Chapter 22
Reflection and Refraction
of
Light
A Brief History of Light
1000 AD
It was proposed that light consisted of tiny particles
Newton
Used this particle model to explain reflection and refraction
Huygens
1670
Explained many properties of light by proposing light was wave-like
A Brief History of Light, cont
Young
1801
Strong support for wave theory by showing interference
Maxwell
1865
Electromagnetic waves travel at the speed of light
A Brief History of Light, final
Planck
EM radiation is quantized
Implies particles
Explained light spectrum emitted by hot objects
Einstein
Particle nature of light
Explained the photoelectric effect
Dual Nature of Light
Experiments can be devised that will display either the wave nature or the
particle nature of light
Nature prevents testing both qualities at the same time
The Nature of Light
"Particles" of light are called photons
Each photon has a particular energy
E = h ƒ
h is
Planck’s constant
h = 6.63 x 10-34 J s
Encompasses both natures of light
Interacts like a particle
Has a given frequency like a wave
Electromagnetic Waves, Summary
nA
changing magnetic field produces an electric
field
nA
changing electric field produces a magnetic
field
nThese
fields are
in
phase
nAt
any point, both fields reach their maximum
value at
the same time
Electromagnetic Waves are Transverse Waves
nThe
E and B fields are perpendicular to each other
nBoth fields are perpendicular to the direction of motion
nTherefore,
em waves are transverse waves
Properties of EM Waves
nElectromagnetic
waves are transverse waves
nElectromagnetic
waves travel at the speed of light
n
nBecause
em waves travel at a speed that is precisely the
speed of
light, light is an electromagnetic wave
The Spectrum of EM Waves
Forms of electromagnetic waves exist that are distinguished by their
frequencies and wavelengths
n
c = ƒλ
n
Wavelengths for visible light range from 400 nm to 700 nm
n
There is no sharp division between one kind of em wave and the next
The EM Spectrum
n Note
the overlap between types of waves
n Visible light is a small portion of the spectrum
n Types are distinguished by frequency or
wavelength
Geometric Optics – Using a Ray Approximation
Light travels in a straight-line path in a homogeneous medium until it
encounters a boundary between two different media
The ray approximation is used to represent beams of light
A ray of light is an imaginary line drawn along the direction of
travel of the light beams
Ray Approximation
A wave front is a surface passing through points of a wave that have
the same phase and amplitude
The rays, corresponding to the direction of the wave motion, are
perpendicular to the wave fronts
Reflection of Light
A ray of light, the incident ray, travels in a medium
When it encounters a boundary with a second medium, part of the incident
ray is reflected back into the first medium
This means it is directed backward into the first medium
Specular Reflection
Specular reflection is reflection from a smooth surface
The reflected rays are parallel to each other
All reflection in this text is assumed to be specular
Diffuse Reflection
Diffuse reflection is reflection from a rough surface
The reflected rays travel in a variety of directions
Diffuse reflection makes the road easy to see at night
Law of Reflection
The normal is a line perpendicular to the surface
It is at the point where the incident ray strikes the surface
The incident ray makes an angle of θ1 with the normal
The reflected ray makes an angle of θ1’ with the
normal
Law of Reflection, cont
The angle of reflection is equal to the angle of incidence
θ1= θ1’
Refraction of Light
When a ray of light traveling through a transparent medium encounters a
boundary leading into another transparent medium, part of the ray is reflected
and part of the ray enters the second medium
The ray that enters the second medium is bent at the boundary
This bending of the ray is called refraction
Refraction of Light, cont
The incident ray, the reflected ray, the refracted ray, and the normal all
lie on the same plane
The angle of refraction, θ2, depends on the properties of the
medium
Following the Reflected and Refracted Rays
Ray j is the incident ray
Ray
k is the
reflected ray
Ray
l is refracted
into the lucite
Ray m is internally reflected in the
lucite
Ray n is refracted as it enters the air from the lucite
More About Refraction
The angle of refraction depends upon the material and the angle of
incidence
The path of the light through the refracting surface is reversible
Refraction Details, 1
Light may refract into a material where its speed is lower
The angle of refraction is less than the angle of incidence
The ray bends toward the normal
Refraction Details, 2
Light may refract into a material where its speed is higher
The angle of refraction is greater than the angle of incidence
The ray bends away from the normal
The Index of Refraction
When light passes from one medium to another, it is refracted because the
speed of light is different in the two media
The index of refraction, n, of a medium can be defined
Index of Refraction, cont
For a vacuum, n = 1
For other media, n > 1
n is a unitless ratio
Frequency Between Media
As light travels from one medium to another,
its frequency does not change
Both the wave speed and the wavelength do change
The wave fronts do not pile up, nor are
created or destroyed at the boundary, so ƒ must stay the same
Index of Refraction Extended
