Homework 3 Solutions

7 hence light absorption must remove 337 magnitudes

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Unformatted text preview: ased on the spectral properties of water absorption, explain why the clear ocean appears blue. Red sunlight incident on water is more likely to be absorbed, whereas blue light passes through more deeply. That light may be reflected back (from the seafloor) or scattered (by water molecules via Rayleigh scattering), so we see in all directions more blue light both in and above the water. (b) [10 pt] If we dive deep enough underwater, it becomes dark. At what point would we see no sunlight whatsoever? The faintest stars we can see with our eyes are magnitude ≈ 7, whereas the Sun’s apparent magnitude is  ­26.7. Hence, light absorption must remove 33.7 magnitudes of light, a factor of 10 ­ 33.7/2.5 = 10 ­13.5 of the original sunlight intensity. Radiative transfer, in the absence of any additional scattering or absorption, predicts an intensity decline of: I (s) = I (0)e−κλ ρs Taking the minimum value of κλ ≈ 10 ­4 m2/kg, and assuming ρ ≈ 1 g/cm3 = 103 kg/m3 (the density of water does not vary appreciably with depth): I (s)/I (0) = e−0.1s = 10−13.5 so s = 310 m, or about 1000 ft. This is commonly referred...
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This document was uploaded on 02/26/2014 for the course PHYS 160 at UCSD.

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