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Transcript
```VCE Physics
Unit 2
Topic 2
Wave Like Properties of Light
View physics as a system of thinking about the world rather than information
that can be dumped into your brain without integrating it into your own belief
systems.
Unit Outline
•
•
•
•
•
•
•
•
•
•
Describe transverse waves in terms of
amplitude
wavelength
period and frequency
Calculate wavelength, frequency, period and speed of travel of light waves, v =
fλ = λ/T
Investigate and analyse the behaviour of light using ray diagrams including
reflection, i = r
refraction, Snell’s Law
total internal reflection, critical angle
(any form of image location is not required)
Describe light using a wave model and a particle model.
Explain polarization of visible light and its relation to a transverse wave model
Compare the wave model and the particle model of light in terms of whether
they adequately describe reflection and refraction.
Identify visible light as a particular region of the spectrum of electromagnetic
radiation and that all light travels at the speed of light in a vacuum, c.
Explain the colour components of white light as different frequencies of light
combining to appear white.
Explain colour dispersion in prisms and lenses in terms of refraction of the
components of white light as they pass from one medium to another
Identify and apply safe and responsible practices when working with light
sources and optical devices
Chapter 1 - Waves
This chapter covers the following topics:
•Wave Behaviour
•Wave types: Transverse and Longitudinal
•The Medium
•Polarisation
1.0 Wave Behaviour
There are many types of waves all of which have one common feature:They TRANSFER ENERGY from one place to another.
Some waves (eg. Sound, or Water Waves)
need a MEDIUM through which to travel.
The MEDIUM (eg. air, water), although disturbed by the passage
of the waves, does NOT suffer any PERMANENT DISTORTION
due to the waves’ movement through it.
Other waves, eg light waves, microwaves and X rays
don’t require a medium and are so called
“self perpetuating” waves.
In cases where waves require a medium,
it is important to note that the waves
does not drag the medium along with it.
The sea does not build up along the
shore as the waves break !!!!!
1.1 Wave Types - Transverse
There are two basic types of waves:
TRANSVERSE WAVES.
LONGITUDINAL WAVES.
1. TRANSVERSE WAVES are characterised
by having the individual particles of the
medium through which the wave travels,
moving at right angles to the direction of
motion of the wave.
Direction of
motion of the
medium’s
particles
Direction of motion of wave
Notice the “medium” does not move along with the wave.
Pick a spot and follow its motion.
1.2 Wave Types -Longitudinal
2. LONGITUDINAL WAVES are characterised by having the
individual particles which make up the medium through
which the wave travels, moving parallel to the direction of
motion of the wave.
Individual particles
of Medium
Direction of Wave Motion
Direction of Motion of
Particles of Medium
Pick a point in the medium and follow its progress.
Note that it does not move along with the wave, but it is only
displaced from its initial position, returning to its original position
after the wave has passed.
1.3 Wave Types – Electromagnetic
•
•
•
Light is a form of ENERGY.
It is described as ELECTRO - MAGNETIC
EMR is a self propagating wave consisting of
mutually perpendicular, varying ELECTRIC and
MAGNETIC FIELDS.
Changing
Magnetic Field
Direction of
Electromagnetic Wave
Movement
Changing
Electric Field
•EMR travels through a vacuum at 300,000 kms-1, (3.0 x 108 ms-1)
and only slightly slower in other mediums eg., air, water or glass
In a single uniform medium (eg air or glass or water or plastic),
the EM waves travel IN A STRAIGHT LINE.
1.4 The Medium
•A “MEDIUM” is any Transparent or Translucent material which
allows light to pass through it.
•Light and, in fact, all E-M waves, DO NOT require a medium for
travel.
•In the absence of a medium (ie. travelling through a vacuum),
Light, and all E-M waves, travel at 300,000 km/s (3.0 x 108 ms-1).
•However, when travelling through a medium, Light and all E-M
waves will travel at speeds less than 300,000 km/s (3.0 x 108 ms-1).
•In a single, uniform medium (eg. air, plastic, glass, water) Light,
and all E-M waves, travel IN STRAIGHT LINES.
