A coherent parallel beam of microwave of wavelength = 0.5mm falls on Young's double slit apparatus....?.......

Question

A coherent parallel beam of microwave of wavelength = 0.5mm falls on Young's double slit apparatus.The separation b/w the slits is 1mm. The intensity of microwaves is measured on a screen placed parallel to the plane of the slits at a distance of 1m from it........If the incident beam falls normally on the double slit apparatus , find the y-coordinates of all the interference minima on the screen.

Answer 1

See the ref. You can't use the small-angle approximation for this because λ/d is so large. Two minima will fit on the screen to either side of the center. The formula is:

θ = arcsin(mλ/d)

y (exact) = Dtan(θ)

For minima, the values of m are 0.5 and 1.5.

For m = 0.5, θ = ±0.25268 rad, y = ±0.2582 m

For m = 1.5, θ = ±0.84806 rad, y = ±1.1339 m