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

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Lecture 5, p 1 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 y y Lecture 5: Applications of Interference and Diffraction

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Lecture 5, p 2 Today Circular Diffraction circle6 Angular resolution (Rayleigh’s criterion) circle6 Minimum spot size Interferometers circle6 Michelson circle6 Applications
Lecture 5, p 3 The size of the spot is determined by the diameter, D , of the aperture, and wavelength, λ , of the incident light. Diffraction by a circular aperture is similar to single-slit diffraction. But note the difference: Image plane 0 0 I I 0 θ θ o θ D Image plane Point object a λ θ 0 Slit 0 1.22 D λ θ ≈ Circular aperture The “Airy disk”. The central lobe contains 84% of power. 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.

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Lecture 5, p 4
Lecture 5, p 5 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 -1.22 λ /D 0 1.22 λ /D 0 I I 0 Observation screen: Image Plane: Observation screen: The focusing effect of the lens is independent of the diffraction effect due to the aperture

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Lecture 5, p 6 Exercise: Expansion of a Laser beam D d 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. 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 7 Act 1 D d 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 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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Lecture 5, p 8
Lecture 5, p 9 Exercise: Focusing a laser beam D laser d D lens f 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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