Chapter 6. Light Source and Detectors

Quantum- element units of energy

Quantum optics: photoelectric effect

laser emission

blackbody radiation

6.1 Light Sources

1. Light Sources

An object is a source of light.

A direct source produces light, e.g. the sun, light bulb, fire.

An indirect source does not produce light, e.g. an illuminated object.

An extended object may be regarded as a set of point sources.

(a) Thermal source: sun, wax candle, kerosene lanterns, electric light bulb

light--the consequence of the temperature kerosene lanterns: carbon freed by the combustion process

electric light bulbs: a filament is heated. carbon filaments, metal filaments

Incandescent lamps: be heated to incandescence

Refractory metals: a high melting point

Tungsten: 3410C ; evaporates,

Some halogens( iodine), retard the process

How tungsten filaments works

(b) Fluorescent lamps

Fluorescent lamps

High-pressure mercury lamps

High-pressure xenon lamps

(c) Stimulated emission: laser, LED

2. Blackbody Radiators

(a) Black body(a) Black body : is an ideal absorber, also a perfect emitter A good way of making a blackbody is to force reflected

light to make lots of reflections: inside a bottle with a small opening

6.1 Light Sources

The spectral distribution of that radiation is a function of temperature alone; the material as such plays no role

Classical theory failed Ultraviolet catastrophe

Quantization of Energy

Planck’s hypothesis: An object can only gain or lose energy by absorbing or emitting radiant energy in QUANTA.

Max Planck (1858-1947)Max Planck (1858-1947)Solved the “ultraviolet Solved the “ultraviolet catastrophe”catastrophe”

All waves have: frequency and wavelength

symbol: Greek letter “nu”) Greek “lambda”)

units: “cycles per sec” = Hertz “distance” (nm)

Electromagnetic Radiation

Note: Long wavelength small frequency

Short wavelength high frequency increasing

wavelengthincreasing frequency

E = h •

Energy of radiation is proportional to frequency.

where h = Planck’s constant = 6.6262 x 10-34 J•s

Light with large (small ) has a small E.

Light with a short (large ) has a large E.

(b) Photon: (b) Photon: the oscillators emit energy, as discrete, elemental units of energy called quanta or photons

Photons

Light also behaves as a stream of particles, called photons.

Light has “wave-particle duality” , meaning that it behaves as waves and as particles.

This is a concept in quantum mechanics.

(c) Black-body radiation (c) Black-body radiation is electromagnetic radiation that is in is electromagnetic radiation that is in thermal equilibrium at a temperature T with matter that can thermal equilibrium at a temperature T with matter that can absorb and emit without favouring any particular wavelengthabsorb and emit without favouring any particular wavelength

(d)d) Plank’s radiation lawPlank’s radiation law

1

1/5

1

2 TCe

CM

3. Wien's Displacement Law 6.1 Light Sources

plot Planck's law for different temperatures

increasing temperature

more energy is emitted

the peak emission shifts toward the shorter wavelengths

KmT

3

max

108978.2

The temperature and the wavelength of maximum intensity satisfy Tmax=constant

Black-Body Radiation

Hole in a cavity is a perfect absorber a perfect emitter

Called a Black Body Wien’s law

T

Kmm 898.2max

Example - Wien’s Law What is the peak radiation emitted by an

object at 100oC ?

This is in the far infrared. What T required for middle of visible range?

T

Kmm 898.2max

nm 7770

K 373

Kmm 898.2

max

Kmm 898.2

T2.898 mm K

5000 K580 nm

Blackbody Radiation: Experimental Results

At 310 Kelvin (=37oC = 98.6oF), only get IR

Intensity

wavelengthUV IRblue yellow red

Blackbody Radiation:Experimental Results At much higher temperatures, get visible look at blue/red ratio to get temperature

Intensity

wavelengthUV IRblue yellow red

Temperature of the Sun

When we look at the visible spectra of the sun, we see that it’s intensity peaks at about 500 nm (green light). From the equation:

= b/T (where b = 2.9 x 10-3m*K)

we get: T = b/ = (2.9 x 10-3m*K) / 500 x 10-9m

6000 K .

4. Stefan-Boltzmann's Law 6.1 Light Sources

The total energy density inside a blackbody cavity is given by integration over all wavelengths

4

0TdMM

Note that Intensity increases with T42

8

Km

W1067.5

Temperature must be in Kelvin, where size of one Kelvin is same as size of one degree Celsius, but T=0K is absolute zero, and T=273K = 0oC (freezing).

5. Klrchhoff's Law 6.1 Light Sources

Kirchhoff's law :an object that is a good radiator at a given wavelength is also a good absorber at the same wavelength

Stefan-Boltzmann's law for gray bodies

factor : the emissivity of the surface

4TM

•Recall that a good absorber is also a good emitter, and a poor absorber is a poor emitter. We use the symbol to indicate the blackness ( =0) or the whiteness (=1) of an object.

Example

If you eat 2,000 calories per day, that is equivalent to about 100 joules per second or about 100 Watts - which must be emitted.

