Two Chapter 12

Interference – Young’s Experiment

• If light is a wave, then two point sources of light should produce an interference pattern.
• If ordinary sources are used then
  • the wavelength is very small and the equation predicts that x is small and most likely not observable.
  • If the sources are not monochromatic (of one frequency and wavelength) then the interference pattern will be constantly changing and this makes it not observable.
• Prior to Young, ordinary sources were used, and so interference was not observed.
• Young (1802 to 1804)
  • Used a single source that fell on a barrier with two slits in it.
  • This meant that both sources were always in phase, because the slits had light pass through them from a single source. This eliminated the monochromatic light problem.
  • Young placed the slits very close together which from

causes x to increase. This eliminated the wavelength problem.

• Young, therefore, first observed an interference pattern for light.
• This presented very strong evidence that light was a wave.
• Light with Young’s experiment, produces an interference pattern that has a series of rings.

• Such interference patterns can be analysed by using the formulas previously developed.

• For light interference patterns, the nodal lines are very narrow but the antinodal lines are not.
• Therefore, the nodal line equations are more useful for light.
• If a flat screen is used, these equations give good approximations of wavelengths if the screen is very distant.
• If the screen is not very distant, then the equations do not work well because the difference between l's becomes significant.
• To solve this later problem, a curved screen is used, where the slits are placed at the centre of the curved screen. This makes all l’s the same.
• If there is no indication that the screen is flat, it is to be assumed that it is curved.

• For the observed interference patterns, the distance between successive nodal or antinodal lines is given by.

• This equation can be generalized to

• DX = distance between the n₂ and n₁ lines, n₂ = the number of the further out nodal line, n₁ = the number of the closer in nodal line. The other symbols are as previously defined.
• Young in 1807 published his results and used the equations to calculate the wavelengths for various colours.
• Young was not taken seriously because of Newton’s influence and reputation.
• Fresnel (1818) presented his mathematical wave model of light.
• Poisson used Fresnel’s work to predict that light passing by a disc should produce constructive interference in the centre of the shadow (a bright spot should be present).

• Poisson noted that since no bright spot was observed, the wave model must be wrong.
• 1818 Dominique Arago tested Poissons prediction and found the bright spot.
• By 1850, the reality of the wave theory was generally accepted.
• There remained one unanswered question.
  • “What is lights medium?”
• At first, air was thought to be the medium.
  • Robert Boyle proved this wrong by placing a bell in an evacuated bell jar. As air was pumped out, when he could no longer hear the bell, he knew that the air was gone, but the bell was still visible.
• Scientists theorized what the medium should be like in order to give light its characteristics.
  • Invisible because we could not see it.
  • Have very low density.
  • Penetrates all matter and fills all space (light is everywhere).
  • A solid (transverse waves, which light is, can only travel in solids).
  • Very stiff (Light has very high speed).
• The name given to the medium is “Ether”
• Many attempts were made to detect the “ether,” but all failed.
• In 1887, Michelson and Morley tried to measure the motion of the Earth through the “ether.”
• They reasoned that if the Earth moved with respect to the “ether,” then the speed of light in different directions must be different.
• They used an interferometer to test this idea.

• If the two path lengths (BD and BC) are identical, then constructive interference occurs. If D is moved l/4 outwards, then the light going to D travels 2 times the extra distance farther (i.e. l/2). Now instead of constructive interference, we have destructive interference.
• If D is moved another l/4 (i.e. a total of l/2), then the light going to D travels 2 times the difference farther (i.e. a total of 1l). This returns us to the conditions of constructive interference.
• And so on.
• If either mirror is tipped slightly, then both constructive and destructive interference occurs at the same time (rings are seen by observer E as with Young’s experiment).
• As D is moved a distance l/4, a bright fringe will turn dark. If moved again a distance of l/4, it will turn back to a bright fringe. We would say that the fringe pattern has shifted one position, and the mirror has moved (1/2)l.
• By counting fringe shifts, we can measure the l of light. Light’s wavelength will be two times the distance D moves divided by the number of fringe shifts observed.
• The interferometer was used to redefine the meter in 1960. It was also used for measuring the speed of light in different media by placing the transparent medium in one of the beams and noting the phase shift.
• As pointed out above, it was also used to measure the Earth’s movement through the “ether.”
• As the interferometer is rotated through 90^o, the path of the light going to mirror D becomes like the path of the light to C and visa versa.
• This change in the nature of the paths should have been noticeable as a shift in fringe pattern.
• When the experiment was done, no shift was observed, which leads us to draw one of two conclusions.
  • The Earth is not moving through the “ether.”
  • There is no “ether” for the Earth to move through.
• To decide which is correct, one simply performs the experiment simultaneously in several locations. If there is “ether,” then at a minimum of at least one location, a shift should happen. This is because it would be highly unlikely that all locations on the Earth’s surface will have the same motion as the “ether” considering the Earth’s complex motion in space.
• The results of the experiment led to the conclusions that:
  • No “ether” exists.
  • The velocity of light is a constant to all observers regardless of their motion.
• This observation violated the Galilean principle of relativity and therefore there must be some physics that is incorrect.
• Einstein in 1905, solved the problem of the medium and relativity violation by redefining the basic concepts of:
  • Length

• Mass

• Time

• L, m, and T are relativistic length, mass and time respectively. T_o, m_o and L_o are rest time, mass and length respectively. v is the speed of the relativistic reference frame with respect to the reference frame taken to be stationary. c is the speed of light = 3.00 X 10⁸m/s.
• Relativistic length, mass, and time are the values of these measured by an observer that is in motion with respect to some reference frame taken to be stationary.
• Rest time, mass and length are the values of these measured by an observer that is not in motion with respect to some reference frame taken to be stationary.
• The implications of these three equations are:
  • As the speed of an object increases, its length in the direction of motion decreases as measured by a stationary observer. The observer that is traveling with the object would not perceive any change in length because her/his meter stick also decreases in length.
  • As the speed of an object increases, its mass increases as measured by a stationary observer. The observer that is traveling with the object would not perceive any change in mass, because the masses she/he compares the object's mass to also increase in mass.
  • As the speed of an object increases, time intervals measured by the observer traveling with the object seem normal, but to the stationary observer, time intervals measured by the moving observer appear longer and longer. In other words, it appears to the stationary observer that the clock moving with the moving observer is slowing down.

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November 21, 2013