Special Relativity…continued, Diffraction Grating Equation and Photo-electric effect

•Relativistic Doppler Shift•Relativistic Momentum and Energy•Diffraction Grating Equation•Photo-electric effect•Homework Hints…

Relativistic Doppler Shift• Doppler Shift for Sound,

vs=speed of sound

vr=radial velocity of source

• Relativistic Doppler Shift– Time Dilation

– Varying distance

For =0 or 180, then:

Transverse Doppler Shift =90

Relativistic Doppler ShiftRedshift/Blueshift parameter z

(radial motion)

(radial motion)

Measure redshift Measure recession velocity!!!

Relativistic Doppler ShiftRedshift/Blueshift

Relativistic Velocity Transformations

Relativistic Headlight Effectexample 4.3.3

Relativistic Momentum and Energy

Kinetic Energy

Total Energy

Rest Energy

Momentum Energy Relation

Momentum

Relativistic Momentum and EnergyThe Derivation of E=mc2

Relativistic Momentum and EnergyThe Derivation of E=mc2

Relativistic Momentum and Energy

Derivation pages 105-106

Newtonian Mechanics “breaks down” at high speed v-->c.

does not hold.

However

does still hold if the momentum becomes….

Four-Vectors

Space-time four-vector

Invariant length

Energy-Momentum four-vector

Invariant length

Lorentz Transformation Lorentz Transformation

Spectral LinesApplication of Spectral Measurements

• Stellar Doppler Shift• Galactic Doppler Shifts• Quasar Doppler Shifts

Radial Velocities

Spectral LinesSpectrographs

• Spectroscopy• Diffraction grating equation

(n=0,1,2,…)

n = order

• Resolving Power

Photoelectric Effect

Classical Expectations•Kinetic energy of ejected electrons should depend on strength of electric field and therefore intensity of light and not the number of ejected electrons.

•Maximum kinetic energy of ejected electrons should not depend on frequency of light.

•Any frequency light should be capable of ejecting electrons.

Observations•Kinetic energy of ejected electrons does not depend on intensity of light!

•Increasing intensity will produce more ejected electrons.

•Maximum kinetic energy of ejected electrons depends on frequency of light.

•Frequency must exceed cutoff frequency before any electrons are ejected

Photoelectric Effect

Einstein took Planck’s assumption of quantized energy of EM waves seriously. Light consisted of massless photons whose energy was:

Einstein was awarded the Nobel Prize in 1921 for his work on the photo-electric effect

Photo-electric Effect

Inertial reference frameRemember that the clocks are located at every point in space

Example 4.3.2 useful

Time Dilation…Light Clock

Worked Problems

Worked Problem