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Lecture 6: Waves Review, Crystallography, and Examples

Single-Slit Diffraction (from L4). Slit of width a. Where are the minima?Use Huygens' principle: treat each point across the opening of the slit as a wave source.The first minimum is at an angle such that the light from the top and the middle of the slit destructively interfere.This works, bec

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Lecture 6: Waves Review, Crystallography, and Examples

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    1. DEMOS: * ---- Computer “slits” program * 162 Laser with multiple slits slides. * 74 Xmas tree and diffraction grating handouts * 1237 CD to show diffraction * 1044 Green and Red lasers to shine thru diff grating * 731 Iridescent butterfly * 320 Phasor wheelDEMOS: * ---- Computer “slits” program * 162 Laser with multiple slits slides. * 74 Xmas tree and diffraction grating handouts * 1237 CD to show diffraction * 1044 Green and Red lasers to shine thru diff grating * 731 Iridescent butterfly * 320 Phasor wheel

    2. Single-Slit Diffraction (from L4) Slit of width a. Where are the minima? Use Huygens’ principle: treat each point across the opening of the slit as a wave source. The first minimum is at an angle such that the light from the top and the middle of the slit destructively interfere. This works, because for every point in the top half, there is a corresponding point in the bottom half that cancels it. You MUST at least get this far, in order for the students to understand the lab and the discussion this week!You MUST at least get this far, in order for the students to understand the lab and the discussion this week!

    5. Multiple Slit Interference (from L4) Multi-slit computer program.Multi-slit computer program.

    6. Act 1 Light interfering from 10 equally spaced slits initially illuminates a screen. Now we double the number of slits, keeping the spacing constant. 1. What happens to the intensity I at the principal maxima? a. stays same (I) b. doubles (2I) c. quadruples (4I) 2. What happens to the net power on the screen? a. stays same b. doubles c. quadruples

    7. Solution Light interfering from 10 equally spaced slits initially illuminates a screen. Now we double the number of slits, keeping the spacing constant. 1. What happens to the intensity I at the principal maxima? a. stays same (I) b. doubles (2I) c. quadruples (4I) 2. What happens to the net power on the screen? a. stays same b. doubles c. quadruples

    8. Solution Light interfering from 10 equally spaced slits initially illuminates a screen. Now we double the number of slits, keeping the spacing constant. 1. What happens to the intensity I at the principal maxima? a. stays same (I) b. doubles (2I) c. quadruples (4I) 2. What happens to the net power on the screen? a. stays same b. doubles c. quadruples

    9. This is not in the printed notes.This is not in the printed notes.

    11. ACT 2: Multiple Slits

    12. Solution

    13. Solution

    14. Light of wavelength l is incident on an N-slit system with slit width a and slit spacing d. 1. The intensity I as a function of y at a viewing screen located a distance L from the slits is shown to the right. L >> d, y, a. What is N? a) N = 2 b) N = 3 c) N = 4 Interference & Diffraction Exercise

    15. Solution Light of wavelength l is incident on an N-slit system with slit width a and slit spacing d. 1. The intensity I as a function of y at a viewing screen located a distance L from the slits is shown to the right. L >> d, y, a. What is N? a) N = 2 b) N = 3 c) N = 4

    16. Light of wavelength l is incident on an N-slit system with slit width a and slit spacing d. 1. The intensity I as a function of y at a viewing screen located a distance L from the slits is shown to the right. L >> d, y, a. What is N? a) N = 2 b) N = 3 c) N = 4 Solution

    20. Diffraction Gratings (1) Diffraction gratings rely on N-slit interference. They consist of a large number of evenly spaced parallel slits. An important question: How effective are diffraction gratings at resolving light of different wavelengths (i.e. separating closely-spaced ‘spectral lines’)? 74 Xmas tree (sodium only)74 Xmas tree (sodium only)

    21. Diffraction Gratings (2)

    22. ACT 2 1. Suppose we fully illuminate a grating for which d = 2.5 mm. How big must it be to resolve the Na lines (589 nm, 589.6 nm), if we are operating at second order (m = 2)? a. 0.12 mm b. 1.2 mm c. 12 mm

    23. Solution 1. Suppose we fully illuminate a grating for which d = 2.5 mm. How big must it be to resolve the Na lines (589 nm, 589.6 nm), if we are operating at second order (m = 2)? a. 0.12 mm b. 1.2 mm c. 12 mm

    24. 1. Suppose we fully illuminate a grating for which d = 2.5 mm. How big must it be to resolve the Na lines (589 nm, 589.6 nm), if we are operating at second order (m = 2)? a. 0.12 mm b. 1.2 mm c. 12 mm Solution

    25. 1. Assuming we fully illuminate the grating from the previous problem (d = 2.5 mm), how big must it be to resolve the Na lines (589 nm, 589.6 nm)? a. 0.12 mm b. 1.2 mm c. 12 mm Solution

    26. NOTE: No interference between the two images. DEMOS: * 2 aperturesNOTE: No interference between the two images. DEMOS: * 2 apertures

    28. Solution

    29. Go over this slide relatively quickly (I used the laser with the holographic tips to demonstrate the basic principle), and the next 3 very fast.Go over this slide relatively quickly (I used the laser with the holographic tips to demonstrate the basic principle), and the next 3 very fast.

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