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Physics A: Problem Set 16: Diffraction, interference, polarization

recommended reading

High Marks: 4:25–4:27, 4:35–4:36
Barron's Let's Review: 12.7 Diffraction and interference of light
physics.info: Diffraction & interference (light), Polarization
Wikipedia: Diffraction, Interference (wave propagation), Double-slit experiment, Discrete spectrum (physics), Continuous spectrum
HyperPhysics: Diffraction of sound
Khan Academy: Interference of light waves
YouTube: The brightest part of a shadow is in the middle
Mr. Machado: 09 Diffraction
Reference table with select items highlighted, page 1 Reference table with select items highlighted, page 2 Reference table with select items highlighted, page 3 Reference table with select items highlighted, page 4 Reference table with select items highlighted, page 5 Reference table with select items highlighted, page 6

sample problem

  1. Suppose you were the owner of a radio station and that you wanted to extend the range of your broadcast. Would it be wise to erect a second transmitting antenna to broadcast simultaneously with the first? How will a second transmitter affect reception? Explain your reasoning.
    The signals from two simultaneously transmitting antennas are going to interfere with one another. The interference pattern they produce will have alternating bands of constructive and destructive interference, something like the illustrations below. In the constructive regions, the signal will be strong. In the destructive regions, the signal will be weak. This is unlikely to be an advantage — unless the constructive regions happened to fall on populated areas and the destructive regions happened to fall on deserted regions.
    Double source interference. The sources are closer together in the image on the right. Do not click on the animations if you have photosensitive epilepsy or a similar condition.
    animate at your own risk animate at your own risk

homework

  1. Why can't sound waves be polarized?
    Sound waves can't be polarized because they are longitudinal.
  2. For what portion of the electromagnetic spectrum could a picket fence be used as a diffraction grating? Explain your reasoning.

    The ridges in a typical diffraction grating that students might use are spaced about 10−6 m apart. This is on the same order as the wavelengths of visible light. The pickets in a picket fence are about 10 cm apart (or 10−2 m, if you prefer). According to one trusted reference, this is solidly in the microwave portion of the electromagnetic spectrum.

  3. For each of the following examples, state whether the source of light produces a spectrum that is mostly continuous or mostly discrete. Compile your results in a table like the one below.
    Identify the spectral type with a check mark (√)
    source continuous discrete
    blow torch    
    candle flame    
    cathode ray tube    
    emission nebula    
    firefly    
    fluorescent tube    
    glow stick    
    incandescent bulb    
    laser    
    LED    
    neon sign    
    plasma display    
    the Sun    
    red hot metal    
    Identify the spectral type with a check mark (√)
    source continuous discrete
    blow torch √  
    candle flame √  
    cathode ray tube   √
    emission nebula   √
    firefly   √
    fluorescent tube   √
    glow stick   √
    incandescent bulb √  
    laser   √
    LED   √
    neon sign   √
    plasma display   √
    the Sun √  
    red hot metal √