Lecture 11: LightLecture 11: Light

The Cosmic Messenger

Basic Properties of LightBasic Properties of Light

light is a form of energy – radiative energyrate of energy output (from Sun, lightbulb,

etc.) is measured in Watts (Joule/s)

The speed of lightThe speed of light

Galileo tried to measure the speed of light using people with lanterns – failed to detect any finite speed

Romer discovered evidence that light has a finite speed in 1676 based on observations of eclipses of the moons of Jupiter

measured accurately on Earth by Fizeau and Foucault in 1850: c = 3 x 108 m/s

The Fizeau-Foucault experimentThe Fizeau-Foucault experiment

Frequency and WavelengthFrequency and Wavelength

all light always travels at a fixed speed (in a vacuum): c = 3 x 108 m/s

frequency () and wavelength () are related by the formula:

= cunits of frequency are cycles per second =

Hertz = Hz = (1/s)

Frequency and Wavelength: Frequency and Wavelength: example problemexample problem

Find the frequency of the first Balmer line of Hydrogen, which has a wavelength of 656.3 nm.

remember 1 nm = 10-9 m, so l = 6.563 x 10-7 m

= c = c/ = (3 x 108 m/s) / (6.563 x 10-7 m)

= 4.57 x 1014 Hz

Frequency and EnergyFrequency and Energy

What is the energy of the photons that produce this Balmer line? Rememberthe frequency = 4.57 x 1014 Hz

E = h E = (6.626 x 10-34 J s)(4.57 x 1014 Hz)E = 3.02 x 10-19 J

Properties of LightProperties of Light

light can be characterized by two numbers– frequency or wavelength– intensity or brightness (amplitude)

What is Light?What is Light?

Most waves propagate through some sort of medium (e.g., water waves, sound waves in air, etc.)

if light is a wave, what does it wave in?the idea of the ‘luminiferous aether’ was

invented to answer this question.

The Aether theory and the The Aether theory and the Michelson-Morley experimentMichelson-Morley experiment

Electromagnetic radiationElectromagnetic radiation

The electromagnetic spectrumThe electromagnetic spectrum

Matter and LightMatter and Light

light interacts with matter in four ways:– emission– absorption– transmission– reflection/scattering

Matter and LightMatter and Light

materials that transmit light are called transparent

materials that absorb light are called opaquethe degree to which a material absorbs light

is called its opacity (high opacity absorbs more light)

objects appear to have different colors because of the way that they transmit or reflect light

Scattering: why the sky is blueScattering: why the sky is blue

and sunsets are redand sunsets are red

FluxFlux= Energy/Area

Asphere = 4R2

Blackbody RadiationBlackbody Radiation

radiation from an opaque body follows two laws:I. the energy flux is proportional to the

temperature of the object to the fourth power (Stephan-Boltzmann law)

F = [5.7 x 10-8 W/(m2 K4)] x T4

II. the average energy of the light (photons) emitted is higher for higher temperature objects (so the wavelength is shorter; Wien’s Law)

peak = (2.9 x 10 6 / T [K]) nm

The Sun as a BlackbodyThe Sun as a Blackbody

The peak wavelength of the Sun’s light is about 500 nm. What is the surface temperature of the Sun?

we can use Wien’s law:

T = (2.9 x 106 nm)/peak

= (2.9 x 106 )/(500 nm)

T = 5800 K

The luminosity of the Sun is 3.90 x 1026 W. Find the temperature of the Sun.

this time we’re going to use the Stephan-Boltzman law:F = [5.7 x 10-8 W/(m2 x K4)] T4

first we need to find the flux at the Sun’s surface. remember flux = energy/area so

Fsun = Lsun/(4R2sun)

Rsun = 6.96 x 108 m

F = 6.41 x 107 W m-2

now we use T = (F/ 5.7 x 10-8 W/(m2 x K4))1/4

T = 5800 K

Other Stars and our SunOther Stars and our Sun

Sirius is the brightest star in the night sky. It appears blue and its peak flux is at 280 nm, in the UV.– is Sirius hotter or cooler than our Sun? What is

its temperature?– compare the energy flux at the surface of Sirius

with that at the surface of our Sun.

The End