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Chapter 38

Chapter 38. Diffraction and Polarization. Outline. Introduction to diffraction Diffraction from narrow slits Resolution of single-slit and circular apertures. Introduction to diffraction.

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Chapter 38

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  1. Chapter 38 Diffraction and Polarization Dr. Jie Zou

  2. Outline • Introduction to diffraction • Diffraction from narrow slits • Resolution of single-slit and circular apertures Dr. Jie Zou

  3. Introduction to diffraction • Diffraction: Waves bend or diffract, when they pass by a barrier or through an opening. The divergence of light from its initial line of travel is called a diffraction. • Diffraction pattern Dr. Jie Zou

  4. Diffraction from narrow slits: Observation • Diffraction pattern of a single slit-observation: The pattern consists of a central bright fringe flanked by much weaker maxima alternating with dark fringes. Dr. Jie Zou

  5. Diffraction of narrow slits: Explanation • Explanation: According to Huygens’s principle, each portion of the slit acts as a point source of light waves. Light from one portion of the slit can interfere with light from another portion, and the resultant light intensity on a viewing screen depends on the direction . Dr. Jie Zou

  6. Dependence of the resultant light intensity on direction  • Large number of small zones, each with a width y. • Phase difference between adjacent zones:  = (2/)y sin • Total electric filed E at point P: EP = Esin(t) + Esin(t+) +…+ Esin(t+N) • It can be shown that: EP =(NE)[sin(/2)/(/2)]sin(t+), where  = N  = (2/) a sin. • Light intensity at P: I = Imax [sin(/2)/(/2)]2. Assumption: The viewing screen is very far from the single slit. Dr. Jie Zou

  7. Light intensity vs. /2 plot • For a single-slit diffraction, most of the light intensity is concentrated in the central bright fringe. • Condition for intensity minima: sin  = m(/a), m = 1, 2,… • The central maximum occurs at  = 0 (central point on the screen). • To a good approximation, the secondary maxima lie midway between the zero points: /2 =3/2, 5/2,… Dr. Jie Zou

  8. Example 38.2 Relative intensities of the maxima • Find the ratio of the intensities of the secondary maxima to the intensity of the central maximum for the single-slit diffraction pattern. Dr. Jie Zou

  9. Resolution of single-slit and circular apertures • The ability of optical systems to distinguish between closely spaced objects is limited because of the wave nature of light. Dr. Jie Zou

  10. Rayleigh’s criterion for resolution • Rayleigh’s criterion: When the central maximum of one image falls on the first minimum of the other image, the images are said to be just resolved. • For a slit with width a, the limiting angle of resolution is: min = /a. • For a circular aperture of diameter D, the limiting angle of resolution is: min = 1.22(/D). Dr. Jie Zou

  11. Example 38.5 Resolution of the eye • Estimate the limiting angle of resolution for the human eye, assuming its resolution is limited only by diffraction (Choose  = 500 nm, and pupil diameter = 2 mm) Dr. Jie Zou

  12. Homework • Ch. 38, P. 1238, Problems: #1, 2, 18. Dr. Jie Zou

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