Question

Light consisting of a mixture of two different wavelengths falls on a two-slit interference apparatus. The centers of the slits are 0.100 mm apart. After passing through the slits, the light falls on a screen 5.00 m from the slits. For each of the two colors, the middle of the bright spot nearest to the central bright spot is at the following distance from the middle of the central bright spot: 2.4 cm; 3.3 cm.

(a) Calculate the two wavelengths. Be careful of units!

(b) Calculate the frequency for light of each of the two wavelengths

Answer 1

(a) For constructive interference, the condition is,

dy_n/D = nλ

=> Position of n^th order bright fringe, y_n = nλD/d

So, the position of the bright fringe nearest to the central maximum, y₁ = λD/d

=> λ = dy₁/D

For the first wavelength, y_1a = 2.4 cm = 2.4 * 10^-2 m,

=> λ_a = dy_1a/D = (0.100 * 10^-3) * (2.4 * 10^-2) / 5 = 4.8 * 10^-7 m

For the second wavelength, y_1b = 3.3 cm = 3.3 * 10^-2 m,

=> λ_b = dy_1b/D = (0.100 * 10^-3) * (3.3 * 10^-2) / 5 = 6.6 * 10^-7 m

(b) f_a = c/λ_a = (3 * 10⁸) / (4.8 * 10^-7) = 6.25 * 10¹⁴ Hz

f_b = c/λ_b = (3 * 10⁸) / (6.6 * 10^-7) = 4.54 * 10¹⁴ Hz