Natural Sciences Ilecture 13: The Nature and Properties of Light1

LIGHT SOURCES incandescent

Luminous objects are ones that give off light – possibilities include stars (Sun), burning materials, sparks, lightbulbs, hot gases, and chemical reactions. Almost all of the natural light that reaches Earth comes from the Sun. Objects giving off light because of their high temperatures – including the Sun – are said to be .A widely accepted model used to understand the production of light is re-ferred to as the – a unifying model that relates light to electricity and magnetism. According to this model, light is produced whenever a charge is accelerated by an external force...electromagnetic wave model

eF Wave consists of electrical and magneticfields. These exchange energy with oneanother as they move off through space.

Physicists have grappled with the nature of light for centuries. A widely accepted model was elusive in large part because light exhibits properties of both particles and waves. Much of this lecture is devoted to reviewing and contrasting those properties. Even today there are some aspects of the behavior of light that are not fully "rationalized" – that is, understood in the context of a general model. (next page)

The wave is shown as propagating in one direction, but bear in mind that it actually moves outward on a spherical surface all directions. Also note that:transverse "vibration" occurs in all directions perpendicular to the direction of propagation, andunlike most other wave phenomena, light can exist without a medium – it can propagate through a vacuum

A cartoon:

2

"old corpuscular"scalar wavevectorial waveelectromagneticquantum (particle)

Greeks, Newton(~1700)Huygens(late 1600s)Fresnel(early 1800s)Maxwell, Hertz(mid 1800s)Planck, Einstein(early 1900s)

rectilinear propagation, refraction, reflectioninterference, diffractionpolarization, double refractionconstant speed in vacuum; constant ratio between mediaphotoelectric effect; Compton scattering; Raman effect

THEORY PROPONENTS(among others) PHENOMENA EXPLAINED

Back to light sources...

blackbody radiation

We saw on page 1 that light – or, more generally, electromagnetic radiation – is emitted whenever a charge is accelerated. The frequency of the emitted wave depends upon the magnitude of the acceleration: the greater the acceleration, the higher the frequency.Remember that visible light is only a small part of the electromag-netic spectrum

The visible electromagnetic radiation we call incandescence is emitted only at high temperatures. However, all bodies (objects) actually oemit electromagnetic radiation at all temperatures above ~ K. This is referred to as , in reference to an idealized perfect emitter/absorber. According to the electromagnetic wave model, it is the acceleration of charged particles near the surface of an object that causes electromagnetic radiation to be emitted. (next page)

gammarays X-rays UV visible micro -waves TV FM AMradioIR!" = 390 - 790 nm

3The temperature of an object determines the energy available for accelerating charged particles, so :the higher the temperature the higher the average frequency of the blackbody radiationBlackbody radiationfrom an object atthree different temp-eratures. Both theintensity and the fre-quency of the radia-tion increase with in-creasing temperature

5.4E144.9E144.6E14increasing frequency (Hz)

intensity of l

ight(relativ

e)o700 C 500 C1, 5 5 , 00 C

increasing wavelength (m)6.5E-7 6.1E-7 5.6E-7

* Prior to "filtering" by Earth's atmosphere

Sunlight: 51% infrared 40% visible 9% ultraviolet colorredorangeyellowgreenblueviolet

! (nm)790 - 620620 - 600600 - 580580 - 490490 - 460460 - 390increasing wavelength (nm)400800

relative inten

sity

radiationfrom Sun*sensitivity ofhuman eye

infrared ultra-violet

o5,487 C is thetemperature ofthe Sun's surface

4200160120

8040

0400 500 600 700wavelength (nm)

light fromnorth skyu g n l mt n ste a p

Sun

sodium vapor

lamp

ity a 5 nintens t 60 min i y !

tens t at

Light from other sources...

PROPERTIES of LIGHTAs noted earlier – and as we will see in some detail shortly – many of the properties of light are readily explained by wave theory. For ease of discussion, the behavior of light is often discussed in terms of the , most aspects of which as similar to things we discussed in connection with sound waves. A key starting point is that light "rays" travel in straight lines, and that rays from a single source are parallel to one another a long way from the source:"light ray model"

wave frontsrays reallylargedistance

5Interactions of light with matterWhen a light ray strikes an object, one of several possible behaviors can be observed, depending on the properties of the object's surface.

