2. Wavefront
All the points that started from a
source at one time make up the
whole of that wavefront,
If it was a single point, it will be a
circular wavefront
If it is a straight line, it will be a
straight wave front
3. The wavefronts are by convention
found at the crests of the waves.
Wavefronts don’t have to be straight.
Wavefronts and rays
4. Wavefronts and rays
Wavefronts can travel in 3D –
consider what happens to the
surface of a pond when you
skim a stone.
Even if a wavefront is curved
initially, it will eventually
seem planar due to the
distance you are from the
course.
5. Wavefronts can also change direction due to the
medium or an obstacle.
Consider, vision correcting lenses, or a telescope,
these allow the field of view to be changed.
A ray is the direction of a wave and is parallel to
the wave velocity.
Wavefronts and rays
6. Longitudinal waves
also have wavefronts
and can be reduced
to rays – the
wavefronts are due to
rarefactions and
compressions.
Wavefronts and rays
7. Huygen’s Principle
Huygen’s principle states that every point
on a wavefront may be regarded as a point
source of secondary circular wavelets. The
new wavefront is formed along the
common tangent to these secondary
wavelets.
8. I = power / area
Amplitude and Intensity
Intensity is the rate energy is being transmitted per unit area
and is measured in (W m-2).
As area is proportional to x2 (where x is
amplitude)
this results in I α A2
9. Wave superposition is the addition of two or more waves
passing simultaneously through a medium.
Superposition is also called interference and can be
constructive or destructive.
Consider, two identical pulses travelling towards each other
along a rope.
The amplitudes x0 of the two pulses add together,
producing a momentary pulse of amplitude 2x0.
Superposition
0
x0
2x0
constructive
interference
10. Consider,two 180° out-of-phase pulses coming
from each end of a taut rope.
The amplitudes x0 of the two pulses cancel,
producing a momentary pulse of amplitude 0.
- x0
0
x0
destructive
interference
11. Polarisation
Interference and diffraction provides the
best evidence that light is wavelike, but
neither can describe if the light is,
transverse or longitudinal in nature.
12. Nature of light
Vibrations in one direction are polarised:
Vibrations in all directions are
unpolarised:
13. Polarisation
A vibrating charge eg. electron, emits
an em wave that is plane polarised, in a
single plane of vibration.
A light source emits unpolarised light
waves.
14. Polarisation - charge
There is no preferred direction of
vibration for the accelerated,
oscillating charges.
The accelerating charge produces em
waves.
For every E,
there is a B at
right angle to it.
17. Polarisation - light
Polaroid sheets can be used as an
analyser to determine whether, light is
polarised or not.
By rotating it through 360o, two maxima
and two minima will be observed, each
separated by 90o.
19. Intensity using Malus Law
A 'head-on' view of the analyser
will help us to find the intensity
of the transmitted beam
The incident beam has amplitude A0.
The component of A0 parallel to the transmission axis of the
analyser is A0cos θ
So the beam transmitted through the analyser
has amplitude A, where
A = A0cos θ
20. Intensity using Malus Law
The intensity of a beam, measured in W m-2, is
proportional to the square of the amplitude.
Thus the intensity I0 of the incident beam is
proportional to A0
2
the intensity I of the transmitted beam is
proportional to A2 = (A0cos θ)2.
So the beam transmitted through the analyser
has intensity I, where
I = I0cos2θ
21. Example
A sheet of Polaroid is being used to
reduce the intensity of a beam of
polarised light. What angle should the
transmission axis of the Polaroid make
with the plane of polarisation of the
beam in order to reduce the intensity of
the beam by 50%?
23. Methods of Producing Polarised Light
1. Selective absorption
Unpolarised light falls on a sheet of
Polaroid with the polarising crystals in
the vertical direction, i.e. polarisation
axis is vertical, only horizontal planes of
vibration are transmitted.
The energy in the vertical plane is
absorbed in exciting the atoms of the
vertical crystal.
24. Methods of Producing Polarised Light
This sheet is called a polariser as it has
turned unpolarised light into,
horizontally plane polarised light.
If a second sheet of Polaroid is then
added perpendicular to the first sheet,
no light will be transmitted.
25. Methods of Producing Polarised Light
The horizontal vibrations that get
through the first sheet, will have their
energy absorbed, in vibrating the atoms
in the second sheet.
This second sheet is called the analyser.
It can determine whether the light is
polarised, and in what direction.
