Download 2- Reflection, Refraction

2nd & 3th N.U.T.S. Workshops
Gulu University
Naples FEDERICO II University
2 – Reflection, Refraction
2nd & 3th NUTS Workshop ( Jan 2010)
Four ways of interaction of light with matter
Light interacts with
matter by:
a) reflection
b) refraction
c) scattering
d) absorption
Medium 1
a)
Reflection
Medium 2
Refraction
b)
c)
d)
Scattering
Absorption
All four types of interaction depends on properties of the two
media. These properties can be described macroscopically by
parameters that summarize the microscopic features of a
medium
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2nd & 3th NUTS Workshop ( Jan 2010)
Reflection of Light
•A beam of light, (represented
as a ray, the incident ray) travels
in a medium
•When it encounters a
boundary with a second
medium, part of the incident
beam is reflected back into the
first medium
Angle of
Incidence
Normal
Angle of
Reflection
Angle of incidence = Angle of reflection
qi=qr
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Angles of Reflection and Incidence are Equal
b) in specular reflection, a smooth surface reflects a light beam
undistorted
c) a rough surface results in diffuse reflection (law of reflection
still hold for each individual ray but the normal changes
direction point by point)
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2nd & 3th NUTS Workshop ( Jan 2010)
Specular Reflection:
An incident parallel beam is
reflected as a parallel beam
Diffuse Reflection:
A parallel beam is reflected as
bunch of diverging rays
Reflection is a way to
bend light beams!
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What type of reflection is more useful?
Well, it depends, what you actually want to get…
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Specular and Diffuse Reflection
Which of the below figures shows specular reflection of light from the
roadway?
With diffuse reflection you see the road;
With specular reflection you see the lights of the car reflected off the road.
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Mirrors are designed to give specular reflection
Therefore the mirror surface is invisible by itself.
There are no point sources of light on mirror surface.
Therefore, looking into a mirror you see reflections of
objects, not the mirror itself.
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(Metallic) Mirrors
Materials like metals (with many mobile electrons) can
completely reflect light of some colors.
 Silver is particularly interesting because it reflects light of all
colors



Gold and copper have a yellowish-brownish color because they
reflect greens, yellows and reds light but not blues or violets
light
Since silver is such a good reflector a coating of silver on glass
makes a good (common) mirror.
If the silver coating is thin enough the mirror can be made to
transmit 50% of the light and to reflect the other 50%. This is
called a half-silvered mirror
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2nd & 3th NUTS Workshop ( Jan 2010)
The Colour of the Light
The colour of the light has to do with the wavelength of the light.
Visible light is only a very thin wavelength interval of the
electromagnetic waves
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Electromagnetic Waves
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The Numbers of Colours of Visible Light
Incorrectly, many text books say that the spectrum of the white light
has seven colour. The same for the colours of the rainbow. Avoid the
trap of teaching that there is sharp transition from one colour to the
following, as the 7 colours schema proposes.
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2nd & 3th NUTS Workshop ( Jan 2010)
The Infinite Numbers of Colours
The number of colours is much
more than seven, ideally one
could say that there is an infinite
number of colours since there are
infinite values of wavelength.
Practically some intervals of
wave length are perceived as
common colours
(e.g. yellow is the colour perceived for the region around 580 nm)
but the number of colours a person can perceive depends on
many factors; a painter usually perceive many more colours that a
layman.
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2nd & 3th NUTS Workshop ( Jan 2010)
Law of specular reflection of a ray from a
mirror
•One of many beams from a
light bulb hits Alex's chin.
Normal
This angle
= this angle
Mirror
The normal to the mirror is an
imaginary line drawn perpendicular
to it from where the incident beam
hits the mirror
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How is an image produced in a mirror?
Part 1: Ray-tracing
To find out how Bob "sees" Alex by looking in the
mirror we trace rays which obey the law of
reflection
Alex
Bob looks at
Alex's image
• Consider an incident ray from
Alex's chin which reflects
according to the law of reflection
at a specific point on the mirror
and goes into Bob's eye.
• A ray from Alex's hair will reflect
Mirror
at one point on the mirror into
Bob's eye (and satisfies the law of
reflection).
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How is an image produced in a mirror?
Part 2: The psychology of ray interpretation




