Consider a light wave passing through a slit and propagating toward a distant screen. Figure P37.53 shows the intensity variation for the pattern on the screen. Give a mathematical argument that more than 90% of the transmitted energy is in the central maximum of the diffraction pattern. Suggestion: You are not expected to calculate the precise percentage, but explain the steps of your reasoning. You may use the identification 1 1 2 + 1 3 2 + 1 5 2 + ⋯ = π 2 8 Figure P37.53
Solution Summary: The author explains that the energy in the central maximum is 90% of the total transmitted light through the slit.
Consider a light wave passing through a slit and propagating toward a distant screen. Figure P37.53 shows the intensity variation for the pattern on the screen. Give a mathematical argument that more than 90% of the transmitted energy is in the central maximum of the diffraction pattern. Suggestion: You are not expected to calculate the precise percentage, but explain the steps of your reasoning. You may use the identification
Laser light of wavelength 460 nmnm is traveling in air and shines at normal incidence onto the flat end of a transparent plastic rod that has nn = 1.30. The end of the rod has a thin coating of a transparent material that has refractive index 1.75.
a)What is the minimum (nonzero) thickness of the coating for which there is maximum transmission of the light into the rod?
b)What is the minimum (nonzero) thickness of the coating for which transmission into the rod is minimized?
To keep unwanted light from reflecting from the surface of eyeglasses or other lenses, a thin film of a material with an index of refraction n = 1.38 iscoated onto the plastic lens (n = 1.55). What is the thinnest film that will minimize reflection for λ = 550 nm, the middle of the visible-light spectrum?
A thin uniform film of refractive index 1.750 is placed on a sheet of glass of refractive index 1.50. At room temperature (20.0°C), this film is just thick enough for light with wavelength 582.4 nm reflected off the top of the film to be cancelled by light reflected from the top of the glass. After the glass is placed in an oven and slowly heated to 170°C, you find that the film cancels reflected light with wavelength 588.5 nm. What is the coefficient of linear expansion of the film? (Ignore any changes in the refractive index of the film due to the temperature change.)
Chapter 38 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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