The frequency stays the same as the wave travels from one medium to the
other
v = ƒ λ
The ratio of the indices of refraction of the two media can be expressed as
various ratios
Snell’s Law of Refraction
n1 sin θ1 = n2 sin θ2
θ1 is the angle of incidence
30.0° in this diagram
θ2 is the angle of refraction
Dispersion
The index of refraction in anything except a vacuum depends on the
wavelength of the light
This dependence of n on λ is called dispersion
Snell’s Law indicates that the angle of refraction when light enters a
material depends on the wavelength of the light
Variation of Index of Refraction with Wavelength
The index of refraction for a material usually decreases with increasing
wavelength
Violet light refracts more than red light when passing from air into a
material
Refraction in a Prism
The amount the ray is bent away from its original direction is called the
angle of deviation, δ
Since all the colors have different angles of deviation, they will spread
out into a
spectrum
Violet deviates the most
Red deviates the least
Prism Spectrometer
A prism spectrometer uses a prism to cause the wavelengths to separate
The instrument is commonly used to study wavelengths emitted by a light
source
Using Spectra to Identify Gases
All hot, low pressure gases emit their own characteristic spectra
The particular wavelengths emitted by a gas serve as "fingerprints" of that
gas
Some uses of spectral analysis
Identification of molecules
Identification of elements in distant stars
Identification of minerals
The Rainbow
A ray of light strikes a drop of water in the atmosphere
It undergoes both reflection and refraction
First refraction at the front of the drop
Violet light will deviate the most
Red light will deviate the least
The Rainbow, 2
At the back surface the light is reflected
It is refracted again as it returns to the front surface and moves into the
air
The rays leave the drop at various angles
The angle between the white light and the violet ray is 40°
The angle between the white light and the red ray is 42°
Observing the Rainbow
If a raindrop high in the sky is observed, the red ray is seen
A drop lower in the sky would direct violet light to the observer
The other colors of the spectra lie in between the red and the violet
Huygen’s Principle
Huygen assumed that light is a form of wave motion rather than a stream of
particles
Huygen’s Principle is a geometric construction for determining the position
of a new wave at some point based on the knowledge of the wave front that
preceded it
Huygen’s Principle, cont
All points on a given wave front are taken as point sources for the
production of spherical secondary waves, called wavelets, which propagate in
the forward direction with speeds characteristic of waves in that medium
After some time has elapsed, the new position of the wave front is the
surface tangent to the wavelets
Huygen’s Construction for a Plane Wave
At t = 0, the wave front is indicated by the plane AA’
The points are representative sources for the wavelets
After the wavelets have moved a distance cΔt, a new plane BB’ can be drawn
tangent to the wavefronts
Huygen’s Construction for a Spherical Wave
The inner arc represents part of the spherical wave
The points are representative points where wavelets are propagated
The new wavefront is tangent at each point to the wavelet
Huygen’s Principle and the Law of Reflection
The Law of Reflection can be derived from Huygen’s Principle
AA’ is a wave front of incident light
The reflected wave front is CD
Read Pages 699-702
Huygen’s Principle and the Law of Reflection, cont
Triangle ADC is congruent to triangle AA’C
θ1 = θ1’
This is the Law of Reflection
Huygen’s Principle and the Law of Refraction
In time Δt, ray 1 moves from A to B and ray 2 moves from A’ to C
From triangles AA’C and ACB, all the ratios in the Law of Refraction can be
found
n1 sin θ1 = n2 sin θ2
Total Internal Reflection
Total internal reflection can occur when light attempts to move from a
medium with a high index of refraction to one with a lower index of refraction
Ray 5 shows internal reflection
Critical Angle
A particular angle of incidence will result in an angle of refraction of
90°
This angle of incidence is called the critical angle
Critical Angle, cont
For angles of incidence greater than the critical angle, the beam is
entirely reflected at the boundary
This ray obeys the Law of Reflection at the boundary
Total internal reflection occurs only when light attempts to move from a
medium of higher index of refraction to a medium of lower index of refraction
Fiber Optics
An application of internal reflection
Plastic or glass rods are used to "pipe" light from one place to another
Applications include
medical use of fiber optic cables for diagnosis and correction of medical
problems
Telecommunications
Sources of Light
A luminous body emits light waves.
The rate at which light is emitted from a body is luminous flux .
The unit of luminous flux is the lumen.
Illuminance is the intensity or lumens per square meter (lm/m2)
and decreases with distance.
This is an example of an inverse square law
Characteristics of Laser Light
LASER…Light Amplification by Stimulated Emission of Radiation
Laser light is coherent (all photons are traveling in phase producing
constructive interference)
Laser light is collimated (spreads out very little)
Laser light is monochromatic (same color of wavelength)
A product of Quantum Physics
Production of a Laser Beam
Fizeau’s Light Experiment
