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Diffraction and Resolution Fraunhofer Diffraction Pattern of a - - PDF document
Diffraction and Resolution Fraunhofer Diffraction Pattern of a - - PDF document
Diffraction and Resolution Fraunhofer Diffraction Pattern of a Single Slit Resolution of Single-Slit and Circular Apertures The Diffraction Grating Homework Fraunhofer Diffraction - Qualitative Each part of the slit acts as a
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Fraunhofer Diffraction - Quantitative
If we divide the slit into two parts, waves from the upper halfinterfere destructively with waves from the lower half when
✂ ✄✆☎✞✝✠✟ ✁ ✡ ☛ ✄ ☞✍✌ ☎✞✝✎✟ ✁ ✡ ☛ ✂ If we divide the slit into four parts, we get ☎✏✝✎✟ ✁ ✡ ✄ ☛ ✂ SLIDE 4
Fraunhofer Diffraction - Quantitative (Continued)
If we divide the slit into six parts, we get ☎✏✝✎✟ ✁ ✡ ✑ ☛ ✂ Therefore, the general condition for destructive interference is ☎✞✝✠✟ ✁✓✒✕✔✗✖✕✘✙✡ ✚ ☛ ✂ ✛ ✚ ✡ ✜ ✢✤✣✥✜ ✄ ✣✦✜ ✑ ✣★✧✩✧★✧✫✪ SLIDE 5
Single-Slit Diffraction Example
A slit of width
✂ is illuminated by red light of wavelength ☛ = 650- nm. For what value of
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Single-Slit Diffraction Example
A slit of width
✂ is illuminated by red light of wavelength ☛ = 650- nm. For what value of
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Resolution of Small Apertures
Two point sources far from the aperture each produce a diffrac-tion pattern.
If the angle subtended by the sources at the aperture is largeenough, the diffraction patterns are distinguishable as shown in Fig. (a).
If the angle is small, the diffraction patterns can overlap so thatthe sources are not well resolved as shown in Fig. (b).
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Condition of Resolution
The limiting condition of resolution is know as Rayleigh’s cri-terion.
When the central maximum of the diffraction pattern of onesource falls on the first minimum of the diffraction pattern of another source, the sources are said to be resolved.
We found that the first minimum in a single-slit diffractionpattern occurs when
☎✏✝✎✟ ✁ ✡ ☛ ✂ Therefore, the limiting angle of resolution (in radians) for aslit of width a is
✁✩✷✹✸✻✺ ✡ ☛ ✂where we have applied the small angle approximation
☎✏✝✎✟ ✁✽✼ ✁ SLIDE 9
Resolution for a Circular Aperture
The limiting angle of resolution for a circular aperture of diameter
✾is
✁ ✷✹✸✻✺ ✡ ✢✴✧ ✄✴✄ ☛ ✾Well resolved Just resolved Not resolved
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The Diffraction Grating
For light incident normally on the plane of the grating withspacing d, the condition for maxima is
✿ ☎✏✝✎✟ ✁✓❀❁✖ ✸❃❂✏❄❆❅ ✡ ✚ ☛ ✛ ✚ ✡ ✱ ✣★✢✤✣ ✄ ✣✩✧★✧✩✧❃✪ SLIDE 11
Diffraction Grating Interference Pattern
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