The Nature of Light

What is light made of?• energy can be transported by either particles or waves-- which is light?

First Theory: The Corpuscular Theory by Newton

• Light consists of a tiny stream of particles that are really, really, really, really, really, small called corpuscles that emanate from a luminous source.

The reasons for this explanation as best known for the time:

1) Rectilinear Propagation-- Light travels in a nearly straight line with minimal curving, much like a ball thrown at very high speed.

It doesn’t go around corners like sound (not true, as we’ll see later).

2) Reflection-- Light reflects just like a steel ball thrown against a steel plate.

3) Refraction-- Light speeds up when it hits water, just like a ball rolling down a hill. This bends it off of its original path.

Table ramp

air

H2O

cwater > cair

Second Theory: The Wave Theory by Huygens

•Huygens Principle helped develop the idea that light was not particles, but a form of electromagnetic waves.

Support for the wave theory that brought about the downfall of the particle theory:A) Huygens’ Principle-- successfully explained rectilinear propagation in wave model.

B) Discovery that cair > cwater by Michelson.

C) Discovery of interference and diffraction of light, something particles cannot do (they thought)!

In studying the photoelectric effect, several holes were punched in the wave theory.

• Photoelectric effect: Certain materials eject electrons when subjected to light.

• Two specific discoveries seemed to indicate that light behaved like particles:

1) As the intensity of the light was increased, more electrons were emitted, but the ejection velocity did not increase.2) At certain frequencies, no amount of intensity would produce emissions.

The Quantum (Modern) Theory of Light by Einstein:

Light has a dual nature: It consists of tiny “bundles” of energy called photons that travel in an electromagnetic wave field.

• the size of the photon would depend upon the frequency of the light.• more intense light would indicate more photons in the stream.• at certain f’s, the photons are too small to produce any emissions.

Double Slit Experiment

Photometry-- the study of lightObjects are either one of two things:

• Luminous- the provide a source of light (the sun, the stars, light bulbs, fire, etc.)• Illuminated- a reflection of light (most of the objects we see).

Measuring the speed of lightBefore 1675, light was considered to be instantaneous.Galileo suggested a finite time for light to travel, but failed in his two mountain experiment to measure that time!

Light traveled way too fast to be measured in this manner with this “technology”

In 1675, Olaus Roemer (great name for a band) established the first value for c: 225,000 km/s

• a good effort, but he was off by about 25%

In 1878, a U of C physicist named Michelson made the first accurate measure of the speed of light:

Michelson measured the distances between the mountains as 35.4 km.The mirror was attached to a motor that had a measured frequency of 31,800 rpm.

d = 2(35,400 m) = 70,800 m f = 31,800 rpm (1 min/60s) = 530 rev/s

T = 1s / 530 rev = .00189 s

∆t = (1/8)(.00189 s) = 2.36 X 10-4 s

v = ∆d

∆t

= 70,800 m

2.36 X 10-4 s

c = 3.00 X 108 m/s

This is a scale representation of the the time for light to travel from earth to the moon (1.3 s):

A man reproduces Michelson’s experiment using an 8 sided mirror and two mountains that are 40.0 km apart. Assuming he had no error, what was the frequency of the mirror in rpms?

∆d = 80, 000 m

c = 3.00 X 108 m/s

f = ?

∆t = ∆d/v = 80,000 m

3.00 X 108 m/s

= 2.67 X 10 -4 s

T = 8(2.67 X 10 -4 s) = 2.13 X 10-3 s

f = 1/T = 1/ 2.13 X 10-3 s = 469 rev/s (60s/min)= 28,100 rpm

1) A student uses an 8 sided mirror spinning at 29,100 rpm and reproduces Michelson’s experiment using mountains that are 38,600 m apart. What value will this data provide for the speed of light?

2) Another student uses an eight sided mirror rotating at 32,300 rpm and calculates the speed of light to be 3.00 X 108 m/s. How far apart must the mountains have been that he used?

Light Behaviors

Interference: The effect of two or more waves on the medium when they travel at the same time through the medium.

Bright lines are produced by constructive interference and dark are produced by destructive interference:

constructive (bright lines): dsinø = nλ

d- distance between slitsn- 0, 1, 2….

destructive (dark lines): dsinø = (n+ ½)λ

A screen with two slits 0.100 mm apart is 1.20 m from a screen. Light of 500.0 nm wavelengths falls on the slits. How far apart will be the interference fringes?d = 1.00 X 10-4 m

λ = 500 X 10-9 mn = 1

x = Ltanø1

Lx1

sinø = nλ/d = 5.00 X 10-3

ø = sin-1 (5.00 X 10-3) = .286

L = 1.20 m

= 1.20tan(.286)

= 6.00 X 10-3 mx = ?

