Question

Coherent light of wavelength 780 nm falls on a rectangular slit of width (horizontal) 3.00 micrometer by 1.50 micrometer (vertical). The resulting diffraction pattern is projected on a screen 75.0 cm from the rectangle. (a) Sketch the 2-dimensional interference pattern indicating clearly the positions of the horizontal and vertical minima. (b) Calculate the approximate relative intensity of all secondary diffraction maxima.

Answer 1

a] The 2D interference pattern on the screen will contain a vertical diffraction pattern due to the width of the slit (horizontal) and a horizontal diffraction pattern due to the height of the slit (vertical).

The position for first diffraction minima due to the horizontal width for the slit is:

Above and below the central maxima.

The position for the first diffraction minima due to the vertical height is:

To left and right from the central maxima.

b]

The relative intensity for maximas in a single-slit diffraction case is given by:

where is the m^th order of the fringes.

For intensity along vertical direction:

=>

and for the intensity along horizontal direction:

=>