Announcements

•Lab is up, observing help Thursday

•HW #1 returned—comment on copying, students missing from Blackboard

•Exams

mid-term probably March 14

final, ??

Discovering the Speed of Light: Chapter 14

Instantaneous Light Travel?(Flick the lights and see)

Early History of Speculations• Most Ancient Philosophers thought light travel instantaneous

Aristotle: "light is due to the presence of something, but it is not a movement”

Heron of Alexandria: light emitted by the eye (reflects and returns), so speed must be infinite since you can see distant stars when you open your eyes.

Kepler: Infinite speed since nothing in space to hinder it

But Empedocles, Islamic philosophers Avicenna and Alhazen all thought something moved, so was finite

Early Experiments

Isaac Beekman (1588-1637), Dutch Philosopher --suggested timing flash of light from a cannon reflected off a mirror, 1 mile away, then back again

Galileo Galileo (1638) suggested two men on hills progressively farther apart --first flashes a lantern and the second flashes back as soon as he sees the first. The unchanging delay for short distances gives reaction time, then increasing delay measures the speed of light. Carried out by Florentine society in 1667, but unsuccessful.

Ole RÖmer

Danish Astronomer, observing Jupiter’s Moons at the Observatory of Paris in 1670’s* noticed a variation in the period between eclipses of Io (~42 hrs) related to time of year (position of Earth relative to Jupiter)

1644-1710

*At the time there was a navigation problem, keeping accurate time at sea to measurelongitude--Romer and others thought Io eclipses would make a good clock

Io Around Jupiter

Time step=1 hour

Looking at Earth from Io

Time step = 1 hour

Question: Why was it difficult for Romer to observe the

eclipses of Io?

a) The period of Io is not a multiple of 24 hours

b) Io is too faint

c) Io is too close to Jupiter to resolve

d) Mixing up Io with other Moons

answer, a)

Io and The Speed of Light, C

•Observer begins timing eclipses when Earth at H•Observer sees next eclipse when Earth at M•Etc,…distance & eclipse time interval Increases…until Earth gets to E•As Earth moves closer to Jupiter, light travel distance & time interval decreases

T0=0+BH/cT1=P+BM/cT2=2P+BL/c

M

Mean period=42 hrs

t

0 1 2 3 4 5 6 7 8 9 10 11 12

Eclipse numberH M L K E

HE/c y=x

Full time delay=HE/c or 2AU/c

Emersions and immersions of Io observed by Romer between 1668 and 1678

And the Answer is…Romer found the full delay to be ~22 minutes (should be 16min40sec) to traverse Diameter of Earth’s orbit around Sun (2 AU). Huygens/Cassini estimated AU to be 1.4x108

km (from parallax of Mars)--so 2x1.4x108km/1.32x103sec=2x105km/sec (should be more like 3x105km/sec)

“A Demonstration Concerning the Motion of Light, Communicated from

Paris, in the Journal des Scavans, and Here Made English.” Philosophical

Transactions, Volume 12 (1677), Report on the Work of Ole Romer

Proof is in the Pudding“The necessity of this new equation of the retardment of light is established by all the

observations that have been made in the Royal Academy and in the Observatory for the space of eight years, and it has been lately confirmed by the emersion of the first satellite observed at Paris the 9th of November [1676] last at 5 hours, 35 minutes, 45 seconds at night, ten minutes later than it was to be expected by deducing it from those that had been observed in the month of August, when the Earth was much nearer to Jupiter”

So Romer then predicted a delayed eclipse by 10 minutes for Nov 9, 1676!

This was the first measurement of a Universal quantity (I.e., extra-terrestial)

Question: Which would cause an error in Romer’s

measurements?

a) Jupiter is moving

b) The Earth is spinning

c) The Red Spot on Jupiter

answer, a), would cause an additional 12 year variationOn top of the 1 year variation from Earth’s motion

Extraordinary Claims Require Extraordinary Evidence

Cassini and others didn’t believe it.

Same phenomenon as walking in vertical rain. Although therain is falling vertically, the trajectory of the rain from yourperspective would be slanted.

Aberration=change in angle from which starlight appears to emanate,

sin ~ =vE/c = 3x101km/s / 3x105 km/s = 1x10-4 [radians]=20 arcsec. Then -20 arcsec when Sun turns around.

Full effect only for stars perpendicular to direction of motion of Earth (I.e., stars at poles of ecliptic plane trace the circleof Earth’s orbit). For stars along plane, only perpendicular motion is seen.

true apparent

App

aren

t vel

ocity

James Bradley, 1725, demonstrates finite speed of light by “Aberration of Light” (or stellar aberration)

cVE

Aberration

Diagram illustrating the effect of annual aberration on the apparent position of three stars at ecliptic longitude 270 degrees, and ecliptic latitude 90, 45 and 0 degrees, respectively

In 1725 Bradley observed theStar γ Draconis to move SouthFrom Dec to March a full 20” !!Over year completed full circle

90 (Pole) April

Jan

July

45

0

Oct

AprilOct

What’s the difference between aberration and parallax?

a) They are the same

b) Same direction, different size

c) Same size, different direction

d) Different direction and different size

Answer, d

Aberration vs. Parallax

--parallax goes opposite Earth’s position, aberration opposite Earth’s motion--aberration is coherent, all stars do it--parallax is individual, depends on distance--aberrations tend to be much bigger

Aberration Seen Towards Pole

Aberration Seen Towards Ecliptic

How well Do we Know the Speed of Light?

At the 1983 Conference Generale des Poids et Mesures the following SI (Systeme International) definition of the metre was adopted:"The metre is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.

This ended speed of light measurements for now

Why do we care? E=mc2 Yield of a bomb, power plant, scale of Universe, etc, etc

Let’s Measure the Speed of Light (or how good is this

toy model)

Avg distance EM=3.8x105 km, time 10 trips with stopwatch

3.8x105 km 1.3 sec

= 3x105 km/sec

Now lets Measure the Speed of Light!

• We use a laser to send a pulse of light down a fiber optic cable and measure when the return pulse appears

• a small (15cm) length, assumed to be negligible in length, is used to measure and remove the delay of the electronics

• Then a 20 meter cable is inserted:speed of light=2x101 m /(delay [seconds])Is this right? Why/why not?

Air, Glass Changes the Speed & Direction of Light: Refraction

n is the “index of refraction”---even air slows light nair=1.0029nglass=1.5, nwater=1.333

Light refracts (bends) when it passes through different mediumAs Snell’s law (to take shortest path): nisini= nrsinr

(enters slower material --> bends towards normal).

Light travels slower in materials by factor nvaccuum/nmaterial

Total Internal Reflection

From slower to faster medium,bends away from normal.If angle just grazing then light stays in…that’s how fiber optic cable works