1. LECTURE 23: Light Propagation of Light Reflection & Refraction
Internal Reflection

2. Propagation of Light: Huygen’s Principle
Each point on a primary wavefront serves as the source of spherical secondary wavelets that advance with a speed and frequency equal to those of the primary wave. The primary wavefront at some later time is the envelope of these wavelets.
plane
wave
spherical
wave

3. Propagation of Light: Fermat’s Principle
The path taken by light traveling from one point to another is such that the time of travel is a minimum.
 constant speed: minimize distance traveled.
 two different speeds: minimize distance traveled at the slower speed.

4. Fermat’s Principle
What's the fastest path to the ball knowing you can run faster than you can swim?
Not the quickest route…
This one is better
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5. Index of Refraction vmedium = c / nmedium
The speed of an electromagnetic wave is different in matter than it is in vacuum.
since e0 > e
vmedium = c / nmedium
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6. Index of Refraction Monochromatic: One wavelength
Chromatic Dispersion: spreading of light according to its wavelength.
medium
index of refraction n
vacuum
exactly 1
air (STP)
H2O (200 C)
1.33
crown glass
1.52
diamond
2.42
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7. Geometric Optics
*Waves whose  << than the objects with which it interacts.
*Assume light propagates in a straight line (rays)
reflected
ray
incident
ray
Material 1
Material 2
refracted
ray
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8. Reflection i -angle of incidence r - angle of reflection
All measured relative to the normal to the interface. i r
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9. Refraction 1 2 n1 n2
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10. Example 1
Which of the following ray diagrams could represent the passage of light from air through glass and back to air? (nair=1 and nglass=1.5)
(a)
(b)
(c)
Air
Glass
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11. Dispersion n(blue)>n(red) Index of refraction frequency white light
1.54
ultraviolet
absorption
bands
Index of refraction
1.52
1.50
frequency
white light
prism
Split into Colors
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12. Dispersion
n()
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13. Total Internal Reflection
incident
ray
reflected
refracted 2 1 r
GLASS
AIR n2 n1
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14. Total Internal Reflection
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15. Relative Intensity of Reflected & Refracted Light
For Normal Incidence:
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16. Quiz 23: November 17, 2015
A light ray travels in a medium with n1 and completely reflects from the surface of a medium with n2. The critical angle depends on
Depends on both n1 n2
n1 only
n2 only
both n1 and n2
neither n1 nor n2

17. Geometric Optics
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18. Refraction
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19. Refraction 1 2 n1 n2 2 1 n1 n2
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20. Snell’s Law 1 1 2 L n1 n2 2
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21. Total Internal Reflection
NOTE: n1 > n2 implies q2 > q1
BUT: q2 has max value = 90o!
q1 > qc
Total Internal Reflection
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22. Quiz lecture 23
A monochromatic ray enters a slab with n1 = 1.5 at an angle qi as shown.
TOP
nair = 1
nglass = 1.5
BOTTOM
nair = 1 qi
A) Total internal reflection at the top occurs for all angles qi, such that sinqi < 2/3
B) Total internal reflection at the top occurs for all angles qi, such that sinqi > 2/3
C) There is no angle qi (0 < qi < 90o) such that total internal reflection occurs at top.
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23. Ray exits to air with same angle as it entered!
Quiz 23. November 12, 2013
A monochromatic ray enters a slab with n1 = 1.5 at an angle qi as shown.
Ray exits to air with same angle as it entered! qi
TOP
n = 1
n1 = 1.5
BOTTOM
n = 1 qi
A) Total internal reflection at the top occurs for all angles qi, such that sinqi < 2/3
B) Total internal reflection at the top occurs for all angles qi, such that sinqi > 2/3
C) There is no angle qi (0 < qi < 90o) such that total internal reflection occurs at top.
Snell’s law:
n sinq is “conserved”
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24. Quiz lecture 23
A ray of light moves through a medium with index of refraction n1 and is incident upon a second material (n2) at angle q1 as shown. This ray is then totally reflected at the interface with a third material (n3). Which statement must be true? n1 n2 n3 q1
N3 is less than n1
n3 < n1
n1 < n3 < n2
n3 > n2

25. Quiz lecture 23
An optical fiber is surrounded by another dielectric. In case I this is water, with an index of refraction of 1.33, while in case II this is air with an index of refraction of 1.00.
Compare the critical angles for total internal reflection in these two cases
a) I > II
b) I = II
c) I < II
Case I
air n =1.00
glass n =1.5
II
water n =1.33 I
Case II
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26. Geometric Optics
In situations in which the length scales are >> than the light’s wavelength, lights propagates as rays
incident
ray
reflected
ray 1 r n1 n2 2
refracted
ray
Reflection:
Refraction:
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