Let’s see how much radiation you emit when the temperature is comfortable, say 75oF=24oC=297K, and pick a surface area, say 1.5m2, that is at a temperature of 93oF=34oC=307K:

Memitted = AT4 =

(5.67x10-8W/m2K4)*(.97)*(1.5m2)*(307K)4 = 733 Watts emitted!

Example continued

But this is not the whole story: besides emitting radiation, we receive radiation from the outside: Mabsorbed = AT4 =

(5.67x10-8W/m2K4)*(.97)*(1.5m2)*(297K)4 = 642 Watts absorbed!

Hence, the net power emitted by the body via radiation is: Mnet = 733 Watts - 642 Watts = 91 Watts. The peak of this radiation is at:

peak = b/T = 2.9x10-3m*K / 307K = 9.5m which is in the infrared (as expected).

6.2 Detectors

thermal detectors

based on absorption and heating

If the absorbing material is black, they are independent of wavelength.

quantum detectors.

based on photoelectric effect

Quantum detectors are of particular interest, both theoretical and practical; some of them are so sensitive they respond to individual quanta.

6.2 Detectors

1. Thermal Detectors

slow to respond

Golay cellGolay cell

a thin black membrane placed over a small, gas-filled a thin black membrane placed over a small, gas-filled chamber. Heat absorbed by the membrane causes the gas to chamber. Heat absorbed by the membrane causes the gas to expand, which in turn can be measured, either optically (by expand, which in turn can be measured, either optically (by a movable mirror) or electrically (by a change in a movable mirror) or electrically (by a change in capacitance). capacitance).

used in the used in the infraredinfrared..

6.2 Detectors ThermocoupleThermocouple

a junction between two dissimilar metals. As the junction a junction between two dissimilar metals. As the junction is heated, the potential difference changes. In practice, two is heated, the potential difference changes. In practice, two junctions are used in series, a junctions are used in series, a hot junctionhot junction exposed to the exposed to the radiation, and a radiation, and a cold junctioncold junction shielded from it. The two shielded from it. The two voltages are opposite to each other; thus the detector, voltages are opposite to each other; thus the detector, which without this precaution would show the absolute which without this precaution would show the absolute temperature, now measures the temperature differential.temperature, now measures the temperature differential.

thermopilethermopile

contains several thermocouples and, therefore, is contains several thermocouples and, therefore, is more more sensitivesensitive. .

6.2 Detectors

bolometerbolometer

contains a metal element whose electrical resistance contains a metal element whose electrical resistance changes as a function of temperature; if instead of the changes as a function of temperature; if instead of the metal a semiconductor is used, it is called a metal a semiconductor is used, it is called a thermistorthermistor. .

Unlike a thermocouple, a bolometer or thermistor does Unlike a thermocouple, a bolometer or thermistor does not generate a voltage; they must be connected to a not generate a voltage; they must be connected to a voltage source. voltage source.

6.2 Detectors 2. Quantum Detectors

the wavelength of the light plays an important role

there is a certain threshold above which there is no effect at all, no matter what the intensity

intense light and dim light cause same of an effect

Photoelectric effect demonstrates the particle nature of light

Number of e- ejected does NOTdepend on frequency, rather it depends on light intensity.

No e- observed until lightof a certain minimum E is used.

Photoelectric EffectAlbert Einstein (1879-

1955)

Photoelectric Effect (2)Photoelectric Effect (2)

Experimental observations can be explained if light consists of

particles called PHOTONS of discrete energy.

• Classical theory said that E of ejected electron should increase with increase in light intensity — not observed!

Discrete Packets of Energy

6.2 Detectors

plate M(photocathode) when irradiated, releases electrons (called photoelectrons)

collector plate C(anode) photoelectrons released by M are attracted by, and travel to C.

As the potential V, read on an high-impedance voltmeter, is increased, the current, I, read on an ammeter, increases too, but only up to a given saturation level, because then all of the electrons emitted by M are collected by C.

V

A

Light

e-

Variable powersupply

6.2 Detectors if C is made negative, some photocurrent will still exist, provided the electrons ejected from M have enough kinetic energy to overcome the repulsive field at C. But as C is made more negative, a point is reached where no electrons reach C and the current drops to zero. This occurs at the stopping potential, V0.

In short: A significant amount of photocurrent is present only if the collector, C, is made positive

When the frequency of the light is increased, the stopping potential also increases.

The electron photo-current can be stopped by a retarding potential. Increasing the light intensity do not change the retarding potential.

6.2 Detectors

If more intense light falls on the photocathode, it will release more electrons but their energies, and their velocities, will remain the same.

The energy of the photoelectrons depends on the frequency of the light: blue light produces more energetic photo-electrons than red light.

The response of a quantum detector is all but instantaneous: there is no time lag, at least not more than 10-8 s, between the receipt of the irradiation and the resulting current.

The light is received in the form of discrete quanta.

Part of the energy contained in a quantum is needed to make the electron escape from the surface; that part is called the work function, W.

