• Notes
• 4

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Answer : The relevant wavelength must be about 500 nm (5 x 10 -5 cm) since this is near the peak of the solar spectrum. Therefore, the absorption coefficient, for the determined value of n i , is 0.01 (4 π ) / (5 x 10 -5 cm) = 2513 cm -1 . Beer’s law states that the transmission of light through a substance is T = exp(-k x). Since the distance through the bottle is 10 cm, the transmission for this value of k is exp(- 2513 cm -1 x 10 cm) = 0.000. Thus the determined value of n i must be far too large since you would not be able to see through a bottle if the transmission was 0.000. Problem 8: The temperature of the Earth is around 288 K, and the temperature of the sun’s photosphere is around 5800 K. (a) What is the ratio of the total thermal irradiance emitted by the Earth to that of the sun? (b) What are the wavelengths of maximum emission for the Earth and for the sun? Answer: (a) Use Stefan-Boltzmann: F = σ T 4 F (Earth) / F (sun) = (288) 4 / (5800) 4 = 6.08 × 10 -6 (b) Use Wien’s Law: Peak λ = 2897 / T (units = μ m) Earth: λ = 2897 / 288 = 10 μ m Sun: λ = 2897 / 5800 = 500 nm Problem 9: The electric field vector for elliptically polarized light can be written as: j ˆ )} ( exp{ i ˆ )} ( exp{ y y x x t i A t i A E φ ω φ ω + + + = r Based on this, write down the full Jones vector for right circularly polarized light.

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Answer: Right circularly polarized light means that A x = A y A rcp and 2 / π φ φ + = x y so )) 2 / ( exp( ) exp( E rcp rcp π φ φ + = x x i A i A r Problem 10: An aircraft flying over a cloud that’s at an altitude of 7.4 km measures a total longwave irradiance of 188 W m -2 . What is the temperature of the cloud? Answer: Rearrange F = σ T 4 to get T = (F/ σ ) 1/4 = (188 W m -2 / 5.67 × 10 -8 J s -1 K -4 ) 1/4 = 240K
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• Fall '10
• Randell
• Light, Tfood, warm food

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