Lect03 - Diffraction Spectroscopy y d L Spectra of atoms...

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Diffraction & Spectroscopy Diffraction image of DNA taken by Rosalind Franklin in 1953 – the first evidence of the helical structure of DNA y L d θ Spectra of atoms reveal the quantum nature of matter

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Overview Overview *Derivations in Appendix of lecture 2 (also in Young and Freeman, Secs. 36.2 and 36.4) z Multiple-slit Interference formula* z Diffraction Gratings z Spectral Resolution z Optical Spectroscopy z Window on the nature atomic scale world z X-ray Crystallography z Window on the atomic scale structure of matter z Single-Slit Diffraction* z Interference + Diffraction See Text. Young and Freeman Chapter 36
Last Lecture: Last Lecture: General properties of N General properties of N - - Slit Interference Slit Interference The positions of the principal maxima of the intensity patterns always occur at φ = 0, ± 2 π , ± 4 π, . .. is the phase between adjacent slits] ( i.e., dsin θ = ± m λ , m = 0, 1, 2,… ) . The principal maxima become taller and narrower as N increases. The intensity of a principal maximum is equal to N 2 times the maximum intensity from one slit. The width of a principal maximum goes as 1/N. The # of zeroes between adjacent principal maxima is equal to N-1. The # of secondary maxima between adjacent principal maxima is N-2. 0 −2π I 0 16I 1 N=4 0 −2π I 0 25I 1 N=5 0 −2π I 0 9I 1 N=3 −λ/ d 0 λ/ d φ θ φ θ −λ/ d 0 λ/ d −λ/ d 0 λ/ d φ θ

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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 power I at the principal maxima? a. stays same (I) b. doubles (2I) c. quadruples (4I) 2. What happens to the net power I on the screen? a. stays same (I) b. doubles (2I) c. quadruples (4I) Changed order
Act 1 - 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 power I at the principal maxima? a. stays same (I) b. doubles (2I) c. quadruples (4I) 2. What happens to the net power I on the screen? a. stays same (I) b. doubles (2I) c. quadruples (4I) If we double the number of slits, we expect the net power on the screen to double. How does it do this… z The location and number of the principle maxima (which have most of the power) does not change. z The principle maxima become 4x brighter. z But they also become only half as wide. (A/2) z Therefore, the net power (integrating over all the peaks) increases two-fold, as we would expect. (P goes as IA)

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Last lecture: N Last lecture: N - - Slit Interference Slit Interference (see (see Appendix of previous lecture for derivation) Appendix of previous lecture for derivation) z The Intensity for N equally spaced slits is given by: L y and d sin d = = θ λ δ π φ 2 2 1 ) 2 / sin( ) 2 / sin( = N I I N * * Your calculator can probably plot this up. Give it a try.
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Lect03 - Diffraction Spectroscopy y d L Spectra of atoms...

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