The research group of a glass manufacturer is working on development of a coating that would render glass highly transparent to radiation at wavelengths below 0.7μm and highly reflective to radiation above 0.7μm. An application of special interest is to the inner surface of glass light bulbs.

(a) Explain the advantages of having a light bulb whose inner surface is perfectly transparent (τλ = 1) to radiation for λ < 0.7μm and perfectly reflecting (pλ = 1) for λ > 0.7μm.

(b) Consider such a light bulb with a tungsten filament whose spectral emissivity is characterized by the distribution of Problem 12.29. What is the electric power required to maintain a filament temperature of 3000 K if the filament diameter and length are D = 0.8 mm and L = 20 mm? What is the power requirement if the coating can only provide complete reflection for λ > 2.0μm, with complete transmission maintained at lower wavelengths?