Question

In a Young’s double-slit experimental set-up with slit separation 0.6 mm a beam of light consisting of two wavelengths 440 nm and 660 nın is used to obtain interference pattern on a screen kept 1.5 m in front of the slits. Find the least distance of the point from the central maximum where the bright fringes due to both the wavelengths coincide.

Answer 1

Given: λ₁ = 440 nm

λ₂ = 660 nm

d = 0.6 mm = 6 × 10⁻⁴ m

D = 1.5 m

For coincidence of bright fringes:

n₁λ₁ = n₂λ₂

n₁(440) = n₂(660)

`n_1/n_2 = 660/440`

`n_1/n_2 = 3/2`

n₁ = 3, n₂ = 2

For interference maxima:

y = `(n lambda D)/d`

= `(n_1 lambda_1 D)/d`

= `(3 xx 440 xx 10^-9 xx 1.5)/(6 xx 10^-4)`

= `(1980 xx 10^-9)/(0.6 xx 10^-3)`

= 3.3 × 10⁻³ m

= 3.3 mm

∴ The least distance from the central maximum where the bright fringes due to both wavelengths coincide is 3.3 mm.