Lecture 23-Lecture 23-11Review: 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

1 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

2 2 1 1sin sinn n Snell’s Law

Medium 1

Medium 2

2 1n n

/ 1i

i

i

i

c n c

f f nn

where is the wavelength in vacuum

Lecture 23-Lecture 23-22Total Internal Reflection

In general, if sin 1 > (n2 / n1), we have NO refracted ray; we have TOTAL INTERNAL REFLECTION.

All light can be reflected, none refracting, when light travels from a medium of higher to lower indices of refraction.

e.g., glass (n=1.5) to air (n=1.0)

1sin

sin

2

1

1

2 n

n

2 1

But cannot be greater than 90 !

12 1sin /c n n Critical angle above which this occurs.

medium 2

medium 1

Lecture 23-Lecture 23-33 Examples

1 1sin 48.8

1.33c

Fish’s view of the world

Prism used as reflectors

Optical fiber

1 1.33sin 62.5

1.5c

in water

1 1sin 41.8

1.5c

in air

(e.g., glass with n=1.5)

1 1sin 41.8

1.5c

(e.g., glass with n=1.5)

Lecture 23-Lecture 23-44Chromatic 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)

Lecture 23-Lecture 23-55Mirage and Rainbow

Mirage

hot air cold airn n

water droplet

rainbow

red is outside.

intensity max at 42

Lecture 23-Lecture 23-66Double Rainbow

Primary rainbow

Secondary rainbow

Lecture 23-Lecture 23-77Polarization 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.

linearly polarized

unpolarized

partially polarized

Looking at E head-on

Linear combination of many linearly polarized rays of random orientations

components

equal y- and z-amplitudes

unequal y- and z-amplitudes

Lecture 23-Lecture 23-88Elliptic (or circular) polarization

1 2 21cos cosE E kz tt E kz ������������� �

1 21 2. ., ,e g E E i E E j

����������������������������

x

y

E rotates unless E1 and E2 are in phase (or out of phase by ).

|E| changes unless amplitudes E1 = E2 and the phase difference is /2.

Elliptic polarization

Constant |E| case is called circular polarization

Lecture 23-Lecture 23-99Polarizer: polarization by absorption

An electric field component parallel to the transmission axis is passed by a polarizer; a component perpendicular to it is absorbed.

20 cosI I cosyE E

So if linearly polarized beam with E is incident on a polarizer as shown,

Zero if =/2, I0 if =0

If unpolarized beam is incident instead,

20 0cos / 2I I I

Polarization can rotate in time if linearly polarized beams of different phases are combined.

transmission axis

dichroism (tourmaline, polaroid,…)

Lecture 23-Lecture 23-1010Non scored test quiz

• A beam of un-polarized lights with intensity I is sent through two polarizers with transmission axis perpendicular to each other. What’s the outgoing light intensity?

a) ½ I b) 2 Ic) 0d) 1.5 I

Lecture 23-Lecture 23-1111

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:

cos12 EE 2EI

2 22 1 0

1cos cos

2I I I = 0 if = /2

(i.e., crossed)

Lecture 23-Lecture 23-1212Polarization by Reflection

• Unpolarized light can be brokeninto two components of equalmagnitude: 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) lightis partially polarized: due todifference in the reflectivity ofthe two components (larger forthe perpendicular component).

Full polarization occurs at Brewster’s angle where

90B r 2

1

tan B

n

n

1 2 2sin sin cosB r Bn n n

Lecture 23-Lecture 23-1313Example: Sunglasses cut down glare

transmission axis

Lecture 23-Lecture 23-1414

Physics 241 –Quiz a

Unpolarized light of intensity I0 is sent through 3 polarizers, each of the last two rotated 45 from the previous polarizer so that the last polarizer is perpendicular to the first. What is the intensity transmitted by this system?

a) 0.71 I0

b) 0.50 I0

c) 0.25 I0

d) 0.125 I0

e) 0

Lecture 23-Lecture 23-1515

Physics 241 –Quiz b

Unpolarized light of intensity I0 is sent through 3 polarizers, each of the last two rotated 60 from the previous polarizer so that the last polarizer is rotated by 120 from the first. What is the intensity transmitted by this system?

a) 0.25 I0

b) 0.125 I0

c) 0.0625 I0

d) 0.03125 I0

e) 0

Lecture 23-Lecture 23-1616

Physics 241 –Quiz c

Unpolarized light of intensity I0 is sent through 3 polarizers. The second one is rotated 90 from the first polarizer, but the last one is again aligned in the same direction as the first. What is the intensity transmitted by this system?

a) 0.71 I0

b) 0.50 I0

c) 0.25 I0

d) 0.125 I0

e) 0