Transcript ray_optics_su2014

Light & Optics
Light Phenomena: Reflection,
Refraction, Dispersion
Updated 2014Jul23
Dr. Bill Pezzaglia
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Outline
A.
The Law of Reflection
1.
2.
3.
B.
The Law of Refraction
1.
2.
3.
C.
Fermat’s principle, Snell’s Law
Critical angle, total reflection
Refractive images
Dispersion of Light
1.
2.
3.
D.
Reflection Law of Euclid and Heron
Images in a Mirror
Reflection Intensity
Prism disperses colors
Newton’s experiments
Sellmeier equation
References
A. Reflection
1. The law of reflection (principle of
least distance)
2. Image in a plane mirror
3. Intensity of Reflection
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A. Law of Reflection
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1. The Law of Reflection
(a) The Law of Reflection (Euclid 300 BC)
b. Principle of Least Distance
• Heron of Alexandria
Light follows path of least distance
(e.g. when reflecting off of water)
•Which path should an ant take to get to the opposite
end of the box fastest?
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2. Mirror and Virtual Images
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“real” you
mirror only
needs to be half as
high as you are tall. Your
image will be twice as far from you
as the mirror.
“image” you
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3. Reflection & Transmission
• Speed of light can be calculated from
electrical permittivity () and magnetic
permeability () properties of the media
• Speed of light “v” in media is slower
where “n” is index of refraction (about
1.5 for glass).
• As a wave (such as light) in media 1,
with index n1, enters a denser media
(index n2) where the speed changes,
part of the wave will be reflected.
Reflected intensity given by:
• For glass (n=1.5) we calculate that 4%
is reflected, 96% transmitted
1
c
v

 n
 n2  n1 

R  
 n2  n1 
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B. Refraction
1. Fermat’s Principle of Least Time
& Snell’s law (1621)
2. Total Reflection (Snell’s window)
3. Refractive Images
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1. Fermat’s Principle
Lifeguard Dilemma: What is
the fastest path to drowning
man? Note you can run twice
as fast as you can swim.
•Run straight to river, then
swim
•Run further to shore adjacent
swimmer then swim
•Optimal path obeys Snell’s
Law This is the path light
(sound, any wave) will take!
Lifeguard Tower
1
1
sin 1  sin  2
v1
v2
1b. Snell’s Law (1621)
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n1 sin 1  n2 sin  2
Path of wave is
bent toward
normal when
enters media
with lower
wavespeed (i.e.
higher index of
refraction)
2a. Total Reflection (Snell’s Window)
• At the “critical angle” the
refracted beam is at 90, so it
can’t get out.
• Greater than this “critical
angle” there is 100% reflection
• Snell’s Window: from
underwater a fish sees the
entire area above surface in a
cone. Outside the cone light is
totally reflected
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2b. Total Reflection
• Total reflection will only occur n1 sin  c  n2 sin 90  n2
if going from dense media to
 n2 
less dense!
 c  arcsin  
• For glass (n=1.5) the critical
angle is 42
• Optical fibers are designed so
the light is always 100%
reflected, and bounces down
the fiber.
 n1 
 1 
 c  arcsin    42
 1.5 
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3. Refraction and Images
• The bottom of a river will appear to be
shallower than it really is. Why?
• The apparent depth:
d
d '
n
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C. Dispersion
1. Phenomena
2. Newton’s Experiments
3. Sellmeier Equation
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1. Dispersion of a Prism
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Early theories were that a prism created
color. White light goes in, colors come out.
2a. The Components of Light
1672 Newton shows that the prism does not
create color, it merely separates (“disperses”)
the colors in the white light
The second prism does not create more colors.
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2b. The Components of Light
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1672 Newton further shows that a second prism can
recombine colors to make white light. Hence white
light is a mixture of all colors.
3a. Speed in Media
•
•
•
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In media (such as glass) the speed is slower. This
causes “refraction” the bending of light.
The speed usually depends upon the wavelength,
called “dispersion”. This causes the colors to be
spread out.
This work
was done
by
Newton
3b. Sellmeier Equation (1871)
• In media the speed of light
depends upon wavelength
(color)
• Sellmeier Equation (1871)
shows index of refraction
decreases for bigger
wavelength, approaching n0
• Index of refraction goes to
infinity at “color” 0 of media
(e.g. green for emerald)
n ( )  1 
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n0  1
2
 0 
1  
 
2
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References
•
•
http://www.thestargarden.co.uk/RefractionReflectionDiffraction.html
http://www.olympusmicro.com/primer/lightandcolor/reflectionintro.html