VLE 3 Wave optics
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9. Double slit and grating
71
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Young‘s double slit experiment
The Young’s double slit is a further experiment to prove light is a wave.
Setup: single slit to generate coherent beam
The two close slits:
72
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Double slit (1)
After the double slit there are two cylinder waves which interfere.
The observation is done in the distance d behind the double slit.
r2
r1
73
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Double slit (2)
Most of the time s >> a (a few thousand times)
The optical path difference
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between |
S1 P and S2 P can be approximated |
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with |
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S1 B |
S1 P |
S |
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or with |
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S1B r1 r2 |
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With this approximation sin r1 r2
a
With |
r1 r2 |
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there is constructive interference (m = 0, 1, 2 …). |
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Thus |
sin m |
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(At the maxima in 0 as the zeros fringe) |
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a |
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74
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Double slit (3)
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Furthermore: tan |
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Therefore: |
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s tan arcsin |
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For small angles: |
ym s |
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Distance between two fringes:
ym 1 ym as m 1 as m
Or: y as
Conclusion: Width and distance of the fringes are a function of the wavelength
(red fringes are wider than blue)
source: http://www.tf.uni-kiel.de, 09.12.2008
75
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Comparison of interference patters of diffrent apertures
1 slit
2 slits
3 slits
4 slits
5 slits
source: Hecht, E. „Optik“
76
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Grating
Gratings are regular arrangements of diffraction elements. They are grouped as followed:
Transmissions- |
Transmissions- |
Reflection-phase |
Amplitude grating |
phase-grating |
grating |
Multiple slits |
Incised glass |
Incised mirror |
77
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Transmission-Amplitude-grating
Calculation is the same as for the double slit:
sin m m a
But: The maxima have a higher contrast.
Maximal order:
mmax a
Gratings are described with the line density [1/mm] grating constant (= line distance) in [µm]
78
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Blazed grating
With a normal grating most of the energy is diffracted in the zeros' order.
A blazed grating is a reflection grating, which is optimised to diffract a certain wavelength best.
The reflection which has the most energy is shifted to higher orders.
For the angle :
12 arcsin m 
a
Blazed gratings are used for making a beam monochromatic in spectrometer
79
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Questions
1.Which parameters describe a harmonic wave?
2.How big the phase difference has to be, so that the intensity doubles (f1 = f2, A1 = A2)?
3.What is the maximal shift you can measure with a Michelson-Interferometer?
4.What is the connection between speed of light and refractive index?
5.Which methods are suited to measure the wavelength of a laser?
6.How does the diffraction pattern look after an obstacle?
80
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany