I E Irodov Solutions for Chapter: OPTICS, Exercise 7: THERMAL RADIATION

The temperature of one of the two heated black bodies is $T_1=2500 \mathrm{K}$. Find the temperature of the other body, if the wavelength corresponding to its maximum emissive capacity exceeds by $\mathrm{\Delta \lambda }=0.50 \mathrm{\mu m}$ the wavelength corresponding to the maximum emissive capacity of the first black body. Wein's constant, $b=2.898\times {10}^{-3} \mathrm{mK}$

The spectral composition of solar radiation is much the same as that of a black body whose maximum emission corresponds to the wavelength $0.48 \mathrm{\mu m}$. Find the mass lost by the Sun every second due to radiation. Evaluate the time interval during which the mass of the Sun diminishes by $1$ per cent. Wein's constant $b=2.9\times {10}^{-3} \mathrm{mK}$, mass of Sun is $1.97\times {10}^{30} \mathrm{kg}$, speed of light $c=3\times {10}^8 {\mathrm{ms}}^{-1}$, the Stefan-Boltzmann constant $\sigma =5.67\times {10}^{-8} \mathrm{J} {\mathrm{s}}^{-1}$, emissivity for Sun $e=1$ and the radius of the Sun is $6.95\times {10}^8 \mathrm{m}$.

A copper ball of diameter $d=1.2 \mathrm{cm}$ was placed in an evacuated vessel whose walls are kept at the absolute zero temperature. The initial temperature of the ball is $T_0=300 \mathrm{K}$. Assuming the surface of the ball to be absolutely black, find how soon its temperature decreases $\mathrm{\eta }=2.0$ times. Density of copper is $8.9 {\mathrm{gcm}}^{-3}$, specific heat capacity of copper is $0.39 {\mathrm{Jg}}^{-1}{\mathrm{K}}^{-1}$, the Stefan-Boltzmann constant $\sigma =5.67\times {10}^{-8} {\mathrm{Js}}^{-1}$.

An isotropic point source emits light with wavelength $\mathrm{\lambda }=589 \mathrm{nm}$. The radiation power of the source is $P=10 \mathrm{W}$. Find

(a) the mean density of the flow of photons at a distance $r=2.0 \mathrm{m}$ from the source.

(b) the distance between the source and the point at which the mean concentration of photons is equal to $n=100 {\mathrm{cm}}^{-3}$.

Planck's constant $h=6.626\times {10}^{-34} {\mathrm{JHz}}^{-1}$ and speed of light $c=3\times {10}^8 {\mathrm{ms}}^{-1}$

From the standpoint of the corpuscular theory, demonstrate that the momentum transferred by a beam of parallel light rays per unit time does not depend on its spectral composition but depends only on the energy flux ${\mathrm{\Phi }}_{\mathrm{e}}$.

A laser emits a light pulse of duration $\mathrm{\tau }=0.13 \mathrm{ms}$ and energy $E=10 \mathrm{J}$. Find the mean pressure exerted by such a light pulse when it is focused into a spot of diameter $d=10 \mathrm{\mu m}$ on a surface perpendicular to the beam and possessing a reflection coefficient $\mathrm{\rho }=0.50$, speed of light $c=3\times {10}^8 {\mathrm{ms}}^{-1}$.

A short light pulse of energy $E=7.5 \mathrm{J}$ falls in the form of a narrow and almost parallel beam on a mirror plate, whose reflection coefficient is $\mathrm{\rho }=0.60$. The angle of incidence is $30°$. In terms of the corpuscular theory, find the momentum transferred to the plate. Speed of light $c=3\times {10}^8 {\mathrm{ms}}^{-1}$.

A plane light wave of intensity $I=0.20 \mathrm{W} {\mathrm{cm}}^{-2}$, falls on a plane mirror surface with a reflection coefficient $\mathrm{\rho }=0.8$. The angle of incidence is $45°$. In terms of the corpuscular theory, find the magnitude of the normal pressure exerted by light on that surface. Speed of light, $c=3\times {10}^8 {\mathrm{ms}}^{-1}$.