UNIT 4 – THE WAVE NATURE OF LIGHT
Chapter 9 – Waves and Light
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9.1 – Wave in 2-D
o A transverse wave is a periodic disturbance where particles in the medium oscillate at
right angles to the direction in which the wave travels
 Recall: the medium can be water, air, etc.
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o
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A wave originating from a point source is circular
 Ex. dropping an object in water
 i.e. ripples
A wave originating from a linear source is straight
 Ex. a bullet shot from a gun
A continuous crest or trough is a wave front
 Constant frequency and speed
To show direction of travel (transmission) of a wave front, an arrow is drawn at right
angles to the wave front
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Recall: wave equation
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For a wave travelling in different mediums
o
Reflection from a straight barrier
 When a wave front hits a straight reflective barrier it is reflected back along its
original path
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If it hits the barrier at an angle either than 90 degrees
 The incident wave forms an angle of incidence, i, and reflected ray
forms angle of reflection, r
o Angle i = angle r
 The reflected ray has equal wavelength, speed, and frequency to the
incident ray hitting the barrier
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The normal ray represents where the incident ray hits the barrier
 Forms a 90 degree angle
Refraction is the bending effect on a waves direction that occurs when the wave
enters a different medium at an angle
 The angle formed by the normal and the refracted ray is the angle of
refraction, R
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If speed decreases between medium, refracted ray bends toward the normal
 i.e. light traveling from air to water
if speed increases between medium, refracted ray bends toward barrier; away from the
normal
 i.e. light travelling from water to air
o
This is why an object in a pool may seem closer to someone
standing outside a pool
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Ex. 1. The speed of light through a diamond is unknown as it travels 3.0 x 108
m/s through air first. Determine the speed of light as it travels through a
diamond.
When refraction occurs some energy usually reflects and refracts
 Called partial reflection-partial refraction
For large incident angles the refraction can be parallel to the barrier or not exist at all
 Called total internal reflection
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9.2 – Diffraction of Water Waves
o Diffraction is the bending effect on a wave’s direction as it passes through an opening or
by an obstacle
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9.3 – Interference of Waves in 2-D
o Constructive interference occurs when waves build each other up, producing a resultant
wave of greater amplitude than the given waves
o Deconstructive interference occurs when waves diminish one another producing a
resultant wave of lower amplitude than the given waves
 To produce a fixed pattern the interfering waves must have the same frequency,
wavelength, and amplitude
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Interference pattern between 2 identical sources
 i.e. S1 and S2
node is where the 2 waves meet and forms
deconstructive interference
o
The pattern remains consistent if frequency of the 2 sources, distance between them,
and relative phase stay constant
 If frequency increases, wavelength decreases which makes the nodes closer
together and increases their number
 If distance increases, nodes increase
o
Difference in path length in an interference pattern is the absolute difference between
the distance of any point P from 1 source and the distance of the same point P from the
other source
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Can take a point on any node on either side
However for any point Pn, the difference in path length is the distance AS1
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Where θn is the angle of the nth nodal line
d is the distance between the sources
o
If Pn is far away from the sources
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Where B is the right bisector
 Equal distance between point sources and
forms 90 degree angle
PnC is essentially parallel to PnS1
PnC is perpendicular to AS2
CB is perpendicular to S1S2
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Ex. 1. Determine the wavelength of a 2 point source which are 37.4 cm apart
and form an angle of 21 degrees for a point on the 4th node.
9.5 – Wave interference
Constructive interference (bright light)
- - - - - - - Deconstructive interference (darkness)
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o
If light has wave properties
Young’s experiment
 Placed 1 incandescent light directed through 2 pinholes placed very closer
together
 Light was diffracted through each pinhole so each hole now acted as a
point source
o Since the sources are close the spacing between nodal lines was
large
 The 2 interfering beams of light were always in phase
 Creates bands of light and dark
o Called interference fringes or maxima
(light) and minima (dark)
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Deconstructive interference
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Constructive interference
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If L is large when compared to d, it almost appears as a constant for all
nodal lines
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Where ∆x is distance between adjacent nodal lines
d is separation of slits
L is perpendicular distance from slits to screen
Ex. 1. What is the distance between the 1st and 10th nodal line, if the
interference pattern forms on the screen 5.2 m away and the slits which are 0.3
mm apart have a wavelength of 4.8 x 10-8 m.