/d

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

i.e., X_n = Y_n

n₁λ₁D/d = n₂λ₂D/d

n₁λ₁ = n₂λ₂

n₁/n₂ = λ₂ /λ₁

= 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.]