Consider a two-color pyrometer such as in Problem 12.69 that operates at \(\lambda_{1}=0.65 \mu \mathrm{m}\) and \(\lambda_{2}=0.63 \mu \mathrm{m}\). Using Wien's law determine the temperature of a sheet of stainless steel if the ratio of radiation detected is \(I_{\lambda_{1}} / I_{\lambda_{2}}=2.15\).

Data From Problem 12.69:-

A two-color pyrometer is a device that is used to measure the temperature of a diffuse surface, \(T_{s}\). The device measures the spectral, directional intensity emitted by the surface at two distinct wavelengths separated by \(\Delta \lambda\). Calculate and plot the ratio of the intensities \(I_{\lambda+\Delta \lambda, e}\left(\lambda+\Delta \lambda, \theta, \phi, T_{s}\right)\) and \(I_{\lambda, e}\left(\lambda, \theta, \phi, T_{s}\right)\) as a function of the surface temperature over the range \(500 \mathrm{~K} \leq T_{s} \leq 1000 \mathrm{~K}\) for \(\lambda=5 \mu \mathrm{m}\) and \(\Delta \lambda=0.1,0.5\), and \(1 \mu \mathrm{m}\). Comment on the sensitivity to temperature and on whether the ratio depends on the emissivity of the surface. Discuss the tradeoffs associated with specification of the various values of \(\Delta \lambda\).