DIFFRACTION
**understand diffraction + draw diffraction patterns from: a rectangular slit, a sharp edge, a thin tube, &
a circular aperture
**1st minimum in single-slit diffraction past a slit of width b is approx. at an angle theta = wavelength
lambda / b
**draw intensity patterns for a single slit of finite width & for 2 slits of negligible width
**show effect of slit width on intensity pattern of 2 slits
--diffraction: spreading of a wave as it goes past an obstacle or thru an aperture; extent of spreading
depends on size of aperture compared to the wavelength involved: narrow behaves like a point source
w/ equal intensities being transmitted in all directions whereas a wide slit can result in no effective
diffraction at all
--math can be complex & depends on physical set-up
--Fresenal versus Fraunhofer diffraction: diverging rays (spherical wave fronts) arriving at aperture v.
parallel waves (plane wave fronts)
--Huygen’s principle: a wave front may be considered to be constructed from an infinite # of point
sources; the position of the next wave front can be determined by considering the waves produced by
each point source w/in the previous wave front so that the overall diffraction pattern at an aperture of a
given width b is the result of superposition of all the individual point sources in the wave front across
the width of the slit
--to calculate the variation with angle of the intensity of wave energy received after passing thru an
aperture, consider the overall path difference across the slit - as the angle increases, the path difference
between the point sources across the aperture increases:
sin theta = path difference across aperture / slit width, b
At a certain angle, the path difference across the slit will = one whole wavelength; waves from point
sources in ½ section of slit will all cancel the corresponding point source in the other ½ section:
Results in first minimum, taking place when path difference = b sin theta = lambda, or
sin theta = wavelength / b OR theta = wavelength / b, provided theta is small
theta = angle btwn the straight thru direction & the first minimum of the diffraction pattern measure in
radians; lambda = wavelength measured in m; b is slit width measured in m
At some larger angles, path difference across slit = 1-1/2 wavelengths w/ waves from point sources in 2
of the sections cancel, leaving the amplitude reduced to a 1/3 of the maximum – this is first maximum –
intensity at this angle (which is proportional to the square of the amplitude) will be 1/9 of the initial
value
Next minimum occurs at theta = 2* lambda / b; next maximum at 1/25 of the intensity of the initial