Introduction
1. A common feature of all waves is that
A: They all transfer energy from one place to another
B: They all require a medium for propagation
C: They carry the medium along with them
D: They permanently distort the medium through which they travel
2. There are two main types of waves. They are known as
A: Transverse and Long
B: Travelling and Longitudinal
C: Square and Perpendicular
D: Transverse and Longitudinal
3. Light is a form of EMR, which means light is
C: Electron Miniature Rendition
Introduction 2
4. Light travelling through a translucent material suffers a 50% reduction in its speed. Its
speed through the material is
A: 3.0 x 108 ms-1
B: 1.5 x 104 ms-1
C: 1.5 x 108 ms-1
D: 3.0 x 104 ms-1
5. Our ability to reach out and grasp an object in our hand depends upon which one or more
of the following properties of light
A: Light is made up of a series of colours added together
B: Light travels in straight lines
C: Light travels at 3.0 x 108 ms-1
D: Light is a form of radiation
1.5 Polarisation
We now know that light is an Electromagnetic Wave made up of mutually
perpendicular, varying electric and magnetic fields.
The diagram on the previous slide showed only ONE pair of Electric and
Magnetic fields.
In reality, the are many pairs of Electric and Magnetic fields, each
perpendicular, spread around the line of the direction of propagation.
Line of Propagation
E
For clarity, only the Electric Fields are shown
Polarising Filter
Plane
Polarised
Light
Polarising Filter
Suppose a light globe is
giving out light rays.
We will focus on one
direction of propagation Polarising Axis
only.
Little or no
The polarising filter (simply called a
light
Polarising Axis
POLARIOD), only allows light parallel to the
emerges
polarising axis to pass through.
A second filter with its axis at 90o to the first
will block most, if not all, light from passing
to the eye.
Chapter 2
This chapter covers the following topics:
• Amplitude
• Frequency
• Period
• Wavelength
• Speed
2.0 Wave Properties.
Amplitude
•
Amplitude is a measure of the size of a disturbance above or below a mean or
average value.
Distance
Amplitude
Mean or
Average Value
Point of Max. Displacement
above the mean or average
position
Time
Point of Max.
Displacement below the
mean or average position
2.1 Wave Properties.
Frequency
•
•
Frequency (symbol f ) is most
generally defined as the number of
events which occur during a time
interval.
Distance
Low Frequency
In terms of Light Waves it
represents the number of complete
light waves passing a given point in
a given time.
•
In the SI system, frequency is
defined as the number of events or
cycles per second.
•
The UNIT for frequency is the
HERTZ (Hz), where 1 Hz = 1 cycle
per second
Time
High Frequency
2.2 Wave Properties.
Period
D
•
Time •
0.02
Period (T) = 0.02 s
f = 1/T
= 1/0.02
= 50 Hz
0.04
Period (symbol T) is defined as the
time it takes for one event to occur.
It is the time it takes for one complete
light wave to pass a given point.
•
Period is the measure of a time
interval, thus has the unit seconds (s).
•
Period and frequency are the inverse
of one another thus:
f
1
T
Thus, a wave of period 0.02 s has a frequency of 50 Hz
2.3 Wave Properties.
Wavelength
•
•
•
Wavelength, (symbol , Greek Letter
LAMBDA), is a measure of the
on a wave undergoing similar
motions.
Thus the distance between two
wavelength.
Wavelength is a distance measure,
hence the unit for  is metres (m).

Compression
Rarefaction
Transverse Wave
Longitudinal Wave
Compression

Rarefaction
2.4 Wave Properties.
Wave Speed
• Wave Speed (symbol v) is a
measure of how quickly a
“wavetrain” is moving.
• The wave speed is dependent
on the frequency and
wavelength of the wave train.
• The relation is summarised in
the so called
“WAVE EQUATION”,
v = f
where;
v = Speed (ms-1),
f = Frequency (Hz)
 = Wavelength (m).
•This is a most important equation used in many areas of the course.
2.5 Wave Properties.
When an object is illuminated it casts a shadow. The shadow may have strictly
defined edges, a so called, “sharp” shadow, or it may have ill defined edges, a
The factor which decides what type of shadow is produced is the SIZE of
Screen
the light source.
