Diffraction and Resolution Fraunhofer Diffraction Pattern of a - - PDF document

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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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SLIDE 1

Diffraction and Resolution

Fraunhofer Diffraction Pattern of a Single Slit Resolution of Single-Slit and Circular Apertures The Diffraction Grating Homework
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SLIDE 2

Fraunhofer Diffraction - Qualitative

Each part of the slit acts as a source of waves. Light from one part of the slit can interfere with light from

another part.

The resulting intensity on the screen depends on the angle ✁ .
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SLIDE 3

Fraunhofer Diffraction - Quantitative

If we divide the slit into two parts, waves from the upper half

interfere destructively with waves from the lower half when

✂ ✄✆☎✞✝✠✟ ✁ ✡ ☛ ✄ ☞✍✌ ☎✞✝✎✟ ✁ ✡ ☛ ✂ If we divide the slit into four parts, we get ☎✏✝✎✟ ✁ ✡ ✄ ☛ ✂
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SLIDE 4

Fraunhofer Diffraction - Quantitative (Continued)

If we divide the slit into six parts, we get ☎✏✝✎✟ ✁ ✡ ✑ ☛ ✂ Therefore, the general condition for destructive interference is ☎✞✝✠✟ ✁✓✒✕✔✗✖✕✘✙✡ ✚ ☛ ✂ ✛ ✚ ✡ ✜ ✢✤✣✥✜ ✄ ✣✦✜ ✑ ✣★✧✩✧★✧✫✪
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SLIDE 5

Single-Slit Diffraction Example

A slit of width

✂ is illuminated by red light of wavelength ☛ = 650
  • nm. For what value of
✂ will the first minima appear at ✁ = 15 ✬ ?
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SLIDE 6

Single-Slit Diffraction Example

A slit of width

✂ is illuminated by red light of wavelength ☛ = 650
  • nm. For what value of
✂ will the first minima appear at ✁ = 15 ✬ ? ☎✞✝✠✟ ✁ ✡ ✚ ☛ ✂ ✂ ✡ ✚ ☛ ☎✏✝✎✟ ✁ ✡ ✛ ✢✭✪ ✛✯✮✤✰✍✱✳✲ ✚ ✪ ☎✞✝✎✟ ✢ ✰ ✬ ✡ ✄ ✰ ✢✴✢ ✲ ✚ ✡ ✄ ✧ ✰✶✵ ✚
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SLIDE 7

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 large

enough, the diffraction patterns are distinguishable as shown in Fig. (a).

If the angle is small, the diffraction patterns can overlap so that

the sources are not well resolved as shown in Fig. (b).

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SLIDE 8

Condition of Resolution

The limiting condition of resolution is know as Rayleigh’s cri-

terion.

When the central maximum of the diffraction pattern of one

source 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 diffraction

pattern occurs when

☎✏✝✎✟ ✁ ✡ ☛ ✂ Therefore, the limiting angle of resolution (in radians) for a

slit of width a is

✁✩✷✹✸✻✺ ✡ ☛ ✂

where we have applied the small angle approximation

☎✏✝✎✟ ✁✽✼ ✁
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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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SLIDE 10

The Diffraction Grating

For light incident normally on the plane of the grating with

spacing d, the condition for maxima is

✿ ☎✏✝✎✟ ✁✓❀❁✖ ✸❃❂✏❄❆❅ ✡ ✚ ☛ ✛ ✚ ✡ ✱ ✣★✢✤✣ ✄ ✣✩✧★✧✩✧❃✪
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SLIDE 11

Diffraction Grating Interference Pattern

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SLIDE 12

Homework Set 3 - Due Mon. Apr. 5

Read Sections 27.6 - 27.8 Answer Questions 27.14 & 27.22 Do Problems 27.19, 27.26, 27.29 & 27.32