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 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

✂ ✡ ☛ ✄ ✡ ✁ ✂ ☛ ✁ ✄ ☛ ✡ ✁ ✂ 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 ☎✏✝✎✟

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

Single-Slit Diffraction Example ✂ is illuminated by red light of wavelength ☛ = 650 A slit of width ✁ = 15 ✂ will the first minima appear at nm. For what value of ✬ ?

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

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).

✁ ✁ ✂ ☛ ✡ ✂ ✡ ☛ 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 ☎✏✝✎✟

✾ ✁ ✡ ☛ ✾ Resolution for a Circular Aperture The limiting angle of resolution for a circular aperture of diameter is ✷✹✸✻✺ ✢✴✧ ✄✴✄ Well resolved Just resolved Not resolved

✚ ☛ ✄ ✿ ✱ ✡ ✚ ✡ ✛ The Diffraction Grating � For light incident normally on the plane of the grating with spacing d, the condition for maxima is ✁✓❀❁✖ ✸❃❂✏❄❆❅ ✣★✢✤✣ ✣✩✧★✧✩✧❃✪ ☎✏✝✎✟

Diffraction Grating Interference Pattern

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