Question

The complex refractive index of a substance is given by n-n' + in". The relationship of n" to k" is k" For the case described above that the time averaged flux is given by FFo exp (-2k") argue that the depth that radiation penetrates into a substance is 32 Satellites use infrared wavelengths of ~ 10 μm to detect the surface temperature of the Great Salt Lake. The complex component of the refractive index at these wavelengths is ~ 0.1. With reference to your answer to the question above, what temperature of the Great Salt Lake exactly are the satellites "seeing"?

Answer 1

"n = n' + cn"" (a) Also k"" = w/c n"" = 2 pi n""/lambda (1) Flux F vector = F_0 vector exp (-2k"" vector middot x vector) = F_0 vector e6-2k"" vector middot x vector = F_0 vector e^-2 w/c n"" vector middot n vector = F_0 vector e^-2 211/lambda n"" middot x vector = F_0 vector e^-4 pi/lambda (n - n'/i) i/i n vector = F_0 vector e^-4 pi/lambda (n - n'/i^2) i - n vector Therefore we get delta = -1/4 pi/lambda (n - n') i delta = -lambda/4 pi (-n"") delta = lambda/4 pi n"" ""Hence proved"" \r\n delta = lambda/4 pi n"" delta = 10 times 10^-6/4 pi times 0.1 = 0.78 times 10^-5 m lambda/n"" T = b (Wiens displacement) 10 times 10^-76 m/0.1 times T = 2.898 times 10^-3 t = 28.98 T = 29 k"