Videos
SP212
Chapter 36 - Diffraction
Final Countdown video
Michaelson Interferometer Green
https://youtu.be/D7BZWIJK64Y
Red https://youtu.be/j-u3IEgcTiQ
Interference (first 3 minutes are good)
http://www.youtube.com/watch?v=VyePASErr5Q
Maj Jeremy Best USMC
Physics Department, U.S. Naval Academy
April 20, 2016
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
April 20, 2016
1 / 14
Diffraction
April 20, 2016
2 / 14
Background
We encountered diffraction when we discussed
interference last chapter, now we’ll focus on it.
Diffraction is the spreading out of a light ray from a
single aperture. Because it involves only one aperture,
you might think the derivation of a diffraction pattern is
simpler than for interference fringes, but you’d be wrong.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
April 20, 2016
3 / 14
Although Huygens proposed the wave
nature of light in the late 1600’s and
Young used it to explain his double slit
experiment in the early 1800’s, very few
scientists believed it. They all believed
in Newtonian Physics, which says that
light is composed of particles. Particles
would only go straight through a
narrow slit and not create patterns that
we see here.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
April 20, 2016
4 / 14
Background
Diffraction
So there was a prize offered in 1819 by
the French Academy of the Sciences to
explain the wave nature of light.
Augustine Fresnel won the prize by
writing an essay saying that light would
create a bright spot of light if it
diffracted around a sphere due to wave
interactions.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
April 20, 2016
5 / 14
Diffraction Intensity - Qualitatively
For our purposes, we will skip to the formula for locating
the minima (dark spots) of a diffraction pattern:
a sin θ = mλ m = 1, 2, 3, ...
Where a is the width of the slit. Note that as the slit
gets narrower the diffraction spread gets wider .
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
April 20, 2016
6 / 14
Resolvability - Rayleigh’s criterion
Diffraction by a circular aperture is very
involved. I will not reproduce the details
here, but will state the main result. The
angular size of the first minimum of a
circular diffraction pattern is given by:
sin θ = 1.22
λ
d
Where λ is the wavelength of the light,
and d is the diameter of the aperture.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
April 20, 2016
7 / 14
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
April 20, 2016
8 / 14
Resolvability - Rayleigh’s criterion
Rayleigh’s Criterion
We consider two objects resolvable (that is, we can tell
them apart), if the central maximum of one aligns with
the first minimum of the other. This is called Rayleigh’s
Criterion.
Since the angles involved are small, we can use our old
friend the small-angle approximation:
sin θR ≈ θR = 1.22
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
April 20, 2016
9 / 14
Real Double Slit Diffraction
April 20, 2016
10 / 14
Diffraction Grating
We talked about the double slit
experiment last chapter, but we
implicitly assumed the slits were
really small. Technically, infinitely
small in fact. For real slits with a
finite width, we get a more
complex interference pattern
because we must take diffraction
into account.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
λ
d
April 20, 2016
11 / 14
The final optical element we will discuss
is the diffraction grating. A diffraction
grating consists of a large number of
narrow slits. By using many many slits,
we produce a very sharp diffraction
pattern, consisting of a number of lines.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
April 20, 2016
12 / 14
Diffraction Grating
The End
First you must determine the grating
spacing, the distance between each line.
If N line occupy a width w , the grating
spacing is d = w /N. The location of
each line (in angular terms) is then
Better is the end of a thing than the beginning
thereof.—Ecclesiastes
d sin θ = mλ m = 0, 1, 2, ...
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
April 20, 2016
13 / 14
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
April 20, 2016
14 / 14