Lecture 22: Light

Key Ideas:

Light is Electromagnetic Radiation

Light as Waves or Photons

Light carries energy at the speed of light

• Waves, or
• Particles (Photons)

The Electromagnetic Spectrum

Sequence of photon energies

Luminosity vs. Apparent Brightness

Inverse Square Law of Brightness

Doppler Effect

Due to relative motion between source & observer

Way to measure speeds at a distance

Electromagnetic Radiation

Two complementary ways to describe light

• Electromagnetic Waves
• Photons (particles of light)

Wave Nature of Light

• Periodic (repeating) changes in the strengths of coupled electric and magnetic fields.
• Electromagnetic waves travel through a vacuum at the speed of light.
• Doesn't need a medium to "wave" in.

c = 299,792.458 km/sec

This speed is independent of the wavelength or frequency of the light wave! The speed of light, c, is the only constant of nature we can state "exactly", only because our metric system of measuring lengths is defined in terms of the speed of light. This seems a somewhat circular argument, but what it amounts to is saying that our measurement system is tied directly to the speed of light.

Particle Nature of Light

Photon:

Massless particles that carry energy at the speed of light.

Photons are characterized by their Energy, which is proportional to their Frequency, f.

Photon Energy:

E = hf

In words:

Higher Frequencies mean Higher Energies

Note: Energy, E, is a "particle property", whereas frequency, f, is a "wave property". They are related through Planck's Constant, h. Planck's constant is one of the "Fundamental Constants" of Nature (another one we've met in this lecture is the speed of light, c). One can think of Planck's constant as serving as the "link" between the wave and particle natures of light, and indeed h is the fundamental constant in "quantum mechanics", the modern view of matter and radiation as entities ("quanta") that have the properties of both waves and particles.

The Electromagnetic Spectrum

Photon Energy

low energy = low frequency = long wavelength

Examples of low-energy photons: Radio Waves, Infrared

high energy = high frequency = short wavelength

Examples of high-energy photons: Ultraviolet, X-rays, Gamma Rays

Type of Radiation	Wavelength Range
Gamma Rays	<0.01 nm
X-Rays	0.01-10 nm
Ultraviolet	10-400 nm
Visible Light	400-700 nm
Infrared	700-105 nm (0.1 mm)
Microwaves	0.1-10mm
Radio	>1 cm

The Visible Spectrum

Wavelengths: 400 - 700 nanometers (nm)

Frequencies: 7.5x10¹⁴ - 4.3x10¹⁴ waves/second

We sense visible light of different energies as different colors. The basic colors of the visible spectrum are defined roughly as follows, in order of increasing photon energy:

Color Name	Red	Orange	Yellow	Green	Blue	Indigo	Violet
Approximate Wavelength	700nm	650nm	600nm	550nm	500nm	450nm	400nm

You can remember the order of these colors from lowest to highest energy using the famous mnemonic: ROY G. BIV

Note:The wavelengths assigned to the colors in this table are meant only to be illustrative. Color is a physiological response of our brains to visible light of different energies. Our division of the visible spectrum into named colors is very subjective, and certainly not a matter of uniform divisions at every 50 nm of wavelength! An oft-cited example of the subjectivity of color names is the color "orange". It did not enter the language until the Middle Ages, when the fruit of the same name reached Europe from the Middle East. Before that, the color would have been called a reddish shade of yellow.

How "Bright" is a Light Source?

• "Brightness" measures the number of photons per second emitted by the light source

Luminosity (L):

Measure of the total energy output:

• L is measured in Power Units (energy/sec) like Watts
• L is independent of distance

Luminosity is an intrinsic property of the light source.

Apparent Brightness (B):

Measures how bright an object appears to be as seen from a distance

• B is measured in Flux Units (energy/sec/area)
• B depends on the distance to the source

Brightness is what we actually measure (an observable property).

The Inverse Square Law of Brightness

(Graphic by R. Pogge)

This means that the Apparent Brightness, B of a light source with intrinsic Luminosity L will get fainter as the square of our distance from the source:

(Graphic by R. Pogge)

Apparent Brightness is inversely proportional to the square of the distance to the source

If the source is 2x closer, it appears 4x brighter.

If the source is 2x farther away, it appears 4x fainter.

The Doppler Effect

Examples:

• Sound Waves (Siren or Train Horn)
• Light Waves

• relative speed of the source & observer
• direction of motion (together or apart)

Doppler Effect in Sound

Results:

• The cat on the left hears a higher-pitched squeak because the waves have a shorter wavelength (scrunched together by the mouse's motion).

• The cat on the right hears a lower-pitched squeak because the waves have a longer wavelength (spread out by the mouse's motion).

Doppler Effect in Light

• Light source moving away from the observer, the observed wavelength will get longer, and hence REDSHIFTED

• Light source moving towards the observer, the observed wavelength will get shorter, and hence BLUESHIFTED

A Way to Measure Speeds

The difference between the observed and emitted wavelengths is directly proportional to the speed of the source towards or away from you (v), given by the Doppler Formula:

(Graphic by R. Pogge)

• The size of the shift gives the speed of the source
• The color of the shift (Red or Blue) gives the direction of motion (away or towards you).

The Doppler Effect in Practice

But, we also use the Doppler Effect in light in everyday settings. Some examples:

Traffic Radar Guns:

Radar gun bounces a pulse of microwaves (or infrared laser light) of a known wavelength off a car or truck, measure the wavelength reflected back. The Doppler shift gives the vehicle's speed. Most traffic radar guns are of the portable microwave doppler radar type in this example. A problem of microwaves is that their excess emission can be detected by small receivers mounted in cars and used to warn drivers that a radar gun is in use on the road. Some types of police "radar" guns don't use microwaves but instead use laser ranging techniques called LIDAR. This works by time-of-flight calculation rather than the Doppler effect.

Doppler Weather Radar:

Similar principle, bounce microwave radar signals of known wavelength off of clouds, measure the wavelength reflected back. The Doppler shift and its sign (blue or red) gives the speed and direction of the clouds. The strength of the returned signal also gives the amount of rain or snow falling.

Light the Messenger

The light "encodes" important information about the source of the light

1. Luminosity measures how much energy the object emits in the form of light.
2. Doppler Shift tells us how fast it is moving towards or away from us