Question

A beam of light consisting of two wavelengths 600 nm and 500 nm is used in Young's double slit experiment. The silt separation is 1.0 mm and the screen is kept 0.60 m away from the plane of the slits. Calculate:

1. the distance of the second bright fringe from the central maximum for wavelength 500 nm, and
2. the least distance from the central maximum where the bright fringes due to both wavelengths coincide.

Answer 1

(i) Distance of 2^nd bright fringe from the central maximum = `(2λ"D")/"d"`

= `(2 xx 500 xx 10^-9 xx 0.6)/(1 xx 10^-3)`

= 6 × 10⁻⁴ m

(ii) `("n"λ_1"D")/"d" = (("n" + 1)λ_2"D")/"d"`

Or, nλ₁ = (n + 1)λ₂

Or, `"n"/(("n" + 1)) = λ_2/λ_1`

Or, `"n"/(("n" + 1)) = 500/600`

∴ n = 5

So, least distance from central maximum = `(5 xx 600 xx 10^-9 xx 0.6)/(1 xx 10^-3)` = 18 × 10⁻⁴ m