26. Methods of Producing Polarised Light
2. Reflection
Most light reflected of surfaces such as
water and glass is polarised.
The reflected ray has more vibrations
that are parallel to the reflecting
surface, than at right angles to it.
28. Brewsters Law
The Scottish physicist Sir David Brewster
discovered that for a certain angle of
incidence, monochromatic light was 100%
polarised upon reflection.
The refracted beam was partially polarised,
but the reflected beam was completely
polarised parallel to the reflecting surface.
Furthermore, he noticed that at this angle of
incidence, the reflected and refracted beams
were perpendicular
29. Brewsters Law
Two media of refractive index, n1 n2 respectively.
The angle of incidence= angle of polarisation = ip
Snells law n1sin ip= n2sinθ
31. Brewsters Law
At the Brewster’s angle (polarising angle)
maximum polarisation for the reflected ray
occurs.
Brewster angle is the angle of incidence for
which the angle between, reflected and
transmitted ray is 90o.
What is the polarising angle for a beam of
light travelling in air when it is reflected by a
pool of water (n = 1.33)?
32. Optical activity
Optically active materials can change the
plane of polarisation of a beam of light.
They cause a rotation of the plane
They are common in nature
33. Optical activity
Some materials can rotate the
plane of polarisation of light as it
passes through them.
The liquid crystals used in
calculator displays, digital
watches and lap top computer
screens are also optically active.
The amount of rotation in these
crystals can also be altered by
applying an electric field between
the two faces of the screen and
this is how the display is turned
from bright to dark.
34. Determining concentration of
solutions
This process comes about because of the
molecular structure of these materials, and has
been observed in crystalline materials such as
quartz and organic (liquid) compounds such as
sugar solutions.
Polarised light is passed through an empty tube,
and an analyser on the other side of the tube is
adjusted until no light is transmitted through it.
The tube is then filled with the solution, and the
analyser is adjusted until the transmission
through it is again zero. The adjustment needed
to return to zero transmission is the angle of
rotation.
35. The polarimeter
The specific rotation of a given
liquid may be found using a
polarimeter as shown in Figure 2.
The two polaroids are adjusted to
give a minimum light intensity, and
the scale reading noted. A
measured length of solution of
known concentration is then placed
in the inner tube and the polaroids
readjusted to regain a minimum
and the scale is read again. The
rotation of the plane of polarization
of the light by the solution may then
be found from the difference in the
two scale readings.
Describe the use
of polarization in
the determination
of the
concentration of
certain solutions.
37. Certain solutions rotate the plane of polarisation of light
passing through them. The angle through which the plane
of polarisation is rotated depends on the concentration of
the solution.
Measuring the concentration of
solutions
38. Stress analysis
Polarised light can be used to measure strain
in photoelastic materials, such as glass and
celluloid. These are materials that become
birefringent when placed under mechanical
stress.
A celluloid model of a machine part, for
example, is placed between a crossed
polariser and analyser. The model is then
placed under stress to simulate working
conditions.
39. Stress analysis
Bright and dark fringes
appear, with the fringe
concentration highest where
the stress is greatest.
This sort of analysis gives
important information in the
design of mechanical parts
and structures.
40. Outline qualitatively how polarisation
may be used in stress analysis.
The first photograph below shows
a small part of a plastic set square
viewed under normal conditions
The next photograph shows the
same object when placed
between crossed polaroids
41. Liquid Crystal Displays
Perhaps the most common
everyday use of optical activity
is in liquid crystal displays
(LCDs).
A typical LCD on a digital watch
or electronic calculator consists
of a small cell of aligned crystals
sandwiched between two
transparent plates between a
crossed polariser and analyser.
42. Liquid Crystal Displays
Using liquid crystal's inherent polarizing
characteristics, the liquid crystal of the front
panel redirects the entering polarized light,
according to degree of the liquid crystal twist.
To control the liquid crystal twist, an electrical
field is applied. Varying the electric field, sub-
pixel by sub-pixel, results in polarization angle
changes for each sub-pixel.
43. Liquid crystal displays
The screen of an LCD TV is made of millions of liquid crystals. Each
crystal is like the shutter of a camera either blocking the light or allowing it
to pass through. You can control the amount of light that passes through
by applying a voltage to a crystal or pixel. It does this by rotating the plane
of polarisation of the light. A much-simplified diagram of this action is
shown in Figure 1.
