PHY2053 Lecture 25
Ch. 11.7 - 11.8: Reflection and Refraction
Concept of Superposition
• two waves can be at the same
•
•
place at the same time(as
opposed to material objects)
achieved by superposing
(adding) the displacement
from one wave and the
displacement from the other
wave at the same place and
same time
most of our discussions in the
next 3 lectures deal with the
implications / consequences of
superposition
PHY2053, Lecture 25: Reflection and Refraction
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Phasors
• Phasor
• vector of magnitude equal
• Phaser
to the amplitude of
imaginary
device
•
oscillations
weapon
in
Star
Trek
•
angle
wrt
x
axis
matches
•
universe
argument of the cosine
PHY2053, Lecture 25: Reflection and Refraction
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Practical Use of Phasors
• one wave can be represented by a projection of the
rotation of one vector, then
• two waves can be represented by a projection of the
rotation of two vectors (each rotates on its own)
• add phasors as vectors
A+B
• significantly simplifies
superposition calculations
• no need to deal with
B
trigonometry of moving
waves explicitly
A
PHY2053, Lecture 25: Reflection and Refraction
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Example 1
• Two traveling sine waves, identical except for a phase
difference φ, add so that their superposition
produces another traveling wave with the same
amplitude as the two component waves. What is the
phase difference between the two waves?
PHY2053, Lecture 25: Reflection and Refraction
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Reflection
• occurs whenever a wave encounters a boundary
(fixed end, free end, change of medium)
• details of effect depend on the particular boundary
condition
• most common: fixed end and free end
• fixed end: one point has a fixed displacement (=0)
• need to provide solution for moving wave such that
the point in question never moves from 0
• solution: wave with same properties moving in the
other direction, but negative amplitude
• free end - similar - the amplitude gradient has to be
zero → counter-wave has positive amplitude
PHY2053, Lecture 25: Reflection and Refraction
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Example 2
The pulse in the figure travels
to the right on a string
whose ends at x=0 m and
x=3.0 m are both fixed in
place.
When does the string first
look completely flat for t>0?
When is the first time for
t>0 that the string looks
exactly as it does at t=0?
PHY2053, Lecture 25: Reflection and Refraction
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Refraction
• wave impinges upon a
boundary between two media
• the velocity of the wave is
different in the two
• at the boundary, the
•
amplitude of oscillation has to
be preserved - frequency is
preserved
wave length has to change
since v changes (v = f × λ)
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Example 3
• Light of wavelength 0.500 μm in air enters the water
in a swimming pool. The speed of light in water is
0.750 times the speed in air. What is the wavelength
of the light in water? If the light entered the water at
45 degrees with respect to vertical, what is the angle
(with respect to vertical) of the ray of light in the
water?
PHY2053, Lecture 25: Reflection and Refraction
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