Lecture 11a:
Wave and ray picture of light
light eye vision
Author: Karen Siu
Modified by Kris Helmerson
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Wave Motion and Light Refraction
Properties of waves; types of waves: longitudinal and
transverse; EM spectrum, reflection, refraction,
geometric ray tracing
Objectives
After study in this topic you should be able to:
• Understand the characteristics of waves
• Distinguish different type of waves
• Be familiar with electromagnetic spectrum.
• Understand reflection, index of refraction and Snell’s Law.
• Understand Total Internal Reflection and Fiber Optics
KS 2019 3
What is a wave?
• A wave is a disturbance that propagates.
• What is “waving” in …
– Pond ripples?
– Surf?
– Sound?
– Radio?
– Light?
– X-rays?
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What is a wave?
• A wave is a mechanism for transmitting energy
and momentum
– Which way is the water surface moving?
– Which way is the wave moving (propagating)?
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Anatomy of a Wave
• Amplitude, X (A in text book) • Frequency f and period T
• Wavelength, λ • Wave velocity v
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Anatomy of a Wave
Position
Displacement versus position, at one instant
Time
Displacement versus time, at one
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position
Reflection and Transmission of Waves
• Consider a wave on a string
approaching a fixed end.
• A wave hitting an obstacle
will be reflected (a), and its
reflection will be inverted.
(Why?)
https://www.youtube.com/watch?v=LTWHxZ6Jvjs
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Reflection and Transmission of Waves
• Consider a wave on a string
approaching a free end.
• A wave hitting an obstacle will
be reflected (b), and its
reflection will be upright.
(Why?)
https://www.youtube.com/watch?v=aVCqq5AkePI
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Transverse and Longitudinal Waves
• Transverse – disturbance is perpendicular to direction of propagation
• Longitudinal – disturbance is parallel to direction of propagation
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Sound waves are longitudinal waves
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Electromagnetic Spectrum
• Light is an electromagnetic wave
• Different frequencies and
wavelengths correspond to different
colours (visible light)
• Electromagnetic (EM) waves are
special in that they don’t require a
medium in which to propagate (cf sound
waves)
• Diffraction and interference (e.g.
holograms), are all evidence of the
wave nature of light but in this lecture
we are mostly going to treat light as a
ray (particle moving in straight line) –
this is known as geometric optics
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Electromagnetic Spectrum
• The speed, wavelength and frequency for EM
waves are related as for all waves, 𝑣 = 𝜆𝑓
Giancoli 22-8
• EM waves have a fixed speed, c = 3.00 x 108
m/s (in vacuum) ⇒ 𝑐 = 𝜆𝑓
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The Ray Model of Light
• Light in a uniform medium travels in straight lines.
• We represent light using rays, shown as straight lines
emanating from an object.
• This is an idealization, but is appropriate when the object
is much larger than the wavelength of light.
• This is known as geometric optics.
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Giancoli 23-1
Law of reflection
• A transparent material is one through which light can be
transmitted.
• An opaque material is one through which light cannot be
transmitted.
• When light strikes a
transparent body
some light is
transmitted and some
reflected.
• Reflection also occurs
at metallic surfaces.
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Diffuse and specular reflections
• When light reflects from a
rough surface, the law of
reflection still holds, but the
angle of incidence varies. This
is called diffuse reflection.
• With diffuse reflection, your eye sees reflected light at all
angles. With specular reflection (from a mirror), your eye must
be in the correct position.
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Refraction – light crossing a boundary
• Recall that EM waves of
any frequency (including
visible light) travel in a
vacuum at c = 3.00 x 108
m/s.
• In general, light slows
when traveling through a
medium (cf vacuum).
• We can characterize any
material by its index of
refraction, n.
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Index of Refraction
• The index of refraction
of the medium is the ratio
of the speed of light in
vacuum (c) to the speed
of light in the medium (v):
𝑐
𝑛=
𝑣
Giancoli
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Light cross a boundary
• For continuity of oscillations across the boundary, we
require frequency to be the same in both media, f1=f2
• What is the wavelength l2 in medium 2? (relative to 1)
Medium 1 = Vacuum Medium 2
(~air) n = n2
n1 = 1 v = v2 < c
v1 = c f 1 = f2
f 1 = f2 l=?
l = l1
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Example – Index of Refraction
• Indices of refraction of some materials for yellow sodium
light (λ=589 nm) are shown in the table below. Calculate
v’ the speed of light in
a) Carbon dioxide
b) Water
Material Air Carbon Water Diamond
dioxide
Index 1.00029 1.00045 1.333 2.417
V (108 m/s) 2.997 ? ? 1.240
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Snell’s Law
• Refraction is the change of direction when light
crosses a boundary from one medium to another
• The angle of the ray in the second medium is the angle
of refraction (between ray and normal).
Giancoli
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Snell’s Law
• The angle of refraction
depends on the indices
of refraction of the two n2
media, and is given by n1 q1
Snell’s law: q2
q2
𝑛! sin 𝜃! = 𝑛" sin 𝜃" q1
Giancoli
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Example - Refraction
• How many fish do you see?
• How many fish are in the tank?
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Example - Refraction
• A ray of light, which is traveling in air, is incident on a
glass plate at a 45° angle. The angle of refraction in the
glass
a) is less than 45°.
b) is greater than 45°.
c) is equal to 45°.
d) could be any of the above; it all depends on the index of
refraction of glass.
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Total Internal Reflection
• If light passes into a medium with a
smaller index of refraction, n2<n1, the
speed increases and the angle of
refraction is larger
• The angle of incidence for which the
angle of refraction will be 90° is called
the critical angle:
𝑛" $
𝑛"
sin 𝜃! = sin 90 =
𝑛# 𝑛#
• If the angle of incidence is larger than
this, no transmission occurs. This is
called total internal reflection.
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Example – Total Internal Reflection
• The critical angle for a beam of light passing from water
into air is 48.8°.
• This means that all light rays with an angle of incidence
greater than this angle will be
a) Absorbed
b) Totally reflected
c) Partially reflected and partially transmitted
d) Totally transmitted
Giancoli Fig 23-24
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Total Internal Reflection in Optical Instruments
• Binoculars often use total internal reflection to
give true 100% reflection, which even the best
mirror cannot do.
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Total Internal Reflection in Optical Fibres
• Fiber Optics use total
internal reflection to
transmit light, even along
bent paths
• Light emerges after
multiple reflections with
very little loss of
intensity.
• Q: which is larger, n2 or
n1?
• Uses: telephone/internet
signals KS 2019 27
Total Internal Reflection in Optical Fibres
• A bundle of optical fibers grouped together can
transmit an image
• Application: Endoscopy – arthroscopy,
gastroendoscopy, microsurgery
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Summary - Refraction
• The electromagnetic spectrum includes all
wavelengths, from radio waves through visible
light to gamma rays.
#
• Index of refraction: 𝑛 = $
• Angle of reflection equals angle of incidence
• Law of refraction (Snell’s law): 𝑛! sin 𝜃! = 𝑛" sin 𝜃"
• Total internal reflection occurs when the angle of
incidence is greater than critical angle (n1>n2):
%#
sin 𝜃# = %
$
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Review Questions
• Representative questions from text book
– Chapter 8: 8.1(a-c), 8.2(a-c), 8.8(a-c), and
8.13(b,c)
– Chapter 32: 32.1, 32.2(a,b,h,k), 32.5, 32.8, and
32.10(a-d,i-k)
