Imagine a cavity in which a small hole in one side is opened for a certain Amount of time lambdat. This cavity behaves as a black body as discussed in the lecture. What Ls the maximum distance that radiation can penetrate in the cavity during this time? Now imagine that the energy density (energy per unit volume) of the radiation within the cavity is U. Show that the power radiated through the hole per unit area is with c the speed of light. In the computation, take into account the result in (a).
Explanation / Answer
b) total intensity of electroo magnetic radiation emitted at all wave lengths. in the interval d? at aparticular wavelength The intensity dI = R ( ? ) d ? where R(?) = radiancy , radiancy is related to the energy density at the wave length ? R ( ? ) = ( c / 4 ) u(? ) dI = ( c / 4 ) u(? ) d? d I / d ? = U c / 4 dP / dA = U c / 4 where energy density U = (8p / ?^ 4 ) K T a) the number of stantding waves with wave lengths between ? and ?+d? N ( ? ) = 8p V / ?^ 4 For on dimentional stanrding waves as on a stretched string of length L the allowed wave length ? = 2L / n the number of stantding waves N ( ? ) = 2 L / ?^2 8p V / ?^ 4 = 2 L / ?^2 L = 4p V / ?^2