Announcements 3/23/12 Prayer Handouts from last time: Bessel function (for next lecture), and exam 3 review Yesterday’s lab: worked until early afternoon… xkcd

Reading Quiz The array theorem and the book’s treatment of diffraction gratings are for the __________ approximation. Fresnel Fraunhofer

Reading Quiz The array theorem applies to: small circular holes only narrow slits only any identical apertures

Fourier Transform of shifted function

Array Theorem

Reading Quiz The resolving power of a spectrometer, l/Dl, depends on the: number of slits illuminated on the grating separation between slits of the grating both of the above

Diffraction Grating “Fraunhofer n-slit” animation

1-D slits, infinitely narrow 3 slits, equally spaced (created with parameters so period = 2p)

Back to 1-D slits, infinitely narrow 4 slits, equally spaced

Back to 1-D slits, infinitely narrow 5 slits, equally spaced

Back to 1-D slits, infinitely narrow 10 slits, equally spaced

Back to 1-D slits, infinitely narrow 20 slits, equally spaced

Back to 1-D slits, infinitely narrow 100 slits, equally spaced What have we learned?

The Grating Equation Where will maxima be?

Red light vs. Green light Spectrometer Red light vs. Green light

width = 1/N  separation of maxima Resolving Power N=100 Goes to zero at x=0.0628 = 2p/100 width = 1/N  separation of maxima