Physics 117B02 — March 22

“Ray Optics: Reflection, Refraction, Polarization”

Physics 117B— March 22, 2006

Previous lecture: Chapter 32

• Major theme: electromagnetic waveso Predicted by Maxwell, verified by Hertz o Radiation from accelerated charges (e.g., dipoles)o Harmonic (sinusoidal) disturbance of E and B fieldso Travel with speed c in vacuum, c/n in mattero in vacuum, in mattero EM waves transport energy and momentumo Poynting vector gives power/unit area

• Applicationso Solar heating, laser cutting, welding, surgeryo Radiation pressure (e.g., solar “wind”)

E c

B

E c n

B

S 1 0

E

B

Physics 117B— March 22, 2006

Today’s lecture: Chapter 33

• Major themes: reflection, refraction, polarizationo Rays and wavefronts: Huygens’ principle o Reflection and scattering from interfaceso Dispersion and total internal reflection (rainbows)o Refraction of transmitted rays at interfaceso Polarization effects due to reflection and scattering

• Applicationso Why the sky looks blue (Rayleigh scattering)o Why double rainbows exhibit reversed colorso Why cataracts cause blurred visiono Telecommunication through optical fiberso Medical endoscopes and fiberscopes

Physics 117B— March 22, 2006

Terminology

• Light rays travel perpendicular to phase fronts

• Each point on wave front acts as source of secondary spherical or circular “wavelets” … and

• Phase fronts are the tangents to those spheres or circles (Huygens’ principle)

Physics 117B— March 22, 2006

Limits of ray optics

• When observing EM waves at great distances from their source, it is useful to assume that light travels in a straight line (perpendicular to the wavefronts) unless it encounters an obstacle.

Physics 117B— March 22, 2006

Specular vs diffuse

Light incident on smooth reflecting surfaces is reflected at a specular angle; if the surface is rough, the light scatters in many directions from the asperities in the surface, and there is both specular and diffuse reflection.

Physics 117B— March 22, 2006

Fermat’s principle: reflection

t 1c

h12 y2 h2

2 w y 2

dtdy

1c

y

h12 y2

w y

h12 w y 2

0

y

h12 y2

sin i w y

h12 w y 2

sin r

Fermat’s idea was that light follows the geometrical path that minimizes the transit time. Consider the case of reflection from a surface in air. The total transit time from point A to point B is

The minimum travel time is found by taking the derivative with respect to y and setting it equal to zero:

And that implies the law of reflection. QED!

Physics 117B— March 22, 2006

The critical angle for TIR

• Consider light incident from glass (n=1.5) to air (n=1.0) at several different angles (see figure).

• Snell’s law relates the angle of incidence to the angle of refraction.

n1 sin1 n2 sin 2

15˚

25˚

35˚

45˚ ???

c sin 1 n2 n1

At the critical angle …

Physics 117B— March 22, 2006

Application of TIR: prisms

EXAMPLES

• Cameras

• Binoculars

• Periscopes

• High-power laser beams

• Can you think of others?

• Total internal reflection in glass or crystalline quartz prisms are frequently used in optical systems instead of mirrors. The prisms below all are cut at angles of 45˚ and 90˚. Why?

Physics 117B— March 22, 2006

Optical fibers

• Why communicate with light? (in a word, bandwidth!)

• Added advantage: not subject to electrical interference

• Fiber transmission works because of total internal reflection at core-cladding interface

• Fibers can support multiple transmission paths (multi-mode) or only one (single-mode)

Physics 117B— March 22, 2006

How are fibers made?

• A triumph of modern materials science and engineering!

• Requires exquisite purity and precision during the melting and drawing process…

• While making the fibers economically by the ton

Physics 117B— March 22, 2006

Polarization by Polaroid®

• Polarizers work by preferred direction of absorption

• Long, stringy molecules work for visible light

• If you have owned a pair of polarizing sunglasses …

• Have you noticed a change in brightness of sky when you put them on? What does this mean?

I pol Imax cos2

Malus’s law for polarizedlight passing through apolarizer-analyzer pair

Physics 117B— March 22, 2006

Polarization by reflection

• Reflections can polarize light that was initially not polarized … (Brewster’s angle)

• Since scattering is a form of reflection, what happens to polarized light scattered from a rough surface?

• Then why is it smart to wear polarizing sunglasses when driving in bright sunlight?

tan pol ninc

ntrans

The Brewster angle …

Physics 117B— March 22, 2006

Summing up …

• Light rays travel in straight lines until they run into something

• Even when they bump into something, light rays travel the path that takes the shortest time

• In material media (e.g., glass) the speed of light depends on its color (dispersion)

• When light is reflected from, scattered from or transmitted through a surface, it may be polarized

• The degree of polarization caused by reflection depends on the angle of incidence