1.1. Some visible light detection systems are limited by background or
extraneous light from the surroundings. Usually 300K blackbody radi-
ation is not a problem. To verify this:
(a) Calculate what fraction of the power radiated at 300 K occurs at
wavelengths shorter than
Use the approximation of Eq. (1.26).
(b) For wavelengths shorter than 1 jum, how many photons I second
are emitted by a 1-m^ source with unit emissivity at 300 K. Use a
photon energy corresponding to a wavelength of 1 fjm.
1.2 A long two-wire (single polarization mode) transmission line of
length, L, acts as a resonator with modes determined by nXjl - L, with
n an integer. Find the mode density in the frequency domain and then
find the thermal energy per unit length per unit frequency in terms of
kT and hv. What is the limiting form for low-frequency, that is, hv«
1.3 There is an atmospheric transmission band from 8 to 12 fjm that is
near the peak of the 300 K blackbody spectrum. Estimate the total power
radiated from a 1-m'^ unit emissivity surface in both watts and
photons/second, within this band. Approximate by calculating the power
spectral density at 10
and multiplying by the bandwidth. Compare
with a calculation based on Figure 1.13. Use the average energy of the
photons at 20 iJm.
1.4 The reflectivity of the earth averaged over the solar spectrum, some-
times called the earth albedo (literally, whiteness), is on the average
0.35. Using the solar constant and an earth temperature of
the effective emissivity e averaged over a 300K spectrum. Remember
that the earth receives solar energy from one direction but radiates its
thermal energy isotropically.
1.5 If the emissivity of the earth decreases by 10% of its current value,
find the rise in average temperature, assuming an unchanged albedo.
You may approximate by using differential forms dP and dT,