refraction the invisibility cloak · the invisibility cloak in 1897, h. g. wells created 'the...
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Refraction
&
The Invisibility Cloak
M. Dowlut
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Hunting Fish
Where will you aim your spear if you are fishing?
illusion
At the fish
Close to the fish, as it looks bigger
Close to the fish as there is no fish there
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Hunting FishWhere will you aim your spear if you are fishing?
illusion
At the fish
Close to the fish, as it looks bigger
Close to the fish as there is no fish there
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Phenomenon Associated with Refraction
Credit: https://www.britannica.com/science/refraction
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Refraction of Light
Light travels in straight lines but appears to bend when it
travels into a different medium (substance or matter). This is
due to a change in speed of light.
Table 1. Speed of Light in Various Media
Fastest
Slowest
Media Speed
Vacuum 3.00 x108 m/s
Air Close to vacuum
Water 2.26 x108 m/s
Glass 1.97 x108 m/s
Ruby 1.70 x108 m/s
Diamond 1.24 x108 m/s
Credits:
1.Nelson: Science Perspectives 10; Neslon
Education Ltd (2010)
2. Nelson: Science Connections 10: Neslon
Education Ltd (2011)
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Rules of Refraction1. When Light travels from a “fast” medium
into a “slow” medium, light bends toward
the normal.
Air
Water
incident
ray
refracted ray
i
R
normal
Credit: Nelson: Science Connections 10: Neslon
Education Ltd (2011)
iangle of incidence (angle
between the incident ray and
the normal)
R angle of refraction (angle
between the refracted ray and
the normal)
i is greater than R
=
=
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Rules of Refraction2. When Light travels from a “slow”
medium into a “fast” medium, light
bends away from the normal.
normal
iangle of incidence (angle
between the incident ray and
the normal)
R angle of refraction (angle
between the refracted ray and
the normal)
i is smaller than R
Water
Air
incident
ray
refracted
ray
i
R
Credit: Nelson: Science Connections 10: Neslon
Education Ltd (2011)
=
=
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Rules of Refraction3. The incident ray, the refracted ray
and the normal all lie in the same
plane.
The refracted ray and the
incident ray are on opposite
sides of the boundary and
the normal.
normal
Water
Air
incident
ray
refracted
ray
i
R
Credit: Nelson: Science Connections 10: Neslon
Education Ltd (2011)
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Index of Refraction
The ratio between the 2 speeds is the same as the ratio between the angle of incidence and angle of refraction.
wheren = index of refraction (it is a physical constant)
c = speed of light in vacuum
v = speed of light in mediumNOTE: “n” must always be a value ≥ 1 because “c” will always be larger
than “v”
n = c = sin i
v sin R
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Problem 1:Determine the index of refraction for ruby.
Problem 2:
Determine the index of refraction for diamond.
Sample Problems (Use table 1 from slide 5)
n = c = 3.00 x 108 m/s = 1.8
v 1.70 x 108 m/s
n = c = 3.00 x 108 m/s = 2.4
v 1.24 x 108 m/s
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Refraction in Lenses: What is a lens?
Lens is a transparent object that causes light rays to bend
or refract
There are two types of lenses:
1.Converging or convex
lens:The converging lens is
thicker in the middle and is
thinner at the edges. The
refracted rays come together
(converge) at a point called
the focus (F).
FOFl
Optical centre
PA
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Terminologies in Optical Lenses
Primary Focus or Primary Focal Point (F) is the point through
which light rays parallel to the principal axis
(i) converge through a converging lens
(ii) appear to diverge after going through the diverging lens
Optical Center (O) is the point at the center of the lens
Principal Axis (PA) is the line through the optical center and the
focus on either side
Secondary Focus or Secondary Focal Point (F’) is the focus on
the same side as the incident rays
Focal Length (f) is the distance between the optical centre and the
primary focal point (or secondary focal point)Credit: Nelson: Science Connections 10: Neslon
Education Ltd (2011)
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Refraction on Converging Lens
Light undergoes bending twice (picture 1) when it travels from air through
the lens and from the lens to outside. In picture 2, we usually just draw
the center of the lens as it is thin and depict one refraction as occurring
at the center.
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Rules for Location of Image in a Converging Lens
1. A ray parallel to the principal axis is refracted through the principal focus (F)
2. A ray through the secondary focus (F’)is refracted parallel to the Principal
axis(PA).
3. A ray through the optical centre (O) continues through without any
refraction.
Credit: Nelson: Science Perspectives 10; Neslon Education Ltd (2010)
O
PA
1
23
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S: Size of object (smaller or larger)
A: Attitude (upright or inverted)
L: Location (in front or behind the lens)
T: Type of image (real-can be projected on a screen or
virtual-same side as the object)
SALT Characteristics of Image
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The diverging lens is thinner in
the middle and is thicker at the
edges. The refracted rays
spread apart.
Credit: Nelson: Science Connections 10: Nelson Education Ltd (2011)
Diverging Lenses
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Optical centre
PAF F’
If you want to project
the diverging rays backwards,
it looks as if they come from a
virtual focus
Credit: Nelson: Science Connections 10: Nelson Education Ltd (2011)
Diverging Lenses
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Features of Achromatic Lens
• Consist of two optical components, with two different refractive indices
• Reduces the effect of color dispersion and results in a sharper image as lights of different color are
brought to a sharper focus as seen in figure below:
Credit: https://www.edmundoptics.com/resources/application-notes/optics/why-use-an-achromatic-lens/
Polychromatic Imaging using a Plano-Convex Lens versus an Achromatic Lens
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The Invisibility Cloak
In 1897, H. G. Wells created 'the invisible man'. It took us
more than 100 years to make that a reality. A group of
scientists from Rochester University took advantage of
simple optics that we teach in our schools everyday and
made a device of tomorrow, the invisibility cloak.
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Physics is no different. But perfect paraxial lenses provide a continuous
viewing angles making the hand appear completely cloaked.
t1 = f1 + f2
t2 = 2 f2 (f1+f2)/(f1-f2)
Perfect Paraxial versus Common Lenses
F1 F1F2 F2
t1 t2 t1
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Photo Credit: J. Adam Fenster, University of Rochester
Perfect Paraxial: Multidirectional Cloaking
Inventorship Credit: John Howell, University of Rochester
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F1 F1F2 F2
Why Cloaking?
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The process of shielding something
from view by controlling
electromagnetic radiation using
transformation optics.
Objects are rendered invisible as the
electromagnetic waves are
manipulated around them to make
them disappear.
Metamaterial Cloaking
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ApplicationsEngineers and physicists (Science Now, 2007) have shown that objects
can be hidden by bending of light, sound and water waves.
Antimagnetic cloak can shield an object from a magnetic field.
Potential applications include:
(i) surgeons cutting tissues without seeing their tools
(ii) drivers who can see blind spots without side mirrors
(iii) soldiers can hide from enemies
Credits: https://www.wired.com/2011/09/magnetic-invisibility-cloak/
http://research.ijcaonline.org/volume82/number13/pxc3892289.pdf
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15 cm15 cm t1 t2 t1
WhiteScreen
Viewingposition
Rail
F1 F1F2 F2
The Ray Diagram
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F1 F2
R1
R2
R3
R4
R5 Focal Lengthof F1 lens
Distance from the F1 lens
Hei
gh
t fr
om
th
e ra
il
Sample Result