incidentlight

reflected transmitted

absorbedReflectionparallel

diffusenorma

l #r#i #i #r=As we discovered in our treatment of waves a couple of weeks ago, refraction is conceptually trickier than reflection. Let's try a slightly different approach to an explanation this time. The first concept to get straight is the :index of refractionn = cvindex of refractionof medium of interest speed of light in vacuumspeed of light inmedium of interest

in n acide t r y ted rareflec

y

6medium

oair (0 C)oair (30 C)glassdiamondicewateralcohol

n = c/v1.000291.000261.502.421.311.331.36

Refractive indicesof some familiar media:

The angle of refraction is not equal to the angleof incidence. Let's try to understand why...norma

l#r

#i #i #r=Illustration of refraction (lower v)as light enters amedium of higher refractive index

incident ray fa e a

re r ct d r y

(*after S. Glashow; "From Alchemy to Quarks"; Brooks/Cole 1994)

Schematic of a light wave*light speed

!arrows show instantaneousorientation of electric field entire pattern moving at light speed

The only misleading aspect of this schematic representation is that itsuggests alternation of the electric field strictly in a plane. This is notgenerally the case (although it is for polarized light, as we'll see)...

7

normal

#r#i

#i #r=

REFLECTIONLet's use theschematic onp. 6 to revisitreflection andrefraction...(see lecture 10)

!i

normal

#r

#i

!r#i #r=AB

n > nB Arefractive index: v < vB Alight speed:

f = fB Av = !f

frequencies mustmatch at the interface!(see page 6 of lecture 10)

Wave Equation

! < !r i.. .

First, how about a light ray passing into a medium of higher n?REFRACTION

8

!i normal#i

#r

#i #r=ABn < nB Arefractive index: v > vB Alight speed:

f = fB Av = !f

frequencies mustmatch at the interface!

Wave Equation

! > !r i.. .

Now let's try a ray passing into a medium of lower n?REFRACTION (cont'd)

!r

sin # v ni A Bsin # v nr B A= = Snell's Law of refractionUnder the right circumstances,refraction of light allows you tosee around corners

9Refraction in a prism and in lensesAs long as we're on the subject of refraction and refractive indices, let's revisit an old friend – the prism. A prism disperses the colors (wavelengths) of visible light because the various wavelengths are slowed by different amounts as they enter the glass of the prism. Since their speeds in the glass are different, they are refracted at different angles: The higher the fre-quency of the light (i.e., the shorter the wavelength), the more it's path is "bent" in the prism.redorangeyellowgreenblueindigoviolet

h e ligw it ht

The separation of white (polychromatic) light into its constituent wave-lengths is referred to as . Some materials are better at this than others; diamond is excellent, which is the main reason for its brilliant "fire". Dispersion of sunlight by myriad raindrops produces rainbows.The general phenomenon of refraction is exploited in virtually every common optical device, ranging from the simple magnifying glass to eyeglasses, telescopes, microscopes and cameras (even eyeballs) – anything that uses a lens:

dispersion

light raysconvergingdiverging

In general, glasses exhibiting low disper-sion are desirable for use in lenses. High dispersion would cre-ate "color fringes" around imaged ob-jects.

10REFRACTION: What is wrong with this picture??A sketch like the one below illustrating refraction of light in a prism appeared in a basic textbook written by a (living) Nobel laureate physicist. It's likelythat he would catch the errors in the drawing now, but they were not noticed when the book went to press. Given what you've learned about refraction, can you explain what's wrong?

whi e l ghtt ivioletindigobluegreenyelloworangered

The Critical Angle in refractionAs described on pages 7-9, light rays are "bent" or redirected when the light enters a medium having a different refractive index. If the angle of incidence is just right, the refracted ray can be redirected along the interface o(i.e, the angle of refraction can be 90 )...

waterairo90total reflection

critical angle

11Now for something completely different...

Consider waves on a swimming pool generated by a pulsating board at one end:DIFFRACTION

"shadow"

"shadow"

no shadows

A wide opening in an obstacle has little effect on the wavefronts other than to create shadows.

Wavecrests (analogous to wavefronts) propagate in a straight path

A narrow opening in the obstacle (~ 1!) acts as a "point source" of waves on the other side, leaving no shadows.

view incross-sectionviews from top

12Newton's views about light...Newton knew that water waves exhibit the behavior shown in the bottom panel on page 9. This could be thought of as "bending" of waves around corners under certain circumstances. Because Newton believed that light always casts a shadow, he surmised that light does not show this behavior and therefore must not be a wave phenomenon. What he didn't know, of course, is that the wavelength of light is extremely short, so a very narrow slit is needed to see the effect. is also required – that is, the light must be of a single wavelength.Diffraction is nicely illustrated by passing a monochromatic beam of light through two parallel slits...Monochromatic light

monochromaticlight source

two slits of width d< 1 mm wide

This experiment was first done by Thomas Young in 1801

parallel brightlines on screenlines are equal-ly spaced, with separation of !L/dL

What's going on in this demonstration?Where intersections of the diffracted wave fronts occur, there is constructive interfer-ence of the waves – and bright lines appear on the screenincident beamwavefronts

screen

diffractedwavesQuestion of the day: Can you explain why the discrete bright lines would not be produced if the light were polychromatic?

