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, v s =speed of sound v r =radial velocity of source Relativistic Doppler Shift –Time Dilation –Varying distance For  =0  or 180 , then: Transverse Doppler Shift  =90 

Relativistic Doppler Shift Redshift/Blueshift parameter z (radial motion) Measure redshift  Measure recession velocity!!!

Relativistic Doppler Shift Redshift/Blueshift

Relativistic Velocity Transformations

Relativistic Headlight Effect example 4.3.3

Relativistic Momentum and Energy Kinetic Energy Total Energy Rest Energy Momentum Energy Relation Momentum

Relativistic Momentum and Energy The Derivation of E=mc 2

Relativistic Momentum and Energy Derivation pages 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

Spectral Lines Application of Spectral Measurements Stellar Doppler Shift Galactic Doppler Shifts Quasar Doppler Shifts

Radial Velocities

Spectral Lines Spectrographs 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 frame Remember that the clocks are located at every point in space

Example useful

Time Dilation…Light Clock

Worked Problems

Worked Problem