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PHYS 101
Kenneth Ragan

Phys 101 Alanna Houston November 27, 2007 - Last class: - - The bright fringes are more closely spaces than in air. - Example: A think piece of glass is placed in front of one of the two slits in a young’s experiment so that the two waves arrive at the slit 180 degrees out of phase. Describe the interference pattern. o Out of phase half a wavelength o When in phase, bright spot halfway between slits (no piece of glass) o Dark spot in the middle when the piece of glass is placed in front of one slit but there will be the same pattern shifted by a half fringe - In the two slit experiment, the waves emitted are coherent (both sources emit a wave crest at that instant) This has a well-defined phase and wavelength relationship that gives us interference - In general, multiple light sources give incoherent light and they have no fixed phase relationship to another and therefore we do not get interference in real life - The spreading of white light into a spectrum is often called dispersion - Most prisms also give a rainbow spectrum because the index of refraction is a function of the wavelength varying by several percent over the range of visible light Phys 101 Alanna Houston - Dispersion with total internal reflection. - The second rainbow is cause by double reflections inside the raindrops - - Note that the order of colours is reversed due to the second reflection! Single Slit Diffraction: - Any sharp object will have diffraction around its edges but this is not always visible because most sources of light are not point sources. Phys 101 Alanna Houston - - - Example: Light of 750 nm goes through a slit 1.0x10^-3 mm wide. How wide is the central maximum in a) degrees, and b) cm, on a screen 20 cm away from the slit? o We consider the central maximum to be from the first minimum on one side to the first minimum on the other side o Phys 101 Alanna Houston o o Dsintheta = mlambda DARK o Dsintheta = lambda o Sintheta = 750x10^-9/1.0x10^-6 = 0.750 o Theta = 48.5 degrees o A) 2 x 48.5 degrees = 97 degrees o B) 2x = 2 x 20cm x tan(48.5) - How do we relate diffraction from slits to diffraction from barriers? Babinet’s principle o The diffraction image of an object will be exactly the same as the diffraction pattern from its complement (replacing object with aperture of some shape) o The diffraction pattern of a thin strand is the same pattern as the diffraction pattern of a single slit of the same diameter (and the angle is the same, lambda / D) - Diffraction from a solid disk has a bright spot at its centre (called a Poisson or a Fresnel spot) - You would orient a loudspeaker vertically in a PA system because if you have a small slit, lambda is fixed, the larger the theta is and vice versa - Diffraction still occurs in the individual slits of the two-slit interference experiment. Note that typically the slit width D is much smaller than the slit separation d so the diffraction pattern has minima that occur at much larger angles than the maxima of the interference pattern. If you look closely at a two-slit pattern, you see that it is imposed on the wider diffraction pattern. - Two-slit interference can also be called multi-slit interference. A device with many slits is often called a diffraction grating. - The only difference is that the maxima for a diffraction grating are much sharper than in the two-slit case. They are often used to measure spectra. o Phys 101 Alanna Houston o Interference: - In everyday life, we see interference by thin films if the film
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