Chapter 36 Diffraction Part 1

1. Chapter 36 Diffraction Part 1 Single Slit Diffraction Diffraction and the Double Slit apparatus Intensity Formula for single and double slit

2. Definition and Types of Diffraction • Diffraction is the bending of a wave around an object accompanied by an interference pattern • Fresnel Diffraction - curved (spherical) wave front is diffracted • Frauenhofer Diffraction - plane wave is diffracted

3. Examples of Fresnel Diffraction Fresnel Diffraction from a sharp edge Fresnel Diffraction from a circular obstruction Fresnel bright spot

4. Example of Frauenhofer (plane wave) Diffraction

5. Diffraction Minima Flaring of rays greater when silt size is smaller and small compared to the wavelength of light ? What is the anlge of the first minima when

6. Single Slit Diffraction - Minima • Slit has width a • Divide slit into 5 ‘wavelet sources’ – see text for a different number of slit divisions • If the path difference is half a wavelength for any pair, they will cancel • Minimum occurs if all pairs cancel; i.e. 1 and 3 and 5 plus 2 and 4 Dividing the slit in 4 yields Dividing the slit in 6 yields

7. In general for the minima Single Slit Diffraction - Minima

8. Phase Difference between adjacent points in slit

9. Phase Construction which allows us to derive the Intensity at Point P on Screen

10. Single Slit Diffraction - Intensity Distribution • Consider next adding the amplitudes of the electric field vector, including phase for each increment • The resulting electric field is the vector sum as shown in the figure • Now let N go to infinity

11. Single Slit Diffraction - Intensity Distribution • Divide the slit into small increments Dy • Determine the phase difference Db The total phase difference for N increments is

12. (1) Single Slit Diffraction - Intensity Distribution (2) • Combine and square since intensity is proportional to the square of the electric field

13. Single Slit Diffraction - Intensity Distribution • Minima occur when f = mp, except… • when f = 0 a maximum occurs • Other maxima occur at solutions of intensity equation for sin q = 1

14. Double Slit and Diffraction

15. Recall Intensity by Phasor Method for Double Slit

16. Single Slit Diffraction - Envelope for other interference patterns Intensity equation for a double slit

17. For Exam Study such problems • Example 36-5

18. Resolution Diffraction and Rayleigh Criteria

19. Sample Prob. 36-4 • What is distance between peaks on screen?

20. Diffraction Grating • Generalize the double slit in addition to diffraction from each slit • For adjacent slits

21. Grating’s Instensity • Intensity plot as a function of angle

22. Width of lines and the first minima • Angle (and thus distance to …) first min from the central max

23. Distance to the first Minimum • As in the single slit diffraction pattern, the first minimum occurs when the path length difference betwn the top and bottom rays equals • Half-width of any other line depends on location relative to central axis is,

24. Grating Spectrometer • S-source, L1-Lens, S1-slit, C-collimator, L2-Lens, G-grating • Light from source focused by L1 on vertical slit S1 placed in focal plane of L2. Emerging light is a plane wave incident on G-grating: diffracted into diffraction patter, with m=0 order diffracted at angle along central axis of the grating • Lens L3 of telescope focuses light diffracted at angle onto focal plane FF’ within telescope

25. X-ray Diffraction • Standard optical diff. grating cannot be used to discriminate btwn different wavelengths in the x-ray wavelength range ie d=3000nm shows that first max • If could resolve…. • 1912 Max von Laue, crystal lattice forms a natural diffraction gratting for x-rays….Nobel Prize

26. Geometry of X-ray diffraction Bragg’s Law 1915 X-ray diffraction powerful tool for studying x-ray spectra and the arrangement of atoms in crystals. Spectra: a set of crystal planes having known spacing, d, are chosen. They reflect different wavelengths at different angles. A detector that can discriminate one angle from another can be used to determine the wavelength l of radiation reaching it. The crystal itself can be studied with a monochromatic x-ray beam, to determine not only the spacing btwn various crystal planes but also the structure of the unit cell.