Point Source
POINT SOURCES produce
Penumbra
Umbra
Object
EXTENDED SOURCES
Object
Penumbra
Umbra = Region of Full Shadow
Penumbra = Region of Partial Shadow (causes the fuzzy edges)
Extended Source
Wave Formula
6. A wave travelling at 4.52 x 103 ms-1 has a measured frequency of 2.45 x 104 Hz,
Calculate its wavelength.
v = fλ  λ = v/f = (4.52 x 103)/( 2.45 x 104 ) = 0.18 m
7. A wave of frequency 100 Hz will have a period of ?
T = 1/f = 1/100 = 0.01 s
8. A ray of red light travelling through a vacuum at a speed of 3.0 x 108 ms-1 has a
wavelength of 450 nm. Calculate (a) its frequency and (b) its period.
(a) v = fλ  f = v/λ = (3.0 x 108)/(450 x 10-9) = 6.67 x 1014 Hz
(b) T = 1/f = 1/(6.67 x 1014) = 1.5 x 10-15 s
9. What is the meaning of the terms “umbra” and “penumbra” ?
Chapter 3
This chapter covers the following topics:
• Electromagnetic Spectrum
• Colour
• Colour Mixing
• Transparent Materials
• Opaque Materials
3.0 The Electromagnetic Spectrum
The ELECTROMAGNETIC SPECTRUM encompasses all ELECTROMAGNETIC
RADIATION of which VISIBLE LIGHT is but a small part.
Frequency, f (Hz)
1024
1022
1020
1018
1016
1014
1012
108
1010
Gamma rays
High
Energy
UV
10-14
Microwaves
X Rays
Cosmic Rays
10-16
Infra Red
10-12
10-10
In a vacuum, all EM Radiation
travels at the same speed :
v = 3.0 x 108 ms-1
λVIOLET = 4.5 x 10-7 m
= 450 nm
10-8
10-6
10-4
Wavelength, λ (m)
10-2
TV
100
106
104
Waves
102
Low
Energy
104
1 nm = 10-9 m
Visible Light
λRED = 7.5 x 10-7 m
= 750 nm
Notice how small the range of wavelengths is for the visible region of the E-M
Spectrum.
This small range of wavelengths give us our ability to “see” the world.
Imagine how much more complex the world be if our eyes were able to “see”
all the wavelengths of the electromagnetic spectrum.
3.1
Colour
The fact that “white” light is made up of a mixture of colours was first discovered
by Isaac NEWTON (1642 - 1727).
When Newton passed white light through a triangular prism, it was broken up into
its constituent colours.
This “break up” occurs because
This process is called DISPERSION
each colour has a slightly
different wavelength and when
passed through the prism suffers
White Light
a slightly different change in
Red
Orange
direction.
Yellow
Green
Colours associated with definite
Blue
wavelengths are called
Indigo
SPECTRAL COLOURS.
Violet
The colours and their wavelengths:
Colour
RED
ORANGE
YELLOW
GREEN
BLUE
INDIGO
VIOLET
Wavelength (nm)
650
600
580
550
500
470
450
From both the diagram and the table, it
should be obvious that the shorter the
wavelength, the greater the change in
direction.
10. Arrange the following examples of EMR from shortest to longest wavelength
Cosmic rays, Radio waves, Visible light, Gamma rays, Ultraviolet, Microwaves, Infrared,
X Rays, TV.
Cosmic rays, Gamma rays, X Rays, Ultraviolet, Visible light, Infrared, Microwaves,
11. Why can a prism split white light into is component colours ?
The reason that this break up occurs is because each colour has a slightly different
wavelength (or frequency which ever term you want to use) and because of this
each suffers a slightly different change in direction while passing through the prism.
3.2 Colour Mixing
Just as light can be broken up into individual
colours, so individual colours of light can be
recombined to produce white light.
When the various colours of LIGHT are mixed
together we can achieve all colours of the
rainbow, but more importantly, we can produce
white light. This is an ADDITIVE PROCESS.
Subtractive Colour Chart
However, when paints or pigments are added
together , each pigment absorbs, or subtracts,
certain colours, so this is a SUBTRACTIVE
PROCESS.
Thus when every pigment colours is added, all
colour will have been absorbed leaving only black.
