Question

In a double-slit experiment using monochromatic light, the fringe pattern shifts by a certain distance on the screen when a mica sheet with a refractive index of 1.6 and thickness of 1.964 µm covers one of the slits. The mica sheet is then removed and the slits-to-screen distance is doubled so that the new fringe width is the same as the observed fringe shift with the mica sheet. Calculate the wavelength of the monochromatic light used.

Answer 1

Data: n_m = 1.6, b = 1.964 × 10⁻⁶ m, D₂ = 2D₁, W₂ = y₀

The fringe shift with the mica sheet,

y₀ = `(D_1)/(d) (n_m - 1)b`

Subsequent to the removal of the mica sheet and doubling the slits-to-screen distance, the new fringe width is

`W_2 = (λD_2)/d = (λ(2D_1))/d`

Since, W₂ = y₀,

`(2λD_1)/d = D_1/d (n_m - 1)b`

∴ The wavelength of the light used,

λ = `(n_m - 1)/2.b`

= `(1.6 - 1)/2 xx (1.964 xx 10 ^-6)`

= 0.3 (1.964 × 10⁻⁶)

= 5.892 × 10⁻⁷ m

= 589.2nm