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PES 2130 Fall 2014, Spendier
Lecture 22/Page 1
Lecture today: Chapter 35 Interference
1) Diffraction of light
2) Huygens’ principle
3) Young’s Interference Experiment: Double slit
Announcements:
- HW 8 due today
- HW 9 given out
In chapter 34, we considered the propagation of light along a straight path  Ray
Optics”. However we learned in chapter 33, that light is an electromagnetic wave. This
means that it must undergo interference and diffraction just like a mechanical wave.
In this chapter, we will discuss how light waves diffract when they pass through a small
opening and interfere with one another.
Applications of optical interference:
- In nature, coloring of a butterfly wing
- Colors of soap bubbles , oil spot on pavement
- Multicolored reflection from a DVD surface
Application of diffraction:
- Light diffraction is used to measure particle-size
1) Diffraction of light
When a water wave strikes
a barrier that has a small
opening, the wave diffracts
(spreads out) after it passes
through
the
opening.
Surface waves diffract
nearly circularly after they
pass through the opening.
Given that light is a wave, why don’t we see light diffract in a similar fashion after it
travels through a window? After light passes through a window, light continues to travel
in a straight line, casting a sharp-edged shadow with no discernible diffraction.
For the phenomenon of diffraction to occur, the necessary condition is the thickness of
the diffracting medium should be of the order of the wavelength of light used. Hence,
diffraction does not occur when light passes through a window, since the length of the
window is certainly not of the order of the wavelength of light passing through it.
However, the wavelength of water is about the same as the width of the opening and this
is why we see diffraction of water waves.
To observe diffraction with light waves the width of the opening through which the light
passes can be up to two orders of magnitude greater than the wavelength. Thus visible
light with a wavelength on the order of 1µm, diffracts through apertures up to hundreds
of micrometers wide.
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Lecture 22/Page 2
Plane wave passing through a slit:
For a given wavelength λ, the diffraction of light is more pronounced the smaller the slit
width a. The figures show the cases for (a) slit width a = 6.0 λ, (b) slit width a = 3.0 λ,
and (c) slit width a = 1.5 λ. In all three cases, the screen and the length of the slit extend
well into and out of the page, perpendicular to it.
To understand diffraction it is useful to consider the propagation of a wavefront.
Wavefront: a surface on which a wave spreading through space has constant phase
Light as a Wave
The first person to advance a convincing wave theory for light was Dutch physicist
Christian Huygens, in 1678.
Huygens’ wave theory is based on a
geometrical construction that allows us to
tell where a given wavefront will be at
any time in the future if we know its
present position.
2) Huygens’ principle:
All points on a wavefront serve as point
sources of spherical secondary wavelets.
After a time t, the new position of the
wavefront will be that of a surface
tangent to these secondary wavelets.
PES 2130 Fall 2014, Spendier
Lecture 22/Page 3
3) Young’s Interference Experiment: example of the interference of light waves
In 1801, Thomas Young experimentally proved that light is a wave, contrary to what
most other scientists then thought. He did so by demonstrating that light undergoes
interference, as do water waves, sound waves, and waves of all other types. In addition,
he was able to measure the average wavelength of sunlight; his value, 570 nm, is
impressively close to the modern accepted value of 555 nm.
Basic arrangement of Young’s experiment:
Light from a distant monochromatic source illuminates slit S0 in screen A. The emerging
light then spreads via diffraction to illuminate two slits S1 and S2 in screen B. Light
through these two slits are considered two individual point sources. Diffraction of the
light by these two slits sends overlapping circular waves into the region beyond screen B,
where the waves from one slit interfere with the waves from the other slit.
DEMO:
1) Diffraction pattern from grating
2) PHET online simulations
http://phet.colorado.edu/en/simulation/wave-interference
Evidence for the interference is seen where a viewing screen C intercepts the light.
- Points of interference maxima form visible bright rows—called bright bands, bright
fringes, or (loosely speaking) maxima— that extend across the screen (into and out of the
page in Figure above).
- Dark regions— called dark bands, dark fringes, or (loosely speaking) minima—result
from fully destructive interference and are visible between adjacent pairs of bright
fringes.
- The pattern of bright and dark fringes on the screen is called an interference pattern.
PES 2130 Fall 2014, Spendier
Lecture 22/Page 4
Locating bright and dark Fringes
As we discussed in the sound wave module, sound waves undergo interference. Sound
waves coming from multiple speakers will interfere. At some position away from the
speaker you may hear a loud sound and at other positions you may hear a soft or no
sound.
path length difference: L  L2  L1
L

L

 0,1,2,.....
(fully constructive)
 0.5,1.5,2.5,.....
(fully destructive)
We can use a similar approach to describe fringes in the Young’ Interference Experiment
- A plane wave of monochromatic light is incident on two slits S1 and S2 in screen B;
- The light diffracts through the slits and produces an interference pattern on screen C.
- We draw a central axis from the point halfway between the slits to screen C as a
reference.
- We then pick an arbitrary point P on the screen, at angle θ to the central axis. This point
intercepts the wave of ray r1 from the bottom slit and the wave of ray r2 from the top slit.
These waves are in phase when they pass through the two slits because there they are just
portions of the same incident wave. However, once they have passed the slits, the two
waves must travel different distances to reach P.
The phase difference between two waves can change if the waves travel paths of
different lengths. The change in phase difference is due to the path length difference ∆L
in the paths taken by the waves.
To simplify the analysis, we assume that the distance D from the slits to the screen is
large in comparison to the distance d between the slits that the lines from S1 and S2 to P
aver very nearly parallel. (This is usually the case for experiments with light; the slit
separation is typically a few millimeters, while the screen may be a meter or more away.
Using this approximation, the difference in path length is given by:
PES 2130 Fall 2014, Spendier
Lecture 22/Page 5
∆L = r2 – r1 = d sinθ
Connecting this back to what we know about two interfering sound waves:
Constructive interference, bright fringes (two slits)
d sinθ = mλ (m = 0, ±1, ±2, ±3,…)
Destructive interference, dark fringes (two slits)
d sinθ = (m+1/2) λ (m = 0, ±1, ±2, ±3,…)
Thus the pattern on the screen is a succession of bright and dark bands, or
interference fringes, parallel to the slits S1 and S2.
Central maximum: m=0, ∆L = 0 (zero phase difference)
PES 2130 Fall 2014, Spendier
Lecture 22/Page 6
Example 1: Two-slit experiment
Slit separation, d = 0.200 mm and distance between slits and screen, D = 1.00 m
The third bright fringe (not counting the central bright fringe) is found to be displaced my
9.49 mm from the central fringe.
a) Find the wavelength of the light used
b) How far from the central fringe is the third bright fringe (not counting the central
bright fringe) displaced, if we double the slit separation d?