3.3 Colour: Transparent Materials
There are 3 basic types of materials in the world.
TRANSPARENT objects transmit most light reflecting and absorbing very little.
TRANSLUCENT objects transmit some light (usually distorted) while reflecting
and absorbing more of the light than transparent materials.
OPAQUE objects transmit no light and reflect and /or absorb all light.
TRANSPARENT OBJECTS which are coloured (usually called FILTERS) transmit
their colour whilst at the same time absorbing all other colours.
Examples of White Light interacting with various filters are shown below.
White Light
White Light
Red Light
Red Filter
Blue Filter
White Light
Red Light
No Light Emerges
Red Filter
Blue Filter
Blue Light
3.4 Colour:
Opaque Materials
Examples of White Light interacting with various OPAQUE MATERILALS are
shown below.
White Light
White Light
White Light
Red Light
White Light
Red
White
White Light
Blue Light
Blue
White Light
Red Light
Blue Light
No reflected Light
Black
Purple
Opaque objects appear coloured because they reflect their colour while, at the
same time, absorbing all other colours.
Colour
12. How is the process of adding light different from the process of adding pigments ?
When the various colours of light are mixed together we can achieve all colours of the
rainbow, but more importantly, we can produce white light. This is an ADDITIVE
PROCESS. However, when paints or pigments are added together, each pigment
absorbs, or subtracts certain colours, so this is a SUBTRACTIVE PROCESS.
13. As far as light is concerned there are 3 types of materials in the world: Draw a line
between the term and its meaning
Term
Transparent
Translucent
Opaque
Meaning
materials transmit some light (usually distorted)
while reflecting and absorbing more of the light
than other materials.
materials transmit no light and reflect and/or
absorb all light.
materials transmit most light reflecting and
absorbing very little.
Colour and Filters
14. Why is a blue tee shirt blue to an observer ?
Blue tee shirts are blue because the blue fabric absorbs all colours
except blue which it reflects.
15. Describe how you could use 2 simple filters to block out all visible light
Shine light firstly through a blue filter leaving only blue light, then shine that
onto a red filter, no light will emerge from the red filter.
Chapter 4
This chapter covers the following topics:
• Reflection
• Refraction
• Index of Refraction
• Critical Angle
• Total Internal Reflection
• Optical Fibres
• Interference Patterns
4.0 The Properties of Light Reflection
Before studying the Laws of Reflection the idea of a NORMAL needs to be
introduced.
The NORMAL
The NORMAL is an imaginary line drawn
at Right Angles to the Reflecting
Surface. It is used to define the angles
of incidence and reflection.
Reflecting Surface
THE LAWS OF REFLECTION
Incident Ray
Reflected Ray
i
r
Reflecting Surface
i = Angle of Incidence
r = Angle of Reflection
1.
Angle of Incidence = Angle of Reflection
2.
The Incident Ray, the Reflected Ray
and the Normal are COPLANER (all lie
in the one plane) and all lie on the
same side of the reflecting surface.
16. What is a Normal ?
Reflection
The Normal is an imaginary line perpendicular to the reflecting or refracting surface.
17. Two plane mirrors are set up as shown a ray incident on the lower mirror
reflects onto the upper one. Determine the values of the angles marked W, X,
Y and Z.
Mirror
Z
Normal
W = 600;
X = 600;
Y = 300;
Z = 600
Y
X
W
300
100
Mirror
1000
4.1 The Properties of Light Refraction
Refraction is the changing of the direction of travel of a light ray which
generally occurs when light passes from one medium to another (eg when
passing from air to glass).
The reason for the change in direction is that THE SPEED OF LIGHT changes
when passing into the new medium.
The speed is inversely proportional to the density of the medium, ie. The slower
the speed, the denser the medium.
Incident Ray
Incident Ray
Air
Normal
i
Glass
r
i = Angle of Incidence
r = Angle of Refraction
Refracted Ray
Note: If the incident ray is directed in
along the Normal, it will NOT change
its direction when it crosses the
boundary.
For other directions a change in
direction WILL occur.
Since DensityGLASS > DensityAIR
it can be seen that in travelling from a
less dense to a more dense medium
the light ray is refracted TOWARD the
Normal.
