# Lect05 - Lecture 5 Applications of Interference and...

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Lecture 5: pplications of Interference and Diffraction Applications of Interference and Diffraction α=2α c I I 0 I I 0 α=α c I I 0 α=α c /3 0 Sum 2I 0 0 Sum 2I 0 0 Sum 2I 0 y 0 0 0 yy Lecture 5, p 1

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Today Circular Diffraction ngular resolution (Rayleigh’s criterion) z Angular resolution (Rayleigh s criterion) z Minimum spot size Interferometers ichelson z Michelson z Applications Lecture 5, p 2
Diffraction-limited Optics Diffraction has important implications for optical instruments Even for perfectly designed optics the image of a point source will be a little blurry - the circular aperture produces diffraction. Image plane I 0 D Image plane 0 I θ Point object The size of the spot is determined by the diameter, D , of the aperture, and wavelength, λ , of the incident light. 0 θ θ o The “Airy disk”. The central lobe contains 84% of power. Diffraction by a circular aperture is similar to single-slit diffraction. But note the difference: Lecture 5, p 3 a λ 0 Slit 0 1.22 D λ θ≈ Circular aperture

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Slits and circular apertures I 0 Monochromatic light lit I Observation screen: source at a great distance, or a laser. Slit, width a θ - λ /a 0 λ a 0 Pinhole, diameter D I 0 Observation screen: Object at any θ -1.22 λ /D 0 1.22 λ /D 0 I distance: Lens, diameter D Image Plane: Lecture 5, p 4 The focusing effect of the lens is independent of the diffraction effect due to the aperture
Exercise: Expansion of a Laser beam 1985 a laser beam with a wavelength of 500 nm as fired 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. D d If the circular aperture of the laser was D = 4.7 cm , what was the beam diameter d at the space shuttle? Lecture 5, p 5

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Solution 1985 a laser beam with a wavelength of 500 nm as fired 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. D d If the circular aperture of the laser was D = 4.7 cm , what was the beam diameter d at the space shuttle? Half-angle-width of diffraction maximum: 9 5 2 500 10 1.22 1.3 10 radians 4.7 10 o D λ θ × == = × × 3 2 L 2(1 3 10 )(350 10 m) 9 1m θ 53 o d 2L 2(1.3 10 )(350 10 m) 9.1 m ×= Lecture 5, p 6
Act 1 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. D d y o make a smaller spot on the shuttle hat should we do to the beam 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 Lecture 5, p 7

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Solution 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.
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Lect05 - Lecture 5 Applications of Interference and...

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