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1. Lambert-Beer law: light absorption in water [4 points + 2 extra points] Like for scattering, the intensity of light inside an absorbing medium follows the law of Lambert and Beer: I(z,λ) = Io exp (-a (1)z) where a (1) ist the absorption coefficient and z the depth in water below the surface z = 0. The absorption coefficient for water in the visible light range is given in the figure:
10 (m-1) 1 Absorption coefficient a 0.1 T TTTTIL 0.01 ப 0.001 400 450 500 550 600 650 700 750 800 Wavelength / (nm)
= (a) We consider light at two values of the wavelength: 1 500 nm and 700 nm. Convert the absorption coefficient in a mean-free path for the two values given: A500 and A700. In this context the mean-free path is called absorption length. [1 Point] (b) Calculate the density of water molecules: water has a mass density of Pm = 103 kg m-3 and a molar mass of M 18 g/mol. [1 Point] (c) Use the density to calculate the absorption cross-sections of 500 and 0 700 for both wavelengths. [1 Point] (d) Discuss why red light is more strongly absorbed than blue light - do you see some resonance in the plot? [1 Point] (e) (Extra task for 2 extra points) Neglecting the damping y «w, the cross-section is related to the frequency or wavelength by: w4 1 o(w) - e4 678-c4m2 6.6 x 10-29 m². 2 2 wž ? (ouă – 602) (22/12 - 1) Use this formula and the values from (a) to (d) to estimate the wavelength of the resonance in the infrared closest to 700 nm. Note that the resonance may be at longer or else shorter wavelength!