Cool Things Light Does

It moves at about 300,000 km/sec!

Measurements of the Speed of Light

Date Author Method Result (km/s) Error

1676 Olaus Roemer Jupiter's satellites 214,000

1726 James Bradley Stellar aberration 301,000

1849 Armand Fizeau Toothed wheel 315,000

1862 Leon Foucault Rotating mirror 298,000 +-500

1879 Albert Michelson Rotating mirror 299,910 +-50

1907 Rosa, Dorsay Electromagnetic constants 299,788 +-30

1926 Albert Michelson Rotating mirror 299,796 +-4

1947 Essen, Gorden-Smith Cavity resonator 299,792 +-3

1958 K. D. Froome Radio interferometer 299,792.5 +-0.1

1973 Evanson et al Lasers 299,792.4574 +-0.001

1983 Adopted value 299,792.458

Back to the Cool Things Light Does

RefractionLight refracts, which means that it bends when passing from one medium to another. When light enters a more dense medium from one that is less dense, it bends towards a line normal to the boundary between the two media.

Taking Advantage of RefractionThe greater the density difference between the two materials, the more the light bends. One place where this is used is in lenses for a variety of optical devices, such as microscopes, magnifying glasses, and glasses for correcting vision. An example of an image formed from a lens is shown below.

DispersionAnother aspect of light that is quite familiar is dispersion. If a beam of white light enters a glass prism, what emerges from the other side is a spread out beam of many colored light. The various colors are refracted through different angles by the glass, and are ``dispersed'', or spread out.

ReflectionOne obvious property of light is that it reflects off of surfaces. Among other things, this gives rise to the images we see in mirrors.

Internal ReflectionAn effect that combines both refraction and reflection is total internal reflection. Consider light coming from a dense medium like water into a less dense medium like air.

Relect/Refract ComboWhen the light coming from the water strikes the surface, part will be reflected and part will be refracted. Measured with respect to the normal line perpendicular to the surface, the reflected light comes off at an angle equal to that at which it entered, while that for the refracted light is larger than the incident angle. In fact the greater the incident angle, the more the refracted light bends away from the normal. Thus, increasing the angle of incidence from path “1” to “2” will eventually reach a point where the refracted angle is 90°, at which point the light appears to emerge along the surface between the water and air. If the angle of incidence is increased further, the refracted light cannot leave the water. It gets completely reflected. The interesting thing about total internal reflection is that it really is total - 100% of the light gets reflected back into the more dense medium, as long as the angle at which it is incident to the surface is large enough.

Fiber optics uses this property of light to keep light beams focused without significant loss.

RainbowsRainbows are phenomena that involve refraction, dispersion, and internal reflection. In order to see a rainbow, it is necessary to look at a portion of the sky containing raindrops with the Sun directly behind you. White light from the Sun enters the raindrops, and gets refracted and dispersed inside the raindrop.

Maybe Too Much Information

When the dispersed light hits the back of the raindrop it gets internally reflected, and when it emerges it gets dispersed even more. Because it refracts more, blue light always emerges from the raindrop above the red light. Consequently, only one color reaches your eye from any given raindrop. What color you see depends on the angle at which you look.

In general you must look slightly higher up in the sky to see red light and lower to see blue light. So you what you see is a band of color in the sky, with red on top and blue on the bottom, and all the colors of the rainbow in between.

The reason rainbows appear as an arc in the sky is that the colors you see are determined by the angle that your line of sight makes relative to the position of the Sun behind your head. As your look along the blue arc of a rainbow, for example, this angle remains constant.

DiffractionAnother property that light exhibits is that it diffracts, which loosely speaking means it bends around the corner when it passes through an opening.

Interference

The final property of light to discuss is interference, a phenomenon that occurs when two light beams meet.

If the two beams enhance each other to give a brighter beam, it is called constructive interference

If they beams interfere in a way that makes the total beam less bright, it is called destructive interference.

Interference

Described of as a Wave

Clearly, Light Can Be

Waves Seem to WorkThe properties of light we have described - reflection, refraction, diffraction, and interference - can all be explained in terms of light viewed as a wave. The success of these descriptions of the properties of light was a triumph of the wave picture, and by the 1850s this model of light was the generally accepted one.

Review the Properties, Part 1Refraction: is very easily understood within the wave model of light if one recalls that light “slows down” as it enters a more dense medium. The part of the wave front that is already in the water is going more slowly than the part that is still in the air. As a necessity, the wave front in the water “turns” inward.

Review the Properties, Part 2Dispersion: Now that we understand refraction as due to the change in the speed of light as it enters a more dense medium, we can also understand what causes dispersion. All colors of light go at the same speed in vacuum, but they travel at different speeds inside matter. For example, blue light travels a bit faster, in general, than red light. This in turn makes the blue light bend more, and the colors go their separate ways,

Review the Properties, Part 3

Interference: For constructive interference, the waves meet in phase, i.e. so that the crests of each wave coincide. In destructive interference, the waves meet out of phase, so that the crest of one wave coincides with a trough of the other wave, and they cancel each other out.

Review the Properties, Part 4Diffraction: is readily explained in terms of light waves. It is will known that when waves can come in two basic shapes. Plane waves are waves in which the crests are essentially straight lines that follow one another like lines of soldiers walking in formation. Circular waves consist of crests that move out from a point source in circles of ever-increasing radii.