4.2 The Properties of Light The Laws of Refraction
THE LAWS OF REFRACTION.
The first law of refraction is also known
as SNELL’S LAW
Incident Ray
Air
Normal
i
Glass
r
i = Angle of Incidence
1. Snell’s Law. For a given pair of media,
the ratio of the Sine of the angle of
Incidence to the Sine of the angle of
Refraction is a constant (n).
Mathematically: Sin i/Sin r = n
n is called the “Index of Refraction” or
more simply the “Refractive Index”
r = Angle of Refraction
Refracted Ray
2. The Incident Ray, the Refracted Ray
and the Normal to the refracting
surface at the point of incidence are
COPLANER and the Incident and
Refracted Ray are on opposite sides
of the refracting surface.
4.3 The Properties of Light The Index of Refraction (1)
ABSOLUTE REFRACTIVE INDEX.
If one of the media involved in the Refraction process is a VACUUM, the constant,
n, in Snell’s Law becomes “THE ABSOLUTE REFRACTIVE INDEX”.
Values of the absolute refractive index for various materials are:
Note the closeness of the values for
Vacuum and Air. In all cases in this
Material
Absolute Refractive
course, nAIR can be taken to be equal to
Index
nVACUUM = 1.00
Vacuum
1.0000
Air
1.0003
RELATIVE REFRACTIVE INDEX
Water
1.33
If neither of the mediums involved in a
Oleic Acid
1.46
Quartz
1.46
refraction process is a vacuum, each will
Perspex
1.50
have its own Absolute Refractive Index
Crown Glass
1.52
and the constant (n) in Snell’s Law must
Diamond
2.42
reflect that fact.
In general for two mediums with Absolute Refractive Indexes n1 and n2, Snell’s
Law becomes:
n1Sin i = n2 Sin r
 Sin i/Sin r = n2/n1
The ratio n2/n1 is usually quoted as n12 and is called the “RELATIVE
REFRACTIVE INDEX” for light travelling from medium 1 to medium 2
4.4 The Properties of Light Index of Refraction (2)
An example may be
useful in understanding
“Relative Refractive
Index”
Normal
Plastic
nG = 1.50
i
Water
nW = 1.33
RRI’s less than 1 mean the light is travelling
into a less dense medium.
r
Normal
Plastic
nG = 1.50
r
Water
nW = 1.33
i
A block of Plastic is floated on water
A beam of light passes through the plastic
and enters the water.
In this situation the Relative Refractive Index
(RRI) for light travelling from Plastic to Water,
nPW = nW/nP = 1.33/1.50 = 0.89
If the position is reversed and the light travels
from the water into the plastic.
The Relative Refractive Index for light
travelling from Water to Plastic,
nWP = nP/nW = 1.50/1.33 = 1.13
RRI’s greater than 1 mean the light is
travelling into a more dense medium.
Refraction
18. State Snell’s Law in mathematical terms
Sin i/Sin r = a constant
19. Calculate the angle of refraction for light passing from air (n = 1.00) at
an incident angle of 460 into diamond (n = 2.42)
nair Sin i = ndiamondSin r  r = Sin-1 (1.00 Sin 46/2.42) = 17.30
20. What is the difference between an absolute refractive index and a
relative refractive index ?
If one of the media involved in the refraction process is a vacuum, the constant, n, in
Snell’s Law is called the “ABSOLUTE REFRACTIVE INDEX”. If neither medium is a
vacuum the constant, n, in Snell’s Law is called the “RELATIVE REFRACTIVE INDEX”
21. A beam of light passed from perspex into oleic acid with an angle of refraction of
720 . What was the beam’s incident angle ? noleic acid = 1.46; n perspex = 1.50.
Draw a clear, fully labelled diagram of this situation.
nperspex Sin i = noleicSin r  i = Sin-1(1.46 Sin72/1.5) = 680
4.5 The Properties of Light Critical Angle
When light travels from a more dense to a less dense medium (eg. from water
to air), it refracts AWAY from the Normal.
As the angle of incidence (i) increases eventually
a value of i will be reached which produces and
angle of refraction of 900.
