Question

4) (Howell Homework 3.6) A smooth ceramic dielectric has an index of refraction n= 1.58, which is independent of wavelength. If a flat ceramic disk is at 1100 K, how much emitted energy per unit time is received by the detector when it is placed at 0 = 0° or at 0 = 60°? Use relations from the EM theory. 0.6 Detector 0.6 cm 0.3 m Detector 0.3 m Disk0 .5 cm

Answer 1

The intensity per unit area per unit time,

$\overline S = (\frac{\mu _{0} p_{0}^2 \omega ^4}{32\pi^2c}) \frac{cos^2\theta}{r^2}\bar r$

Here P0 = qd here q = 1.6*10^-19C

Here d - diameter of disc- 0.5 cm

For q =o

$\overline S = (\frac{\mu _{0} p_{0}^2 \omega ^4}{32\pi^2c}) \frac{1}{r^2}\bar r$

Here the frequency of phonon given by

E = h.w=KT



= ا

Here temperature, T=1100 K

Now, w = 8.369*10^13 rad/s

Now s = 6.6*10^-6 watt /m2.s

For area of detector, A= 2.83*10^-5 m2

Hence the intensity recorded by detector at

q=0°

S = s. A. Cos q =1.867*10^-10 J/s

q = 60°

S = s. A. Cos q = 0.933*10^-10 J/s