When plane waves come to a barrier, such as a wall, they are stopped. But if the wall has a narrow opening, some of the wave gets through. If the opening is sufficiently narrow, specifically it must be of the same size as the wavelength of the wave, then the part of the wave that gets through is a circular wave, that looks like it is coming from a point source (i.e. the opening).

Light as a Wave Also ExplainsDoppler Shift

We are Familiar With the Shift in Sound Waves

Doppler Shift in Sound Waves

(a) Sound of a train moving towards us is higher pitched

(b) Sound of a train moving away from us is lower pitched

Doppler Shift in Light Waves

QuickTime™ and aGIF decompressor

are needed to see this picture.

If source approaches, light appears bluer than it is.

If source recedes, light appears redder than it is.

Doppler Shift

Wavelength is shorter when approaching

Stationary waves

Wavelength is longer when receding

Doppler Shift / Redshift

Redshift, z, is a non-relativistic approximation to the Doppler shift

=

vc=z =

A Fly in the Ointment

Evidence for Particles Newton’s Corpuscular Theory of Light - light consists of small particles, because it:

• travels in straight lines at great speeds• is reflected from mirrors in a predictable way

Position x

Momentum p = mv

Why the Photon is Necessary

Electron transitions in the Bohr model of the atom and the subsequent emission of light provides an example of when light should be viewed as a photon. There are two further pieces of evidence of this particle-like nature of light:

• photon scattering• photoelectric effect

ScatteringOne experiment which provides conclusive proof of a particle nature of objects is to scatter two objects off of each other, as in the collision of two billiard balls. This experiment with light and small atoms has been done, and is called Compton scattering.

The results of this experiment are completely at odds with predictions made if light is viewed only as a wave. Measurements show that the frequency of the scattered wave is changed, which does not come out of a wave picture of light. However, when the light is viewed as a photon with energy proportional to the associated light wave, excellent agreement with experiment is found.

Photoelectric EffectAnother compelling proof for the photon nature of light is the photoelectric effect. In this effect, light is shone at a metal plate and it is found that electrons are ejected. These electrons then get accelerated to a nearby plate by an external potential difference, and a photoelectric current is established.

This effect, which arises in devices such as automatic door openers, burglar alarms, light detectors, and photocopiers, cannot be explained using a wave picture of light.

Einstein’s Photoelectric Effect

• Only light with a frequency greater than a certain threshold will produce a current

• Current begins almost instantaneously, even for light of very low intensity

• Current is proportional to the intensity of the incident light

Planck’s Quantum Postulate

• Energy of radiation can only be emitted in discrete packets or quanta, i.e., in multiples of the minimum energy

E = hf where h is a new fundamental

constant of nature: h = 6.63 x 10-34 Joules sec

Light is Packets of Energy Called Photons

We Believe in Photons

• Red light is used in photographic darkrooms because it is not energetic enough to break the halogen-silver bond in black and white films

• Ultraviolet light causes sunburn but visible light does not because UV photons are more energetic

• Our eyes detect color because photons of different energies trigger different chemical reactions in retina cells

So, What is Light?

Light consists of a varying electric and magnetic field

Different Wavelengths Lead To:

Cool Thing About Light

It can be thought of as both a particle and a wave, so called “particle-wave duality”

Lower energy (longer wavelength) light acts predominately like a wave

High energy (shorter wavelength) light acts predominately like a particle

Cool Things Light Can Tell Us

It can tell us what you are made out of

It can tell us if you are moving toward or away from us

It can tell us how far away you are or (if we already know that) how energetic you are

It can tell us your temperature

1/R2 Falloff

Intensity of light falls off as we move away from the source

Light at a Distance• Objective: Your detector in orbit around Earth has measured a certain amount of energy from the direction of a faraway source.

Your job is to determine how much energy the source actually emitted. Assume the source emits energy equally in all directions.

Think About It!• A light emits equally in

all directions. • What does this mean

about the amount of light you will measure in any given square cm as you move further and further away from the light source?

• At r1, the light per unit area, L1 = L/4(r1)2. •And at r2, the light per unit area, L2 = L/4(r2)2.

• Solving each equation for L gives us

L= L1 x 4(r1)2 = L2 x 4(r2)2.

Think of it in terms of a ratio... the amount of light per unit area at r2 relative to the amount of light per unit area at r1 is then

L2/L1 = (r1)2/(r2)2.

Add the Mathematics!

Think About What This Means

If r1 is 5 cm and r2 is 10 cm, then there is 1/4 as much light per square cm at r1 as at r2. The distance changes by a factor of 2, but the amount of light per square cm changes by a factor of 4.

• What if r1 was 5 and r2 was 50?• How much less light per cm2 do you have there?

Conclusion•We say that the intensity, or amount of light per square cm, changes as 1/distance squared (i.e., 1/r2) away from the source.

•How does this help us to achieve our Objective? If we measure X amount of energy per square cm in our detector, then we know that the source must have emitted energy equal to 4r2 times X!

Blackbody Radiation

A blackbody is an object which totally absorbs all radiation that falls on it

Any hot body (blackbodies included) radiates light over the whole spectrum of frequencies

The spectrum depends on both frequency and temperature

Fun With Lenses and Mirrors

Convex Lenses

Concave Lens