Normal
Air
nA = 1.00
This angle of incidence is called the
CRITICAL ANGLE (iC)
rr
i
iC
Water
nW = 1.33
The size of the critical angle for this pair of media
can be calculated from Snell’s Law
nW Sin iC = nA Sin r
1.33 Sin iC =1.00 Sin 900
Sin iC =1/(1.33)
 iC = 48.80
4.6 The Properties of Light Total Internal Reflection
If the angle of incidence increases beyond the Critical Angle, the light ray will
no longer leave the denser medium.
The surface of the denser medium will act like a plane mirror reflecting the
beam back with an angle of reflection equal to the angle of incidence.
Normal
nA = 1.00
i r
nW = 1.33
4.7 The Properties of Light
Optical Fibres
Optical Fibres are the basis of modern high speed, high volume
communication systems allowing telephone systems, Cable Television and
interconnected computer systems to operate in an efficient and timely
manner.
Optical fibres rely on the Total Internal Reflection of a laser beam to transfer
information (usually in digital form) from one place to another.
Laser Beam
Optical Fibre
Each time the laser beam reflects off the inner wall of
the optical fibre, it suffers attenuation (loses some of its
energy), thus, at intervals of about 10 to 20 km along
optical fibre, repeater stations are needed to boost the
power of the laser beam before it is transmitted further
along the fibre.
Individual glass
optical fibres
4.8 The Properties of Light Double
Slit
Interference
When light of a single wavelength is passed through a pair of closely spaced,
narrow slits, an “interference pattern” is produced.
This pattern has a series of equally spaced coloured and black bands spread
across the screen onto which it is projected.
The width of the coloured bands and their spacing depends on the wavelength
of the light used.
Short wavelength, BLUE light produces a pattern with narrow blue bands
which are closely spaced.
Long wavelength, RED light produces a pattern with wider red bands which
Screen
Interference Patterns
using the same slits
This experiment is known as
“Young’s Double Slit Experiment”
BLUE Light
Incident Light
RED Light
Double Slits
Critical Angle
22. Define critical angle.
Critical Angle: that angle of incidence that produces an angle of refraction of 900
23. Determine the critical angle (ic) for light travelling from crown glass (refractive
index = 1.52) into air.
ic = Sin-1(1/1.52) = 41.10
24. What happens to light rays which approach a boundary with a lower refractive
index material at an angle greater than the critical angle for that combination ?
The rays are totally internally reflected
25. What are Optical Fibres and what is the basis of their operation ?
Optical Fibres are flexible glass (or plastic) tubes through which laser light can
travel. Their basis of operation is total internal reflection
Chapter 5
This chapter covers the following topics:
• Image Formation
• Plane Mirrors
• Curved Mirrors
• Lenses
• Ray Tracing
5.0 Image Formation
Images formed by mirrors or lenses are characterised by a number of
properties which need definition.
1. IMAGE TYPE:
There are 2 types of images formed by mirrors and lenses;
(a) REAL IMAGES, these actually exist and can be projected onto a
screen.
(b) VIRTUAL IMAGES, these do not actually exist and CANNOT be
projected onto a screen.
2. IMAGE ORIENTATION:
When compared to the object, the image may be;
(a) upright or erect, ie. in the same orientation as the object, or
(b) inverted or upside down, ie. opposite in orientation to the object.
3. IMAGE SIZE:
When compared to the object the image may be larger than, equal in size
to, or smaller than the object.
4. LATERAL INVERSION:
This occurs when images are laterally transposed ie. Right becomes left and
visa versa.
5.1 Images - Plane Mirrors
The eye “expects” light to travel in straight lines.
In order to see the top of her head, the lady needs a ray to travel along the
path shown.
In order to see her chin she needs a ray to travel as shown.
Mirror
Object
Image
The “expectation” that light travels in straight lines means she “sees” her
image “inside” the mirror, as shown.
The image produced by a plane mirror has the following properties:
•Virtual
•Upright
•Laterally Inverted
•Equal in size to the object
•As far behind the mirror as the object is in front.
Image Formation
26. Images produced by mirrors and lenses are classed as either real or virtual, upright or
inverted, and larger or smaller or the same size as the object. Write definitions for the
underlined words.