13

Thomas Young and later A.J. Fresnel (in 1821) demonstrated that the diffraction behavior illustrated on page 11 is . consistent with light behaving as a waveDESTRUCTIVE INTERFERENCE

aba+b CONSTRUCTIVE INTERFERENCE

aba+b

Recall from lecture 10...

unpolarized light waveelectric fieldorientations

plane polarizedlight wave

POLARIZATION – a final line of evidence for the wave nature of light

In the transverse wave model of electro-magnetic radiation, the electric field (i.e., the "vibration" direction) assumes all orientations perpendicular to the direction of propagation. Polarization of the wave restricts the vibration to a single plane

14Materials possessing an "oriented" electronic structure can polarizelight waves passing through them – which is strong evidence thatlight is a transverse wave... The polarizer could be a single crystal or an organic polymer ("plastic") with aligned molecules. The latter is what Edwin Land developed in the 1930s, and what is still used in Polaroid ® sunglasses.

Two polarizers can block the light wave altogethero oReflected light is partially polarized (for # between ~1 and 89 ). Thisioccurs because the component of the wave that is parallel to thereflecting surface is reflected more efficiently. Polarization is totalat a specific value of # (depends on the material).i

15LIGHT AS A BEAM OF PARTICLES

photoelectrons

Electromagnetic radiation is a form of energy (remember radiant energy from back before the first exam?). As discussed last class, some of the kinetic energy of vibrating molecules at the surfaces of objects is converted into electromagnetic radiation, which travels off through space.A few weeks ago we also observed that radiant energy (electromag-netic waves) is usually converted into heat when it "shines" on an object – the radiant energy stimulates vibration of molecules in the surface of the receiving object. It turns out that heating of a surface is not the only response to incident radiation – can also be produced. These are detectable with a simple device...

(+)( )

( ) (+)el ghti

0amps

THE PHOTOELECTRIC EFFECTThe incident light causes ejection of electrons from the surface of the negative-ly-charged metal plate (this is the photoelectric effect). The electrons are readily detected because they are drawn to the positively-charged plate, creating a current in the circuit.This is the principle upon which solar cells are based.An intriguing characteristic of the photoelectric effect is that – i.e., whether the light source is bright or dim. The intensity of the light determines photoelectrons are produced, but not their kinetic energy. This observation is difficult to explain in terms of the transverse wave model of light. The wave model predicts that the energy of the electrons should be proportional to the intensity of the light. Is there anything that does affect the energy of the photoelectrons? Ans: YES – (which must exceed a critical minimum value).

the kinetic energy of the photoelectrons produced by the incident light is unrelated to the light intensity how manythe wavelength of the incident light

16Another (big) problem with the wave model...

E = n h f

PHOTONSE = h f

About 100 years ago, Max Planck demonstrated that the blackbody radiation emitted from hot objects does not represent a continuum of energies. The distribution can be explained only if the emitted waves are quantized – that is, packaged in discrete quantities (this was a truly radical idea at the time). Planck developed the theory of "quantization" of energy: The vibrating molecules that produce blackbody radiation vibrate only at specific frequencies, and they emit radiation only of specific energies. The quantized energy is given by

Five years after Planck's seminal work, Einstein used Planck's idea in revisiting the photoelectric effect. He described the energy in a light wave in terms of – that is, small packets, or quanta, possessing specific amounts of energy. The energy of the photons in a monochromatic beam of light is related to the frequency of the light through Planck's constant

frequencyPlanck's constant(6.626E-34 J-s)an integer (1,2,3,...)

The jury is still outSo, when all is said and done, is light a wave or a photon beam? The somewhat unsatisfying answer is that light exhibits properties of both waves and particles. We use whichever model suits the needs of the moment. (Light is one topic on which we get to have our cake and eat it, too!). In our acceptance of this dilemma, there's an implicit understanding that light is unique – as a scientific phenomenon, it has no perfect analogs in other, more familiar, phenomena.