optical

Fig. 2. Blackbody spectral density versus wavelength for several temperatures.
By integrating the spectral density (Eq. 1) over all wavelengths, one obtains the total radiated
intensity (power per unit area) S e (T) at the temperature T :
S e (T) = 2π5 k 4 B
15c 2 h 3T4 = σ B T 4 (2)
where σ B = 2π 5 k 4 B /15c2 h 3 = 5.67×10 −8 W/m 2 -K 4 is the Stefan-Boltzmann constant.
From the plots in Fig. 2, it can be seen that ε e (λ; T) has a maximum at some λ = λ max for
each T. Taking the derivative of Eq. 1 with to respect to λ and setting it equal to zero gives
an equation which can be solved for λ max as a function of T :
This is known as the Wien displacement law.
λ max = ( 2.90 × 10 −3 m-K ) T −1 (3)
Actual thermal radiation devices are not quite ideal, theoretical blackbodies. Real devices do
not have perfect absorbance but reflect some fraction of any incident radiation. The deviation
from perfect absorbance by a particular material is given by a function a e (λ; T) < 1; because
of the balance between absorption and emission of radiation, this quantity is referred to as
either absorptivity or emissivity. For real devices approximating a blackbody, the formulas
for ε e (λ; T) and S e (T) must be multiplied by the absorptivity a e (λ; T) characterizing the
device. In the optics lab experiment on blackbody radiation, the radiator involves a tungsten
filament; the absorptivity function for tungsten is shown in Fig. 3.
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