1 / 9

Lecture 10

Lecture 10. Wave propagation. Aims: Fraunhofer diffraction (waves in the “far field”). Young’s double slits Three slits N slits and diffraction gratings A single broad slit General formula - Fourier transform. Fraunhofer diffraction. Diffraction.

maida
Download Presentation

Lecture 10

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 10 Wave propagation. • Aims: • Fraunhofer diffraction (waves in the “far field”). • Young’s double slits • Three slits • N slits and diffraction gratings • A single broad slit • General formula - Fourier transform.

  2. Fraunhofer diffraction • Diffraction. • Propagation of partly obstructed waves. • Apertures, obstructions etc... • Diffraction régimes. • In the immediate vicinity of the obstruction: • Large angles and no approximations • Full solution required. • Intermediate distances (near field) • Small angles, spherical waves, • Fresnel diffraction. • Large distances (far field) • Small angles, and plane waves, • Fraunhofer diffraction. • (More formal definitions will come in the Optics course)

  3. Young’s slits • Fraunhofer conditions • For us this means an incident plane wave and observation at infinity. • Two narrow apertures (2 point sources) • Each slit is a source of secondary wavelets • Full derivation (not in handout) is….Applying “cos rule” to top triangle gives

  4. 2-slit diffraction • Similarly for bottom ray • Resultant is a superposition of 2 wavelets • The term expi(kR-wt)will occur in allexpressions. We ignoreit - only relative phasesare important.Where s = sinq.

  5. cos-squared fringes • We observe intensitycos-squared fringes. • Spacing inversely proportional to separation of the slits. • Amplitude-phase diagrams. Spacing of maxima Resultant Slit 1 Slit 2

  6. Three slits • Three slits, spacing d. • Primary maxima separated by l/d, as before. • One secondary maximum.

  7. N slits and diffraction gratings • N slits, each separated by d. • A geometric progression, which sums to • Intensity in primary maxima a N2 • In the limit as N goes to infinity, primary maxima become d-functions. A diffraction grating. Spacing, as before N-2, secondary maxima

  8. l/t Single broad slit • Slit of width t. Incident plane wave. • Summation of discrete sourcesbecomes an integral.

  9. Generalisation to any aperture • Aperture function • The amplitude distribution across an aperture can take any form a(y). This is the aperture function. • The Fraunhofer diffraction pattern is • putting ks=K gives a Fourier integral • The Fraunhofer diffraction pattern is the Fourier Transform of the aperture function. • Diffraction from complicated apertures can often be simplified using the convolution theorem. • Example: 2-slits of finite widthConvolution of 2d-functions with asingle broad slit.FT(f*g) a FT(f).FT(g) Cos fringes sinc function

More Related