Consider a two-color pyrometer such as in Problem 12.89 that operates at 1 = 0.65 m

Consider a two-color pyrometer such as in Problem 12.89 that operates at λ₁ = 0.65
μm and λ₂ = 0.63 λm. Using Wien’s law (see Problem 12.27) determine the temperature of a sheet of stainless steel if the ratio of radiation detected is I_λ1/I_λ2 = 2.15.

Data From Problem 12.89

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  he surface at two distinct wavelengths separated by Δλ.  Calculate and plot the ratio of the intensities  I_{λ + Δλ,e} (λ+ Δλ, θ, ϕ, T_s) and I_λ,e (λ,θ, ϕ, T_s) as a function  of the surface temperature over the range 500 K ≤ T_s ≤ 1000 K for λ = 5 μm and Δλ = 0.1, 0.5,  and 1 μm. 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 Δλ.