VLE 3 Wave optics
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Newton rings
Newton rings are generated by interference at thin layers.
Lens
Plate
Multiple reflection occur at the boundaries of lens and plate. These beams interfere. The distance between lens ant plate generate a optical path difference between the partial beams.
→ Usage of lens characterisation
41
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Lens characterization with monochromatic light
Error free lens |
Lens with errors |
source: http://wwwex.physik.uni-ulm.de, 07.10.09
The distance between two rings is equal to the height difference (between plane glass plate surface and lens surface) of /2.
The ring diameter decreases with high distance to the lens centre because the gradient of the distance change is rising.
42
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Calculation of the Newton rings
Path of the light ray through air gap inclusive 180° Phase shift caused by reflection:
s 2d
2
Condition for destructive interference is that the optical path is an odd multiple of the half wavelength:
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2k 1 |
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Combine and cross out |
2d k |
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For r²: |
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r 2 |
d 2R d |
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Because d << R: r 2 |
2dR |
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So: |
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r 2 |
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2R |
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Lens
Glass plate
source: www.fkg-wuerzburg.de, 07.10.09
Position of the k-th dark stripe is seen from the centre:
rk 
k R
43
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Michelson interferometer (1)
Layout: |
Moveable mirror |
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HeNe laser= 633 nm
Probe beam
Beam-
splitter Fixed reference mirror
Reference beam
Interfering beams
→ Application: high-precision measurement of displacements/ distances
44
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Michelson interferometer (2)
Initial state:
Reference beam
= 633 nm |
→ Amplification |
Probe beam
Displacement of the movable mirror by /4 → Increase of the optical path by /2
Reference beam
/2
→ Cancellation
Probe beam
→ Alternation between „bright“ and „dark“ with a mirror displacement of /4 (= 158 nm)
45
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Michelson Interferometer (3)
Error sources of the Michelson-Interferometer:
The wavelength of the laser is the central measuring tool
→ Unknown change of the wavelength causes errors
Influences of the wavelength by: laser stability, temperature, humidity,… → Measurement of the surrounding condition necessary
Mirrors are very sensitive for tilting (reflected beam sees the double tilting angle)
→ Alternative: Retro reflector
source: www.newport.com
46
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Michelson Interferometer (4)
Forward-backward-counting:
Tilting of the reference mirror
Measuring mirror
The interference fringes move to left or right in dependence of the tilting of the reference mirror. With the right detector setup the direction can be found:
Refrence mirror
Interference fringes |
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on detector: |
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Detector 2 |
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Detector 1 |
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47
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Further interferometer types (1)
Sagnac-Interferometer
source: Demtröder, Experimantalphysik 2
If the interferometer is resting I1 and I2 have the same optical path (s1 = s2). Is it rotating, the mirrors will move while the light is going around. Therefore the distance s1 for I1 is a little bit longer than the distance s2 for I2 .
The generated phase shift is proportional to the angular velocity .
The fringe shift N = t/ is
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with A – area of the |
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Application:
•Measurement of the rotation of the earth (Michelson-Gale-experiment 1925)
•Laser-Gyroscope
48
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
Further interferometer types (2)
Mach-Zehnder-Interferometer
By change of the refractive index and with this the optical path in on arm of the interferometer a phase shift is generated. The phase shiftcan be calculated with the following equation:
n L
With this the refractive index e.g. of gases can be calculated, or the change of the refractive index can be calculated with a precision of up to 10-8.
source: Demtröder, Experimantalphysik 2
49
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany
6. Fresnel-Huygens-Principle
50
Prof. M. Schmidt
Institute of Photonic Technologies, Univ. Erlangen, Germany