Light with a wavelength of 650 nm produces a third order fringe at an angle of 15˚ when it falls on two narrow slits. How far apart are the slits?

Monochromatic light falls on two very narrow slits that are .0400 mm apart and creates successive bright fringes on a screen that is 5.00 m away from the slits. The fringes are 5.50 cm apart. What is the frequency of this light?

Light of wavelength 680 nm falls on two slits and produces an interference pattern on a screen 1.5 m away. If the fourth order fringe is 48 mm from the central fringe, how far apart are the slits?

The Visible Spectrum and Dispersion

Color is the sensation of frequency and wavelength of visible light on the human eye.

UV IRDifferent colors actually travel at different speeds through matter and so will refract differently.

This causes white light to spread out after traveling through a prism for example:

Polarization of Light

Light is naturally unpolarized– it vibrates in many planes at once:

Light can be plane polarized by a Polaroid:

Crossing polaroids would block the light completely:

Polarized Lenses (reduce glare):

Polarization of Light Demo

Light MeasurementsIn photometry, there are 4 quantities that are generally measured in practical photometry:

1) luminous intensity (I) “brightness” of a source of light2) luminous flux (F) rate at which light energy is radiated3) Illumination (E) how much light is falling on a given surface

4) Illuminance how much light is reflected off of an illuminated surface

Luminous Intensity (I) one of the seven fundamental physical quantities, it is the measure of the “brightness” of a source of light.

• it is directly comparable to a standard

• the standard was originally a specially made candle, so the unit was called a candel.

• the unit is now called a candela (cd), which is the amount of light emitted by a particular monochromatic source of light with a set intensity and set power.

Luminous Flux (F) That part of the total energy radiated from a luminous source that is capable of producing the sensation of light.

Flux is the “flow” of light outward from a point source.

• the amount of flux that can be radiated is directly proportional to the intensity:

F = 4πI units: lm (lumens)

• this means that a one candela light source will produce 12.6 lm of radiated light energy (flux)

• this is how most light sources are rated!

Illumination (E) the density of the luminous flux on a surface

• depends directly upon the amount of flux that is generated from the source• also depends inversely upon the area over which the flux is spread at the point of illuminance

E =F

A

units:

lm/m2

= 4πI

4πr2E =

I

r2

Illuminance also depends upon whether there is an angle between the flux and the surface:

ø

E = F(cos ø)

AE =

I(cos ø)

r2

ø

A table is placed directly below a 2000.0 lm incandescent lamp so that its surface is 3.00 m below the lamp. What would be the illumination at a spot that is 1.00 m to one side of directly below the lamp?

F = 2000.0 lmr = 3.00 m E = ?

3 m

1m

ø

tanø = opp/adj= 1.00 m

3.00 m

= .333

E = Fcosø

A

= (2000.0 lm)cos18.4˚

4π(3.00 m)2

= 16.8 lm/m2

ø = tan-1(.333)= 18.4˚

At a spot directly below a 115 cd light source, the illumination of a tabletop is measured to be 28.8 lm/m2. At what angle should the table be angled to decrease the illumination to 24.9 lm/m2?

I = 115 cd

E1 = 28.8 lm/m2

E2 = 24.9 lm/m2

ø = ?

cosø = E•r2

I

r2 = I/E = 115 cd

28.8 lm/m2= 3.99 m2

= (24.9 lm/m2)(3.99 m2)

115 cd

= .864

ø = cos-1(.864)

ø = 30.2˚

1) The illuminance at a point 1.85 m directly below a light source is measured to be 46.5 lm/m2. What is the illumination at a point 3.00 m to the right of this spot?

2) How many candelas are needed to provide an illumination of 38.6 lm/m2 on a desk that is angled at 22.0˚ to a light source that is 2.05 m away from the desk?3) At a point 2.00 m below a light source, the illumination is measured to be 45.5 lm/m2. What is the illumination at a point 2.00 m to the left of this spot?

A 1500.0 lm light source is 15.0 cm away from a photometer. A second identical light source is then placed only 12.0 cm away from the photometer. The second lamp is then moved laterally so that it provides equal illumination with the first lamp. How far must it have been moved?