Only the excess energy, beyond the work function, appears as kinetic energy of the electron. The maximum kinetic energy with which the electron can escape, therefore, is

KEmax = h - W

Einstein's photoelectric-effect equation.

6.2 Detectors

Einstein suggested that the linear behaviour is simply a Conservation of Energy.

Energy of Light =Energy needed to get out +Kinetic Energy of electron.

h = W + KE

KE = h - W

Example - Photoelectric Effect

Given that aluminum has a work function of 4.08 eV, what are the threshold frequency and the cutoff wavelength?

15-15

4.08 eV10 Hz

4.14 10 eV scf h

c

c f

c

1240 eV nm300 nm

4.08 eVc

hc

6.2 Detectors

It is often convenient to measure energies on an atomic scale not in joule but in electron volt, eV.

1 eV = (1e)(1V) = 1.60 6 10-19 J

E

eVnm

eVJ

smJs

E

hc 1240

/106.1

)/103)(1063.6(19

834

Photons and Colors

Electron volts are useful size units of energy

1 eV = 1.6 x 10-19 Coul × 1V = 1.6 x 10-19 J.

radio photon: hf = 6.63 x 10-34 Js × 1 x 106 /s = 6.63 x 10-28 J = 4 x 10-15 eV

red photon: f = c/3 × 108 m/s / 7 x 10-7 m = 4.3 x 1014 Hz, red photon energy = 1.78 eV

blue: = 400 nm; photon energy = 3.11 eV .

6.2 Detectors The work function determines the longest wavelength to which a detector can respond: the lower the work function, the longer the wavelength. The lowest work functions are found among the alkali metals.

Photoelectric Properties Of Some Alkali Metals

Alkali Work function (eV) Threshold (nm)

Sodium 2.28 543

Potassium 2.25 551

Rubidium 2.13 582

Cesium 1.94 639

The Photoelectric Effect on Potassium

500400300200wavelength nm0.411.032.054.11stopping potential eV

Determine the work function W

KE=(hc)(1/) － W

From the graph:The plot is essentially KE vs 1/, so that since

KE=hc/ － W

The intercept when (1/)=0 give W= － KE= － ( － 2eV)=2eV

To obtain Planck’s constant h, we need the slope SThen h=S/c.

S=(4 － ( － 2))/(5 － 0) × 10-3=1.2 * 103 eV nmh = 1.2 × 103 × 1.602 × 10-19×10-9 /(3 × 108) J s = 6.4× 10-34 J s cf (6.626 × 10-34 J s)

6-3. Practical Quantum Detectors

In contrast to thermal detectors, quantum detectors respond to the number of quanta, rather than to the energy contained in them.

The simplest type is probably the vacuum phototube, an example of a photoemissive detector.

6.3 Practical Quantum Detectors

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----

ee--

hvhv

Light strikes photocathode (-)

Photocathode emits photoelectrons

Photoelectrons accelerate toward anode (+)

flow of electrons = current

current proportional to # photons incident on photocathode

quantum efficiency:the ratio of the number of photoelectrons released to the number of photons received.

Ordinarily, this efficiency is no higher than a few percent.

Several diodes are combined in series to form a photomultiplier, the efficiency becomes much higher.

• Light strikes photocathode (-)

• Photocathode emits photoelectrons

• Photoelectrons accelerate toward series of increasingly positive anodes (+) at which photoelectrons and secondary electrons are emitted (dynodes)

• Electrons accelerated toward collection anode

6.3 Practical Quantum Detectors

A photocell is the solid-state equivalent of the vacuum photodiode; most often it is a semiconductor.

A semiconductor conducts electricity better than an insulator but not as well as a conductor.

In an insulator, the electrons are tightly bound to their respective atoms.

In a metal, the electrons can move freely; hence, even a small voltage applied to the conductor will cause a current.

6.3 Practical Quantum Detectors

photoconductive detectors : semiconductor, such as cadmium sulfide (CdS), gallium arsenide, and silicon, conduct electricity poorly only in the dark; when exposed to light, they conduct very well.

6.3 Practical Quantum Detectors

photo-voltaic detectors:

made from two semiconductors, one of them transparent to light, for instance a layer of CdS deposited on selenium. When light is incident on the junction, the electrons start moving, but only in one direction producing a current; in other words, the junction converts light energy into electrical energy.

used as solar cells and as exposure meters in photographic cameras.

6.3 Practical Quantum Detectors image tube:not only detects light but also preserves the spatial characteristics of an image.

•contain an array of photoconductors, one for each pixel. When exposed to light, the elements from a latent image that can be read by an electron beam scanning across them.

•the photoelectrons emitted by the cathode can be focused by an electron lens and made visible on a phosphor screen mounted in the same tube.

6.3 Practical Quantum Detectors

•image intensifier:the image is merely amplified.

• image converterthe image is formed in the IR, the UV or the X-ray range and converted into the visible

•microchannel image intensifierthe system is built around an array of many short fibers or capillaries, fused into a wafer.