Light and Continuous Spectra

Energy Production from the Sun:

The Sun dominates the energy ‘budget’ of the solar system

• How much energy does the Sun produce?• How does the energy reach us?

• How does it produce that energy?

Light properties

• Energy• Power• Intensity• Wavelength• Frequency• Speed

Which of the following is NOT a unit of energy?

1. Joule2. Kilowatt3. Kilowatt-hour4. Electron volt

Watt’s the difference between energy and power?

• Consider the units: a Joule (J) is a unit of energy, and a Watt (W) is a unit of power

• 1 W is defined as 1 J/s (Joule per second)• Thus, power is a rate at which energy is

delivered• Example: your “power” bill for electricity is

based on the number of kiloWatt-hours you consume. So is the utility charging you for power or for energy?

“Power” bills

• So when a utility charges you for a kW-hr:• 1 kW = 1000 W; 1 hr = 3600 s• A kW-hr can be converted into an equivalent

in Watt-seconds• Recall that 1 W is defined as 1 J/s, so 1 J = 1

Ws• In other words, your utility is charging you for

energy usage, not power. It’s not a power company

Intensity

Intensity is a power density.Units: W/m2 = W m-2

A

Area

PowerIntensity

Solar IntensityThe Solar Energy Output is 4 x 1026 W.

How much of that hits us?

When the Sun is directly over head, it delivers the equivalent of 22 × 60 watt light bulbs over each square meter (m2) of ground!!!

This amount, 1340 W m-2, is known as the solar constant

How is solar energy delivered from the Sun to the Earth?

As light!!!!

Is the intensity of light reaching the surface always 1340 W/m2?

1. Yes2. No

Electromagnetic Wave: propagating wave of electric and magnetic fields that oscillate perpendicular to each other and the direction of propagation

Electromagnetic Wave

Electric field

Magnetic field

In a vacuum, wave propagates with speed = 3 x 108 m/s(cosmic speed limit)

Wave Properties

frequency (f or ν (nu)): number of peaks that pass a location in a given time (units: Hertz (Hz) = 1/s = s-1)

speed (v): how much distance the wave moves per unit time(for an EM wave v = c = 3 x 108 m/s)

Wave Propertieswavelength (): distance between two consecutive peaks

(units: km, m, cm, mm, m, nm…)

amplitude: height of the wave (or depth of the trough); related to intensity but we won’t use it

Wave Propertiesspeed (v): how much distance the wave moves per unit time

(for an EM wave v = c = 3 x 108 m/s)

frequency (f): number of peaks that pass a location is a given time (units: Hertz (Hz) = 1/s = s-1)

wavelength (): distance between two consecutive peaks (units: km, m, cm, mm, m, nm…)

These three properties are related:

c

f

If wavelength is 10 m and frequency is 100 Hz (oscillations / seconds), what would be the speed of the wave?

1. 10 m/s 2. 1 m/s 3. 1000 m/s 4. 100 m/s

If wavelength is 10 m and frequency is 100 Hz (oscillations / second), what would be the speed of

the wave?

m/s 1000

m 10s 100 1-

fv

vf

The PhotonLight behaves like both a particle and a wave!

Photon: smallest bundle of light energy (i.e., a particle of light)

Photons carry light energy:1. A photon’s energy is proportional to frequency

(Eph f).• A photon’s energy is inversely proportional to wavelength (Eph

-1).

hc

hfEph Plank’s constant (h) = 6.602 x 10-34 Js

Matter actually a wave too!

• All matter exhibits particle and wave properties (Louis de Broglie, 1921)

• For ordinary objects, the wave nature of matter is much too small to measure– The wavelength of a baseball

moving at 80 mph would be about 10-34 meters

• But for small particles, this is wave nature of matter is measurable– The wavelength of an electron is

about 10-10 meters

Electron diffraction pattern showing its wave nature

How is a difference in the frequency or wavelength of light observed?

The Visible Spectrum:

For visible wavelengths COLOR

How does a prism work?• Dispersion: Speed of light in

the prism (glass or plastic) depends on the frequency (color)

• Refraction: Change in speed of light causes a change in its direction

• Result: Blue changes direction most since its speed is the lowest inside the prism. And red changes direction least since its speed is highest inside the prism.

Red R Orange O Yellow Y Green G Blue B Indigo IViolet V

Herschel Thinks Outside the Box:In 1800 William Herschel made a discovery when he tried to determine the

temperature of light.

• He noticed that a thermometer recorded energy from the Sun`s spectrum even when placed beyond the red end of the visible rainbow.

•He called this emission Calorific Rays and it was the first discovery that light had colors invisible to the human eye.

•These rays are known today as infrared light.

Herschel’s work color is associated with a temperature

Visible light is just a small part of the electromagnetic (EM) spectrum

Why are we spending so much time discussing the electromagnetic spectrum?

We rely on remote sensing of EM radiation.

Tells us the temperature and composition

This gives us important clues to the origins of these objects.

Not easy to visit astrophysical objects (the Sun, planets, other stars) and make direct in situ measurements

When we look at the spectrum of the Sun, we see a distinct distribution of colors.

The Solar Spectrum:

Other stars have similar patterns as do most hot objects. The main difference is where the peak color is.

Gustav Kirchoff (1862) called this kind of emitter a ‘blackbody’.

Ideal Blackbodies Blackbody: an object that radiates energy into space in a manner that is

characteristic only of the temperature of the radiator.

Wavelength (nm)

Characteristics of Black Bodies1. Characteristic I vs. curve (shown left)

(all blackbodies radiate in more than one color)2. Curve is related to T only3. Increasing T, increases total intensity4. As T increases, peak moves to lower 5. Wavelength of peak intensity related only to T. Wilhelm Wien (1893) describes the relationship mathematically (now called Wien’s Law), where is measured in nanometers and T is measured in Kelvins:

Calculating The Sun’s Temperature

So how well does this work?

Given Tsun = 6000 K

Which matches the observed solar output curve pretty well.

Ideal Blackbodies

Wavelength (nm)

Amount of light radiated by an object is given by the Stefan-Boltzmann Law (Josef Stefan, 1879; Ludwig Boltzmann, 1884):

Where L is the luminosity (power) emitted by the object (in Watts), T is its temperature (in Kelvins), and is the Stefan-Boltzmann constant, which has the value 5.67 x 10-8 Wm2K4

Visible InfraredUV

Stars may be considered to act like blackbodies

If star A has a surface temperature of 9000 K and star B has one of 3000 K, what is the ratio of the power output of the stars (PowerA/PowerB)?

1. 812. 23. 94. 35. 16

SolutionIf star A is 9000 K and star B is 3000 K, what is the ratio of the power output of the stars (PowerA/PowerB)?

If star A has a surface temperature of 6000 K and star B has one of 3000 K, which star has a longer peak wavelength output?

1. Star A2. Star B

Solution

Since

The colder star, star B, has the longer wavelength.

If star A is 6000 K and star B is 3000 K, which star has a longer peak wavelength output?