DIFFRACTION DIFFRACTION John Parkinson ©

Single Slit Diffraction THE BENDING OF WAVES AROUND CORNERS - PAST AN OBSTACLE OR THROUGH A GAP Barrier Ripple Tank Image Single Slit Diffraction Wave Height - Intensity ©

HUYGEN’s CONSTRUCTION FOR A PLANE WAVEFRONT Subsequent position of wavefront “Every point on a wavefront acts as a source of secondary waves which travel with the speed of the wave. At some subsequent time the envelope of the secondary waves represents the new position of the wavefront.” Secondary sources Original wavefront ©

WAVES WAVES wide gap narrow gap The central maximum is twice the width of the other maxima The central maximum is lower [less energy passes through], but wider

Or for small angles in radians WAVES d = width of the gap For first minimum sin  = l/d Or for small angles in radians  = l/d 

http://webphysics. ph. msstate http://webphysics.ph.msstate.edu/javamirror/ipmj/java/slitdiffr/index.html At this web site you can change the width of the slit and the wavelength to see how theses factors affect the diffraction pattern

The double slit fringes are still in the same place Diffraction by a Double Slit The double slit pattern is superimposed on the much broader single slit diffraction pattern. The bright central maximum is crossed by the double slit interference pattern, but the intensity still falls to zero where minima are predicted from single slit diffraction. The brightness of each bright fringe due to the double slit pattern will be “modulated” by the intensity envelope of the single slit pattern. Single slit pattern The double slit fringes are still in the same place Double slit pattern ©

DIFFRACTION GRATING n=0 n=1 n=2 Each slit effectively acts as a point source, emitting secondary wavelets, which add according to the principle of superposition n=0 n=1 n=2 n=1 corresponds to a path difference of one wavelength n=2 corresponds to a path difference of two wavelengths n=3 corresponds to a path difference of three wavelengths

 For light diffracted from adjacent slits to add constructively, the path difference = AC must be a whole number of wavelengths. Grating A C  Monochromatic light B AC = AB sin  and AB is the grating element = d Hence d sin  = n d = grating element

DIFFRACTION GRATINGS WITH WHITE LIGHT PRODUCE SPECTRA 400nm 500nm 600nm 700nm UV IR John Parkinson ©

A spectrum will result DIFFRACTION GRATING WITH WHITE LIGHT Hence in any order red light will be more diffracted than blue. A spectrum will result Several spectra will be seen, the number depending upon the value of d screen Second Order maximum, n = 2 Grating First Order maximum, n = 1 White Central maximum, n = 0 First Order maximum, n = 1 Second Order maximum, n = 2

Note that higher orders, as with 2 and 3 here, can overlap Be aware that in the spectrum produced by a prism, it is the blue light which is most deviated grating

Hence there are 7 orders in all (white central order + 3 on each side) QUESTION 1 Given a grating with 400 lines/mm, how many orders of the entire visible spectrum (400 – 700 nm) can be produced? Finding the spacing d of the “slits” (lines). d = 1/400 = 2.5 x 10-3 mm = 2.5 x 10-6 m d sin  = n sin  = (n )/d = a maximum of 1 at 900 Why do we use 700 nm? Hence there are 7 orders in all (white central order + 3 on each side)

For red light in the second order For blue light in the second order Question 2: Visible light includes wavelengths from approximately 400 nm (blue) to 700 nm (red). Find the angular width of the second order spectrum produced by a grating ruled with 400 lines/mm. As before d = 2.5 x 10-6 m For red light in the second order For blue light in the second order 34.1 - 18.7 = 15.40