Question

Monochromatic light of intensity I₀=24.0 W/m² is shone through two slits a distance d=2.2mm apart. A screen a distance L=1.0m away from the slits shows the resulting interference pattern.

If at y=8.3cm from the center of the screen the intensity I=10.2W/m², what is the wavelength of the light λ (in μm)?

Answer 1

The intensity formula can be written as I = Io cos²[dy/L]
where Io is the maximum intensity on the screen, Io = 4I, where I_inc is the intensity of the incident light.
Given that d = 2.2 x 10^-3 m
y = 8.3 x 10^-2 m, L = 1 m

cos²[dy/L] = I/Io
= 10.2/(4 x 24) = 0.10625
Taking square root on both the sides,
cos[dy/L] = 0.326
[dy/L] = cos^-1(0.326) = 1.239             [Angles are in radians]
= [ x (2.2 x 10^-3) x (8.3 x 10^-2)] / [1.239 x 1]
= 463.08 x 10^-6 m