Today Ch.36 (Diffraction) Next week, Dec.6, Review This week off. hours: Th: 2:00-3:15pm; F: 1:00-3:00pm Next week off. hours: Tu:2-3:15pm,W:1-3pm,Th:1-3pm Webct homework is due by Dec.12. Check your Midterm Exams Grades on elearning! Final Exam: (Ch.21-25, 27-29, 32,33,35,36) Secs : December 9, Friday: 12:30-2:30 pm Secs , 528: December 12, Monday, 8-10 am

Lecture 24 (Ch. 36) Diffraction 1. Huygen’s principle, bending of the rays 2. Fraunhofer’s diffraction 3. Single slit 4.Two slits with a finite width 5. Resolution of the lens 6. Diffraction grating 7.Spectroscopy 8. x-ray diffraction 9. e diffraction

Huygen’s principle and bending of the rays

1788 – 1827 Augustin-Jean Fresnel Joseph von Fraunhofer (1787 – 1826)

Single slit diffraction How to describe the real picture?

Single slit diffraction

Intensity distribution 1 st max R= 1 st min:1 st max:

Narrowing of the first fringe with increase of the slit width

Circular hole diffraction

The photographs of four very small sources of light taken made with a circular aperture in front of the lens

Rayleigh’s criterion for resolution of two point objects: Two objects are barely resolved if the center of one diffraction pattern coincides with the first minimum if the other. For a microscop 1842 – 1919 John William Strutt, 3rd Baron Rayleigh

Hubble vs Arecibo Hubble: D=2.4m, Arecibo: D=300m,

Giant Magellan Telescope (2016) D 1 =8.5m, D eq =24m

Interferometry: Arrays of telescopes

Two slits with a finite width

Diffraction grating

N-1 minima

With increase of N principal maxima becomes narrower and their amplitude grows as

Grating spectroscopy Spectrum of sunlight produced by a diffraction grating has dark absorption lines due to absorption of the corresponding wavelength by the solar atmosphere. It allows to find out a chemical composition of the solar atmosphere.

x-ray diffraction Wilhelm Röntgen (1845 – 1923) The 1 st Nobel Prize,1901

Bragg condition An x-ray scattering pattern of DNA recorded by Rosalind Franklin led Watson and Crick to discovery of the DNA double helix structure

Louis de Broglie (1892 – 1987)

Electromagnetically induced transparency (EIT) Two undistinguishable absorption passes for light result in cancellation of absorption (transparency). An electron has the wave property. It may be in a superposition of states 1 and 1’. Monohromatic light with a frequency resonant either to one or another atomic transition is absorbed. Bichromatic light containing two resonant frequencies goes through. 1 1’ O.K., Y.I.Khanin, JETP, 1986; O.K., P. Mandel, Phys. Rev. A theory S.E. Harris, PRL, experiment

Electromagnetically induced transparency (EIT) Two undistinguishable absorption passes for light result in cancellation of absorption (transparency). An electron has the wave property. It may be in a superposition of states 1 and 1’. A circular polarized light interacts only with 1-2 (or 1’-2) state and absorbed. A linear polarized light interacts with both 1-2 and 1-2’ states and goes through the medium without absorption. To make medium transparent for light with given circular polarization send through the medium simultaneously light with another circular polarization. The same is true for two beams of different frequencies When the frequency difference coincides with the frequency of the atomic transition 1-1’. 1 1’ 2 1 O.K., Y.I.Khanin, JETP, 1986; O.K., P. Mandel, Phys. Rev. A theory S.E. Harris, PRL, experiment