Problem 5.217

A beam of light of intensity \(I_{0}\) falls normally on a transparent plane-parallel plate of thickness \(l .\) The beam contains all the wavelengths in the interval from \(\lambda_{1}\) to \(\lambda_{2}\) of equal spectral intensity. Find the intensity of the transmitted beam if in this wavelength interval the absorption coefficient is a linear function of \(\lambda\), with extreme values \(x_{1}\) and \(x_{2} .\) The coefficient of reflection at each surface is equal to p. The secondary reflections are to be neglected.