To find the image of Alex we must
learn how Bob’s eye (and our eyes)
Alex
interpret rays
Bob cannot directly know whether the
rays entering his eyes have been
reflected or not!
We interpret all rays coming into
our eye as traveling from a fictitious
image in a straight line to our eye
even if they are reflected rays!
To find the virtual (fictitious) image of
Alex’s chin we extend each reflected
ray backwards in a straight line to
where there are no real rays
Bob looks at
Alex's image
Mirror
To find the location of his hair in the virtual image we extend any reflected ray from his hair backwards
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2nd & 3th NUTS Workshop ( Jan 2010)
How is an image produced in a mirror?
Part 3: The meaning of a virtual image
If we trace rays for every ray from
every part of Alex which reflects in the Alex
mirror we get a virtual image of the
real Alex behind the mirror. It is
virtual because there is no light energy
there, no real rays reach it, and it cannot
be seen by putting a screen at its
position!!
• When all of the reflected rays from
Alex's chin are traced backwards
they all appear to come from the
virtual image of Alex’s chin
– Hence Alex's image is always in
the same place regardless of
where Bob looks

2- Reflection, Refraction
Bob looks at
Alex's image
Mirror
Bob sees Alex's image
in the same place when
he moves his head
Virtual image of Alex
is behind mirror
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2nd & 3th NUTS Workshop ( Jan 2010)
Flat Mirrors Image Location
For simple (flat) mirrors the image location is therefore predictable without
knowing where the observer's eye is and without ray-tracing
Mirror
Mirror
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Mirror
Mirror
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Plane Mirror Exercise 1
Plane Mirror
In the overhead view of the
figure, the image of the stone
seen by observer 1 is at C.
Where does observer 2 see the
image – at A, at B, at C, at D,
at E, or not at all?
Position of an image is defined just as well as position of the object!
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Looking into a Mirror
Looking into a mirror at
yourself:
for an unobstructed, complete
view you only need a mirror,
which is a half of your height.
Question: What is going to happen to your image in
the mirror if you walk away from it?
Answer: Nothing other than it will appear to be further away,
twice the distance of that from you to the mirror.
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Corner Reflector
From the geometry of the corner
Reflector and the law of reflection
An incident light ray reflects in
an anti-parallel direction
independent of the incident
direction!
Adding a third mirror at right angles forms a corner cube which
returns any beam from which it came
Reflecting cubes left on the Moon allows for laser-based
measurements of the Moon’s distance to within 15 cm!
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Multiple Mirrors & Virtual Image
A virtual image can act as a real object and have its own virtual image

Question: Where are the
images of Alex in the 2
mirrors?
a) At A only
b) At B only
c) At A and B only
d) At C only
e) At A, B and C
Mirror
Alex
B
Mirror
A
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C
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“a Mirror Image”
Mirrors are known to turn left into right, that
is to make the image of your left hand look as
your right hand.
It is this effect that gives rise to the expression
“A Mirror Image”
(or “A Specular Image”)
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Chirality
The mirrors actually do a very
special transformation, known
as inversion, which cannot be
reduced to translations and
rotations…
Maybe to turning
inside out? ...
Chiral objects and chiral
molecules…
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Refraction of Light - 1


When a ray of light traveling through a transparent medium
encounters a boundary leading into another 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
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2nd & 3th NUTS Workshop ( Jan 2010)
Following the Reflected and Refracted Rays





Ray  is the incident ray
Refraction is a way to
Ray  is the reflected ray
bend light beams!
Ray  is refracted into the lucite
Ray  is internally reflected in the lucite
Ray  is refracted as it enters the air from the lucite
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2nd & 3th NUTS Workshop ( Jan 2010)
Refraction of Light - 2

The incident ray, the
reflected ray, the refracted
ray, and the normal all lie
in the same plane

