4510HomeworkSet4 - among the focal length the lens diameter...

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Physics 4510 – Optics Fall 2007 Homework Set #4 – due Friday, October 26, 2007 1. (Hecht edition 2 10.7) A single slit in an opaque screen 0.10mm wide is illuminated (in air) by plane waves from a krypton ion laser ( λ o = 461.9 nm). If the observing screen is 1.0m away, determine whether or not the resulting diffraction pattern will be of the far-field variety and then compute the angular width of the central maximum. 2. (Hecht edition 2 10.9) A collimated beam of microwaves impinges on a metal screen that contains a long horizontal slit that is 20 cm wide. A detector moving parallel to the screen in the far-field region locates the first minimum of irradiance at an angle of 36.87 o above the central axis. Determine the wavelength of the radiation. 3. (Hecht edition 2 10.23) No lens can focus light down to a perfect point, because there will always be some diffraction. Estimate the size of the minimum spot of light that can be expected at the focus of a lens. Discuss the relationship
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Unformatted text preview: among the focal length, the lens diameter, and the spot size. Take the f-number of the lens to be roughly 0.8 or 0.9, which is just about what you can expect for the fastest lens. 4. Popular legend has it that military spy satellites can read the numbers on car license plates. Your professor has no security clearance but he imagines it would be difficult for spy satellites to fly below about 100 km because of residual atmospheric gases. He also knows that the Hubble telescope was in its heyday reckoned a great honking big space telescope, and that its diffraction-limited images are collected with a primary mirror of diameter 2.4 m. If the Hubble telescope flew as low as 100 km (it typically flies at more like 500 km altitude), and if it was pointed down towards earth, instead of up at the sky, what is the smallest separation that could be resolvable on the surface of the earth? How does that compare to what you would need to read license plates?...
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