Diffraction and Interference (Light)
Discussion
obstacles and openings
Diffraction is the bending or spreading of light through an opening or around an obstacle.
Goethe "flexibility of light"
Why is it possible to hear around corners, but not see around them?
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double source interference
text
Double source interference. Laser light through two closely spaced slits.
Constructive interference occurs whenever the path length difference euqals a whole number of wavelengths.
ΔL = nλ
small triangle
| sin θ = | nλ |
| d |
big triangle
| tan θ = | x |
| L |
for small angles
sin θ ≈ tan θ
Approximate equation.
| nλ | ≈ | x |
| d | L |
Where…
| λ = | wavelength of source |
| d = | separation between sources |
| L = | distance from source to screen |
| n = | order of the maximum (0, 1, 2, 3, …) |
| x = | distance from central maximum to nth order maximum |
The dark fringes are halfway bewteen the bright fringes.
| (n + ½)λ | = | x |
| d | L |
Better equation.
nλ = d sin θ
Where…
| λ = | wavelength of source |
| d = | separation between sources |
| n = | order of the maximum (0, 1, 2, 3, …) |
| θ = | angle from central maximum to nth order maximum |
The dark fringes are halfway bewteen the bright fringes.
(n + ½)λ = d sin θ
single source interference (self interference)
Single source interference. Laser light through a narrow opening.
multiple source interference (diffraction grating)
Multiple source interference. Laser light through a diffraction grating.
spectroscopy
continuous vs. discrete
Continuous: temperature from Wien's displacement law
The continuous spectrum of daylight. Note the absence of any noticeable gaps.
Discrete: "bar codes" of the elements
The discrete spectrum of excited mercury vapor
The discrete spectrum of excited helium gas
The discrete spectrum of a fluorescent light. These spectral lines are wider since they came from a wider source.
Quotes that need to be paraphrased.
- Two German scientists, Robert Bunsen (a chemist) and Gustav Kirchhoff (a physicist), showed that the dark lines in the spectrum of sunlight corresponded to the bright lines of excited elements seen in laboratories on the Earth.
- Helium was discovered in 1868 by J. Norman Lockyear in the spectrum of a solar eclipse.
- The French astronomer Pierre Janssen (1824–1907) discovered helium in the spectrum of the corona of the Sun during an eclipse in 1868. Shortly afterward it was identified as an element and named by the British chemist Edward Frankland and the British astronomer Joseph Norman Lockyer. The gas was first isolated from terrestrial sources in 1895 by the British chemist William Ramsay, who discovered it in cleveite, a uranium-bearing mineral. In 1907 the New Zeeland born physicist Ernest Rutherford (1871–1937) showed that alpha particles are the nuclei of helium atoms.