lecture8 clh class
DESCRIPTION
physicsTRANSCRIPT
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Interference and Diffraction
http://en.wikipedia.org/wiki/Diffraction
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Huygens-Fresnel Principle
Adapted from: Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
What if we block some of the wavelets?
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Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
Diffraction increases as aperture size
If is large compared to the aperture, the waves will spread out at large angles into the region beyond the obstruction.
Diffraction
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Diffraction Pattern From a Single Slit
Ingle and Crouch, Spectrochemical Analysis
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Diffraction Pattern From a Single Slit
= sin2W x
Ingle and Crouch, Spectrochemical Analysis
For Destructive Interference:
x = /2
W sin =
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Diffraction Pattern From a Single Slit
Ingle and Crouch, Spectrochemical Analysis
For Destructive Interference:
x = /2
W sin = 2
= sin4W x
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Diffraction Pattern From a Single Slit
Ingle and Crouch, Spectrochemical Analysis
For Destructive Interference:
W sin = m
m = 1, 2, 3,
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Ingle and Crouch, Spectrochemical Analysis
Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.
W sin =
sin / W
More accurately:
sin = 1.22 / W
Diffraction Limited Beam Width
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1.222( )Airy
rNA
=
0.61resolutionNA
=
Airy pattern radius from central peak to 1st minimum:
Diffraction-limited resolution:
http://www.microscopyu.com/articles/formulas/formulasresolution.html
Diffraction-Limited Resolution
http://www.microscopyu.com/tutorials/java/imageformation/airyna/index.html -
Eugene Hecht, Optics, 1998.
Diffraction Gratings Plane or convex plate ruled with closely spaced grooves (300-2400 grooves/mm).
http://www.olympusmicro.com/primer/java/imageformation/gratingdiffraction/index.html
http://www.olympusmicro.com/primer/java/imageformation/gratingdiffraction/index.html -
Two parallel monochromatic rays strike adjacent grooves and are diffracted at the same angle ().
Difference in optical pathlength is AC + AD.
For constructive interference:
m = (AC + AD)
m = 0, 1, 2, 3,
Ingle and Crouch, Spectrochemical Analysis
Grating Equation
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m = (AC + AD)
AC = d sin
AD = d sin
Combine to give Grating Equation:
d(sin + sin ) = m
Ingle and Crouch, Spectrochemical Analysis
Grating Equation
Grating Equation only applies if: d > /2
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Are you getting the concept? At what angle would you collect the 1st order diffracted light with = 500 nm if a broad spectrum beam is incident on a 600 groove/mm grating at i = 10? For = 225 nm? For = 750 nm?
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