Real – the light rays actually meet to produce an image that can be projected onto a
screen
Virtual - the light rays do not actually meet and the image cannot be projected onto
a screen
Upright – the image is in the same orientation as the object
Inverted – the image is upside down when compared to the object
27. How far behind a plane mirror is the image of an object formed ?
As far behind the mirror as the object is in front of it.
5.2 Curved Mirrors
There are two kinds of curved mirrors:
1. CONCAVE MIRRORS (Converging Mirrors ). These mirrors force parallel
incoming rays together at one point after reflection.
Concave Mirror
Point at which reflected rays
actually meet.
Called the FOCAL POINT of
mirror
2. CONVEX MIRRORS (Diverging Mirrors). These mirrors force parallel
incoming rays to diverge from an apparent meeting point behind the mirror.
Convex Mirror
Apparent meeting
point of reflected
rays
5.3 Curved Mirrors Properties and Definitions
Before proceeding with image determination, a number of terms associated with
curved mirrors need to be defined.
Concave Mirror
R
f
PA
O
C
A
F
A = Aperture of Mirror (diameter of reflecting surface)
O = Pole of the Mirror (the centre of the reflecting surface)
C = Centre of Curvature (centre of the sphere of which the mirror is a part)
R = Radius of Curvature (radius of sphere of which the mirror is a part)
PA = Principal Axis (a line joining the centre of curvature and the pole of
the mirror).
f = Focal Point (point at which rays, initially parallel to the principal axis, meet
after reflection).
F = Focal Length (distance from pole to focal point).
5.4 Ray Tracing –
Concave Mirrors
In order to determine the position and type of image produced by a concave
mirror, a number of “standard” light rays can be used.
The three most important are illustrated below:
Concave Mirror
Object
PA
Ray 1
Ray 3
f
Ray 2
i
r
Image
Ray 1 - A ray, initially parallel to the Principal Axis, will, after reflection
pass through the Focal Point.
Ray 2 - A ray initially directed toward the pole of the mirror, will, after
reflection, leave the mirror such that angle i = angle r
Ray 3 - A ray, initially directed through the Focal Point, will, after
reflection, leave the mirror parallel to the Principal Axis.
Generally, only two of the three “standard” rays ever need to be used to
locate the position of an image.
5.5 Images - Concave Mirrors
Image type, size and orientation for concave mirrors may be found by using the
ray tracing technique.
Concave Mirror
Object
The Image produced is:
•REAL
•INVERTED
•SMALLER than the Object
f
Image
Concave Mirror
Object
When the object is placed 2f
from the mirror, the image is:
•REAL
•INVERTED
•SAME SIZE as the object
f
Image
Concave Mirror
When the object is put
“inside” the focal length,
the image is:
•VIRTUAL
•UPRIGHT
•LARGER than the Object
Object
f
Image
5.6 Lens Types
There are two basic types of lenses:
1.
CONVEX LENS (Converging Lens). These lenses cause incoming
parallel rays to be refracted to a single point.
Convex Lens
f
2.
f
CONCAVE LENS. (Diverging Lens). These lenses cause incoming
parallel rays to diverge as if they originated from a focal point.
Concave lens
f
f
5.7 Lenses - Properties &
Definitions
Before proceeding with image determination, a number of terms associated with
lenses need to be defined.
C
Convex Lens
R
A
f
PA
f
O
F
F
A = Aperture of Mirror (diameter of refracting surface)
O = Optical Centre of the lens (the very centre of the lens)
C = Centre of Curvature (centre of the sphere of which the lens surface is a part)
R = Radius of Curvature (radius of sphere of which the lens surface is a part)
PA = Principal Axis (a line joining the centre of curvature and the optical centre of
the lens).
f = Focal Points (point at which rays, initially parallel to the principal axis, meet,
after refraction). Note the lens has two focal points.
F = Focal Length (distance from optical centre to focal point(s)).
5.8 Ray Tracing - Lenses
In order to determine the position and type of image produced by a concave
mirror, a number of “standard” light rays can be used.
The three most important are illustrated below:
Convex Lens
Object
Ray 3
Ray 1
f
Ray 2
f
Image
Ray 1 - A ray from the top of the object, initially parallel to the principal
axis, will, after refraction through the lens, pass through the focal
point on the far side of the lens.
