Slide 2 John Parkinson 1 Slide 3 2 THE BENDING OF WAVES AROUND
CORNERS - PAST AN OBSTACLE OR THROUGH A GAP Ripple Tank Image
Barrier Wave Height - Intensity Single Slit Diffraction Slide 4 3
Original wavefront Secondary sources Subsequent position of
wavefront HUYGENs CONSTRUCTION FOR A PLANE 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. Slide
5 4 WAVES wide gapnarrow gap The central maximum is twice the width
of the other maxima The central maximum is lower [less energy
passes through], but wider Slide 6 5 WAVES For first minimum sin d
Or for small angles in radians d d = width of the gap Slide 7 6
http://webphysics.ph.msstate.edu/java
mirror/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 Slide 8 7 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.
Diffraction by a Double Slit The double slit fringes are still in
the same place Single slit pattern Double slit pattern Slide 9 8
n=0 DIFFRACTION GRATING Each slit effectively acts as a point
source, emitting secondary wavelets, which add according to the
principle of superposition n=2 n=1 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 Slide 10 9 Grating Monochromatic light C For light
diffracted from adjacent slits to add constructively, the path
difference = AC must be a whole number of wavelengths. AC = AB sin
a nd AB is the grating element = d Hence d sin n d = grating
element A B Slide 11 John Parkinson 10 DIFFRACTION GRATINGS WITH
WHITE LIGHT PRODUCE SPECTRA 400nm500nm600nm700nm UV IR Slide 12 11
DIFFRACTION GRATING WITH WHITE LIGHT Hence in any order red light
will be more diffracted than blue. White Central maximum, n = 0
First Order maximum, n = 1 First Order maximum, n = 1 Second Order
maximum, n = 2 Second Order maximum, n = 2 Several spectra will be
seen, the number depending upon the value of d A spectrum will
result Grating screen Slide 13 12 n=0 n=2n=1n=3 grating 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 Slide 14 13 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 90 0 Why do we use 700 nm? Hence there are 7 orders
in all (white central order + 3 on each side) Slide 15 14 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 = 15.4 0
