Consider a material that is gray, but directionally selective with (alpha_{theta}(theta, phi)=0.8(1-cos phi)). Determine the hemispherical absorptivity

Question:

Consider a material that is gray, but directionally selective with $\alpha_{\theta}(\theta, \phi)=0.8(1-\cos \phi)$. Determine the hemispherical absorptivity $\alpha$ when collimated flux irradiates the surface of the material in the direction $\theta=45^{\circ}$ and $\phi=45^{\circ}$. Determine the hemispherical emissivity $\varepsilon$ of the material.

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