Thermal emissivities of films on substrates

An explicit expression for thermal emissivity of thin films has been derived in terms of optical constants of the substrate and film. At millimicron film thicknesses, the substrate plays a vital rôle in governing the emissivities of the films. For low values of the coefficient of absorption, the emissivity has a value of [epsilon]1([lambda]) for zero film thickness, reaches a minimum at an optimum value of thickness and then increases monotonically to [epsilon]2([lambda]) for very large values of thickness. [epsilon]1([lambda]) and [epsilon]2([lambda]) are, respectively, the emissivities of the bulk substrate and the film material. For large values of the coefficient of absorption, the emissivity passes through a minimum and then a maximum before monotonically decreasing to [epsilon]2([lambda]) (for large values of the thickness), as the thickness is increased.