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# White light in air (n_air = 1.00) is normally incident on a thin film of oil (n_oil = 1.6) floating on a pool of water (n_water = 1. The oil has a...

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1. White light in air (n_air = 1.00) is normally incident on a thin film of oil (n_oil = 1.6) floating on a pool of water (n_water = 1.33). The oil has a thickness of t = 0.5 micrometers (see figure below). (Note that the light ray is shown coming in at an angle only to emphasize how light reflects and refracts. In an accurate picture, the incoming light would be perpendicular to the plane of the boundary.) a) What wavelengths of visible light will be most strongly reflected (i.e. for which wavelengths will the reflected rays undergo constructive interference)? b) What wavelengths of visible light will be most strongly transmitted (i.e. for which wavelengths do the transmitted rays undergo constructive interference)? Suppose that the oil layer is replaced with a soap layer with index of refraction n = 1.25. c) What is the minimum thickness t of the soap layer that will prevent orange light (wavelength = 600 nm) from being reflected? Fig for 1a and 1b 2. A space station orbits earth at an altitude of 390 km. A passenger on board looks down on the Earth wide-eyed, with a pupil radius of r = 4mm. At what minimum distance apart on earth must two bright green (wavelength = 550 nm) lights be placed to be resolvable to the passenger (assume that the only limit to resolution is due to diffraction)? 3. A mix of violet light (violet wavelength = 400 nm) and orange light (orange wavelength = 600 nm) is incident on a diffraction grating made of 1000 lines/cm. What is the angular spread between the second order maximum of the orange light and the second order maximum of the violet light? What is the angular spread between the second order maximum of orange light and the third order maximum of the violet light?

Solution 1:
a) This is a 1-flip interference problem.
For 1-flip, constructive interference occurs when For strongest reflection
say n’=1 b) In this interference we need to find the wavelength...

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