Ray 2 - A ray from the top of the object will pass through the optical
centre of the lens undeviated.
Ray 3 - A ray from the top of the object passing through the near focal
point will, after refraction, emerge from the lens parallel to the principal
axis.
Generally, only two of the three “standard” rays are ever needed to
locate the position of the image.
5.9 Images - Convex Lenses
Image type, size and orientation for convex lenses may be found by using the
The Image produced
ray tracing technique.
is:
•REAL
•INVERTED
•SMALLER
than the Object
Convex Lens
Object
f
f
Image
Convex Lens
Image
f
f
When the object is put “inside”
the focal length, the image is:
•VIRTUAL
•UPRIGHT
•LARGER than the
Object
Object
Rays projected
backwards WILL
meet.
These diverging rays will
never meet.
Ray Tracing
28. What is the process of determining where the image of an object is in a
curved mirror or lens called ?
Ray Tracing
29. How many rays are needed to locate the image of an object in a curved mirror or
lens ?
2
Chapter 6
This chapter covers the following topics:
• Conceptual Modelling
• Light as Particles
• Theories for Light
6.0 Conceptual Modelling
When we observe strange or unusual behaviour in
people, we often try to explain what we see by
supposing the person is suffering some mental
problem.
They may have suffered a skull fracture resulting in brain
damage, have a congenital brain defect, or have problems
due to parental abuse in childhood.
“Conceptual modelling” here refers to the activity of constructing abstract
models of knowledge about the world of light
In attempting to find a explanation for what we see, we “model” various
“concepts”, in other words, we try to find or develop a theory which will fit all
the behaviours we observe.
We have two possible “models” available to fit light’s observed behaviours.
(a) Light is a wave and all
its properties and
behaviours can be
explained by assuming
light is a wave.
(b) Light is a particle
and all its properties
and behaviours can
be explained by
assuming light is a
particle.
6.1 Light as Waves
By assuming light is a wave all the properties and behaviours we have so
far investigated can be explained by using the known properties and
behaviours that waves, in general, exhibit.
For example, waves
undergo reflection
of reflection exactly
Waves refract
according to Snell’s
Law
Refraction
Reflection
Waves produce
interference
patterns.
Interference
6.2 Light as Particles
Just as waves can be
reflected, so too can
particles.
of reflection.
Particles can also undergo
refraction obeying Snell’s
Law. (although speed
predictions are incorrect)
Incident Light
However, one property of light cannot
be explained by the “wave model”.
In the Photoelectric Effect certain
metals eject electrons when
illuminated by particular colours of
light
Ejected Electron
Metal
6.3 Comparing Models
Does our new found knowledge mean that the “wave model” for light
is now to be replaced by the “particle model” ?
Well, no because the particle model has the same limitations as the wave
model, that is, it cannot adequately explain ALL known properties of light.
So how useful is each theory in explaining light properties ?
The table summarises.
Light Property
Particle Theory
Wave Theory
Pressure
Yes
Yes
Reflection
Yes
Yes
Refraction
Partially
Yes
Diffraction
No
Yes
Interference
No
Yes
Yes
No
Photoelectric Effect
6.4 Where to Now ?
This leaves us in the position of not having one single model that
can describe all light’s known behaviours.
So we have developed a hybrid model called the “Wave – Particle
Duality”, where light is assumed to be made up of a stream of
individual particles called “PHOTONS”.
Photons are neither waves nor particles, having
properties similar to particles when travelling
through a vacuum and when in a gravitational field,
while also having properties similar to waves when
refracting and interfering.
Photons can be pictured
as a series of individual
particles each of which
displays some wave like
properties.
Individual Photon
Models for Light
30. What are the two theories which compete to explain light’s behaviour ?
The Wave Model and The Particle Model
31. For which particular light behaviour is the particle model inadequate ?
Refraction
32. For which particular light behaviour is the wave model inadequate ?
Photoelectric Effect
33. What is a Photon ?
A Photon is an attempt to explain light’s behaviour with a model that has both
particle and wave nature
34. What is the wave particle duality ?
The wave particle duality is the currently accepted model for the explanation of
light’s behaviour.
Ollie Leitl 2003
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