Lect04 - Applications of classical wave effects: +...

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Applications of classical wave effects: + important effects that re-appear in quantum physics α=2α c 0 I I 0 y Sum 2I 0 0 0 I I 0 Sum 2I 0 0 α=α c 0 I I 0 Sum 2I 0 0 α=α c /3 yy
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Overview z Circular Diffraction ( foreshadowing of quantum uncertainty) z Angular resolution (Rayleigh’s criterion) z Minimum spot size z Interferometers z Michelson z Sagnac z Applications z Resonance z Group Velocity
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Diffraction - limited Optics z Diffraction has important implications for optical instruments Lens-making is a craft. Even for a perfectly designed lens, however, the image of a point source will be a little “blurry” due to diffractionin passing through the circular aperture of the lens. The image of a point source through a circular aperture is like a single-slit diffraction pattern. But note the difference: The amount of ‘smearing’ of the image is determined by size of the aperture D, and wavelength of incident light, λ. a λ θ 0 Slit 0 1.22 D λ θ≈ Circular aperture Image plane 0 0 I I 0 θ o θ D Image plane Point object
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Transmission of light through slits and circular apertures Transmission of light through slits and circular apertures Monochromatic light source at a great distance, or a laser. Object at any distance: Slit, width a Lens, diameter D Pinhole, diameter D θ −λ/ a 0 λ/ a 0 I I 0 θ −1.22λ/ D 0 1.22λ/ D 0 I I 0 θ −1.22λ/ D 0 1.22λ/ D 0 I I 0 Observation screen: Image Plane: Observation screen: Laser with pinholes Circular-aperture diffraction pattern =“the Airy disk”. Central lobe contains 84% of power.
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Act 1: Act 1: Expansion of a Laser beam In 1985, a laser beam with a wavelength of λ = 500 nm was fired from the earth and reflected off the space shuttle Discovery, in orbit at a distance of L = 350 km away from the laser. 1. If the (circular) aperture of the laser was D = 4.7 cm , what was the beam diameter d at the space shuttle? 2. To make a smaller spot on the shuttle, what should we do to the beam diameter at the source? a. reduce it b. increase it c. cannot be made smaller D d
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Act 1: Act 1: Expansion of a Laser beam In 1985, a laser beam with a wavelength of λ = 500 nm was fired from the earth and reflected off the space shuttle Discovery, in orbit at a distance of L = 350 km away from the laser. 1. If the (circular) aperture of the laser was D = 4.7 cm , what was the beam diameter d at the space shuttle? 2. To make a smaller spot on the shuttle, what should we do to the beam diameter at the source? a. reduce it b. increase it c. cannot be made smaller D d Half-angle-width of diffraction maximum: 9 5 2 500 10 1.22 1.3 radians 4.7 o D λ θ × == = × × 53 o d 2 L 2(1.3 10 )(350 10 m) 9.1 m ≈θ× = × × = Counter-intuitive as this is, it is correct – you reduce beam divergence by using a bigger beam. (Note: this will work until D ~ d) 84% of power is in central lobe.
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Act 2: Act 2: Focusing of a laser beam There are many times you would like to focus a laser beam to as small a spot as possible. However, diffraction limits this.
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This note was uploaded on 09/15/2008 for the course PHYS 214 taught by Professor Debevec during the Spring '07 term at University of Illinois at Urbana–Champaign.

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Lect04 - Applications of classical wave effects: +...

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