Optical fibers: Total internal reflection at the boundaries between the core and cladding.

At high angles on incidence (grazing angles) only small differences of indices of refraction between the core and cladding are needed.

They are made of two different kinds of glass.

co re

clad d ingc n

ns in

290 c

co ren/s ins in 12

http://www.upscale.utoronto.ca/PVB/Harrison/Flash/Optics/Refraction/Refraction.html

Optical fibers: Total internal reflection at the boundaries between the core and cladding.

Dispersion• The index of refraction in anything

other than vacuum depends on the wavelength of light

• This dependence of n on is called dispersion

• The index of refraction for a material usually decreases with increasing wavelength

• The angle of refraction when light enters a material depends on the wavelength of the light

• Violet light refracts more than red light when passing from air into a material

Dispersion• The index of refraction of a material depends on the wavelength of light the angle of refraction when light enters the material depends on the wavelength

• Violet light refracts more than red light when passing from air into a material

What is the difference in the directions of the two beams, read and blue?There is obviously no refraction at the left (entrance) interface, because the angle on incidence is 0.

Right interface – angle of incidence is = 40. Angles of refraction:

516.1700 n538.1400 n

02.77)642.0516.1(s in)40sin(s in 1700

1700 n

34.81)642.0538.1(s in)40sin(s in 1400

1400 n

32.4700400

θn s ins in )s in(s in 1 nθ

Refraction in a Prism

Prism Spectrometer• A prism spectrometer uses a

prism to cause the wavelengths to separate

• The instrument is commonly used to study wavelengths emitted by a light source

Examples of Spectra.Spectra of emission and absorption; line spectra and continuous spectra…

Using Spectra to Identify Gases

• All hot, low-pressure gases emit their own characteristic spectra

• The particular wavelengths emitted by a gas serve as “fingerprints” of that gas

• Some uses of spectral analysis– Identification of molecules– Identification of elements in

distant stars– Identification of minerals

Reflection and polarization.

Is there any dependence of the intensity of reflected light on the angle of incidence?on polarization of light?

How is the reflected wave created in the first place?

How does it depend on the medium the wave is going to?

The primary source of the reflected wave are oscillating charges in the medium the light is going to.

Therefore the direction of polarization corresponds to the direction of oscillation of the charges.

EM Waves by an Antenna

• Two rods are connected to an ac source, charges oscillate between the rods (a)

• As oscillations continue, the rods become less charged, the field near the charges decreases and the field produced at t = 0 moves away from the rod (b)

• The charges and field reverse (c)• The oscillations continue (d)

How does that apply to the light waves?At a particular angle of incidence, called Brewster angle, the light polarized in the plane of incidence-reflection-refraction does not get reflected at all!

You do not need any special coating – just appropriate polarization.

Brewster angle corresponds to the situation, when the reflected wave is supposed to go in the direction of polarization of the wave inside glass (2nd medium).

The directions of the reflected and refracted waves are set by laws of reflection/refraction.

The charges inside glass oscillate in the direction of polarization ( E ) and cannot radiate the reflected wave.

Brewster angle corresponds to the situation, when the reflected wave is supposed to go in the direction of polarization of the wave inside glass (2nd medium).

The charges inside glass oscillate in the direction of polarization ( E ) and cannot radiate the reflected wave.

Brewster angle can be found from the condition that the refracted ray goes at 90° to the reflected ray. Therefore, angle of incidence + angle of refraction = 180° - 90° = 90°

902

co ss ins in 2221 nnn

co s)90sin (s in 2

12 /tan nnUnder what conditions is the polarizing angle smaller than 45º?

It should be n2 < n1.

Angle of incidence is the Brewster angle: 1

90°

At a particular angle of incidence, called Brewster angle, the light polarized in the plane on incidence-reflection-refraction does not get reflected at all!

By the same token, if the incident light is unpolarized, only the component perpendicular to the plane of incidence gets reflected.

Therefore, the reflected light is perfectly polarized perpendicularly to the plane of incidence-reflection-refraction

A shop window photographed at the Brewster angle without and with polarization filter….

Practical conclusions:If you buy a telescope to look at a star living across the street, try to look at the Brewster angle for air-glass - 56.

Do not forget a good polarization filter (polarizer)!