optical

More documents

Recommendations

Info

$X-ray Diffraction (new)$

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. 4
Fig. 3. Absorptivity for tungsten as a function of wavelength and temperature. In the derivation of the blackbody formulas, it is assumed that the blackbody is in equilibrium with (and hence at the same temperature as) its environment. However, in the optics lab blackbody experiment, the device approximating the blackbody is heated to a temperature T significantly above its environment, which is at room temperature T 0 ≃ 300 K; thus the formula for blackbody power radiation must be modified, as will be shown below. Furthermore, the experimental blackbody will also lose energy due to heat being removed by convection in the surrounding air; this power loss is linearly proportional to the difference in the device temperature T and the environment temperature T 0 . The total power lost by the blackbody device due to being out of thermal equilibrium with its environment must be supplied by an external source; in the case of the optics lab blackbody device, this is the electrical power delivered to the tungsten filament. By conservation of energy we have I dc V dc = κ (T − T 0 ) + 〈a e 〉 (T)σ B A ( ) T 4 − T0 4 (4) where I dc is the DC current passing through the tungsten filament, V dc is the voltage drop across the filament, κ is the effective thermal conductivity due to convection in the air, 〈a e 〉 (T) is an average of a e (λ; T) over wavelengths for which data are taken, and A is an estimate of the area of the tungsten filament. With the above formulas, the goals of the optics lab blackbody experiment may be outlined as follows: (a) By measuring the spectral density of the radiation from the tungsten filament and com- 5
Page 1 and 2: OPTICS INTRODUCTION The optics lab
Page 3: explanation of the photoelectric ef
Page 7 and 8: Photoluminescence Photoluminescence
Page 9 and 10: In Fig. 5, the tungsten lamp is ins
Page 11 and 12: silica for a wavelength range of 20
Page 13: 1. Set up the experiment according

optical

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?