The angle of refraction, θ2,
depends on the properties
of the two media (the
refractive index of media
n1, n2 related to speed of
light in the media)
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2nd & 3th NUTS Workshop ( Jan 2010)
Refraction Law (Snell’s Law)
The angle of refraction depends
upon the two materials and the angle
of incidence
sin θ1 n 2

 constant
sin θ 2 n1
The path of the light through the
refracting surface is reversible
Refraction occurs because the speeds of
light, v1 and v2, are different in the two
media
The index of refraction n, of a medium
is defined as
speed of light in vacuum
c
n

speed of light in the medium v
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2nd & 3th NUTS Workshop ( Jan 2010)
Refraction Law and Speeds (of light)
In terms of speeds the law of
refraction becomes:
sin θ1 n 2 c/v 2 v1/c v1




sin θ 2 n1 c/v1 v 2 /c v 2
Snell’s law of refraction is
written in a form symmetric to
the incident and refracted
beams:
n1sinθ1  n 2sinθ 2
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Table of Refraction Index
For a vacuum, n = 1
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Example of Snell’s Law
What is the maximum θ1 for which the beam
will emerge through the bottom of the glass
cylinder?
n sinθ
1
sin q 2 
1
 n 2sinθ 2 , n air  1, n glass  1.52
h/2
h / 22  h2
 1 / 5  0.447
sin q1  nglass sin q 2  1.52  0.447  0.68
q1  sin 0.68  42.80
1
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
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Refraction of Light - 3
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Refraction of Light - 4
When light refracts into a material,
where the index of refraction is
higher, the angle of refraction is
less than the angle of incidence
The ray bends toward the
normal
2- Reflection, Refraction
When light refracts into a material,
where the index of refraction is
lower, the angle of refraction is
greater than the angle of incidence
The ray bends away from the
normal
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Example of Refraction Law
n3  n1  n2
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Another Example of Refraction Law
A material has an index of refraction that increases continuously from top to
bottom. Of the three paths shown in the figure below, which path will be the
path of a light ray as it goes through the material?
(b). When light goes from one material into one having a higher index of refraction, it
refracts toward the normal line of the boundary between the two materials. If, as the
light travels through the new material, the index of refraction continues to increase,
the light ray will refract more and more toward the normal line.
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2nd & 3th NUTS Workshop ( Jan 2010)
Strange Refraction
When light refracts into a material,
Snell’s law of refraction :
where the index of refraction is lower,
the angle of refraction is greater than
1
1
2
the angle of incidence
The ray bends away from the
We have
1
normal
n sin θ  n sin θ2
n  n2
What if q1 is so large that also
n1 sin q1  n2
That we always have
n1 sin θ1  n2 sin θ2
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?
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2nd & 3th NUTS Workshop ( Jan 2010)
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


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
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2nd & 3th NUTS Workshop ( Jan 2010)
Fish Watch
The fish sees the entire world above surface in a cone
of half angle θc. Looking beyond this cone, it sees ??
And what does the fish see beyond the cone??
Reflections back into the water, other creatures of the deep.
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2nd & 3th NUTS Workshop ( Jan 2010)
Critical Angles
n2
sin q c 
for n1  n2
n1
Glass and air:
Water and air:
Air and vacuum:
n2
1
1

q c  sin (2 / 3)  42
n1 1.5
n2
1
1
q c  sin (0.75)  49

n1 1.33
n2
1

q c  88.8
n1 1.00022
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2nd & 3th NUTS Workshop ( Jan 2010)
Hot and Cold Air

Critical angle - an angle of incidence which result in an angle of
refraction of 90°
Cold air and hot air with 10% lower index of refraction
n2 1.0002
q c  89.6

n1 1.00022
2- Reflection, Refraction
It is still 0.4° from the surface!
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Optical Illusions
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Prisms as excellent reflectors
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Optical Fibers
sin q c 
Total internal reflection at the boundaries between the
core and cladding.
ncladding
ncore
q c  90  2
sin 2  sin 1 / ncore
At high angles on incidence (grazing angles) only small differences of indices
of refraction between the core and cladding are needed. They are made of two
different kinds of glass.
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Dispersion





The index of refraction in anything
except a vacuum depends on the color
(wavelength) of the light
This dependence of n on λ is called
dispersion
The index of refraction for a material
usually decreases going from violet to
re (with increasing wavelength)
The angle of refraction when light
enters a material depends on the color
(wavelength) of the light
Violet light refracts more than red
light when passing from air into a
material
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Prism Dispersion
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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
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