1. Review: Laws of Reflection and Refraction
Law of Reflection
A reflected ray lies in the plane of incidence
The angle of reflection is equal to the angle of incidence
Medium 1
Law of refraction
A refracted ray lies in the plane of incidence
The angle of refraction is related to the angle of incidence by
Snell’s Law
Where λ is the wavelength in vacuum
Medium 2

2. Demo 7A-05 Candle Illusion

3. Total Internal Reflection
All light can be reflected, none refracting, when light travels from a medium of higher to lower indices of refraction.
medium 2
medium 1
e.g., glass (n=1.5) to air (n=1.0)
But θ1 cannot be greater than 90 degrees !
In general, if sin θ1 > (n2 / n1), we have NO refracted ray;
we have TOTAL INTERNAL REFLECTION.
Critical angle above which this occurs.

4. ©2008 by W.H. Freeman and Company

5. Examples Fish’s view of the world Prism used as reflectors
(e.g., glass with n=1.5)
Optical fiber
in air
(e.g., glass with n=1.5)
in water

6. READING QUIZ 1 One of the following statements is incorrect.
A laser emits light which has a very long coherence length.
B) An incandescent lamp emits light that has a coherence length
of about three meters.
The Helium-Neon laser emits light through Spontaneous Emission
of photons from an excited state of Helium.
D) The photon energy increases with the frequency of the light.

7. Chromatic Dispersion
The index of refraction of a medium is usually a function of the wavelength of the light. It is larger at shorter wavelengths.
Consequently, a light beam consisting of rays of different wavelength (e.g., sun light) will be
refracted at different angles at the interface of
two different media. This spreading of light is
called chromatic dispersion.
White light: It consists of components of nearly all the colors in the visible spectrum with approximately uniform intensities.
The component of a beam of white light with shorter wavelength tends to be bent more.
Spectrometer (such as a prism)

8. Mirage and Rainbow Mirage rainbow water droplet red is outside.
intensity max at 42

9. Double Rainbow Secondary rainbow Two Interactions Primary rainbow
One Interaction

10. DEMO 7A-20 Effect Of Warm Air on Laser light

11. Warm up quiz 2
Unpolarized light is incident on two polarizers.
The axes of the two polarizers are rotated by
30 degrees with respect to each other. If the intensity of the unpolarized light is IO what is the intensity of the light after it passes through both
polarizers?
√3/2 IO
1/2 IO
3/8 IO
D) 3/4 IO

12. Polarization of Electromagnetic Waves
Polarization is a measure of the degree to which the electric field (or the magnetic field) of an electromagnetic wave oscillates preferentially along a particular direction.
Linear combination of many linearly polarized rays of random orientations
components
partially polarized
linearly polarized
unpolarized
Looking at E head-on
unequal y- and z-amplitudes
equal y- and z-amplitudes

13. Polarizer: polarization by absorption
An electric field component parallel to the transmission axis is passed by a polarizer; a component perpendicular to it is absorbed.
transmission axis
dichroism (tourmaline, polaroid,…)
So if linearly polarized beam with E is incident on a polarizer as shown,
Zero if θ=π/2, or if IO =0
If unpolarized beam is incident instead,
Polarization can rotate in time if linearly polarized beams of different phases are combined.

14. Example: two polarizers
This set of two linear polarizers produces LP (linearly polarized) light. What is the final intensity?
P1 transmits 1/2 of the unpolarized light:
I1 = 1/2 I0
P2 projects out the E-field component parallel to x’ axis:
= 0 if θ = π/2
(i.e., crossed)

15. Demo 7B-22 Two Polarizer Effects

16. Polarization by Reflection
Unpolarized light can be broken
into two components of equal
magnitude: one with its electric
vector perpendicular to the
plane of incidence and the other
with its electric vector parallel
to the plane of incidence.
The reflected (or refracted) light
is partially polarized: due to
difference in the reflectivity of
the two components (larger for
the perpendicular component).
Full polarization occurs at Brewster’s angle where

17. DEMO 7B-23 Polarization by Reflection

18. Example: Sunglasses cut down glare
transmission axis

19. 10:30 QUIZ 3 November 15, 2011
Light is emitted internally in a fluid which has an index of refraction of refraction n =1.75. At the plane interface with the air, what is the critical angle for total internal reflection? Remember the angles are defined with respect to the normal to the plane interface. A) θC = 44.6o B) θC = 34.8o C) θC = 65.2o D) θC = 27.3o

20. 11:30 QUIZ 3 November 15, 2011
Light is emitted internally in a fluid which has an index of refraction of refraction n =2.10. At the plane interface with the air, what is the critical angle for total internal reflection?
Remember the angles are defined with respect to the normal
to the plane interface.
A) θC = 48.2o
B) θC = 14.5o
C) θC = 35.2o
D) θC = 28.4o