Question

A rectangular aperture that is 0.09 mm wide by 0.15 mm high, is illuminated with plane waves from a helium-neon laser of wavelength 695.9 nm. Find the area (in mm2) of the zero'th order diffraction region as measured between the first irradiance nulls, when the pattern is observed on a wall 1.8 m away

Answer 1

lambda=659.9nm

dx=.09mm

dy=.15mm

Half-angle beam divergences to first minimum in x and y directions = theta(1/2)x=lamda/dx=.6599micrometre/90 micrometer=7.33*10^-3

and theta(1/2)y=lambda/dy = .6599micrometre/150 micrometer=4.34*10^-3

since theta is small so tan (theta)=theta

therefore if d=1.8m

hx=length of zero order diffraction along x axis

hy=length of zero order diffraction along y axis

so hx/d=2*theta(1/2)x

or,hx=2.64 cm

hy/d=2*theta(1/2)y

or,hy=1.56 cm

area of the region=hx*hy=411.84 mm2