Emissivity of a flat surface varies with zenith angle

[Callisto]

If the emissivity of a flat surface varies with zenith angle according to

e=E*cos(theta)
where E is the emissivity at zenith.
Would this surface radiate isotropically?

I think that because the emissivity varies then the emitted radiation varies accordingly so the energy measured from any fixed point and at any angle would not be the same so therefore the surface would be an anisotropic source of radiation.

Does this sound like a fair argument?
anybody care to correct me?

Callisto

 

[Antiphon]

If the emissivity of a flat surface varies with zenith angle according to

e=E*cos(theta)
where E is the emissivity at zenith.
Would this surface radiate isotropically?

I think that because the emissivity varies then the emitted radiation varies accordingly so the energy measured from any fixed point and at any angle would not be the same so therefore the surface would be an anisotropic source of radiation.

Does this sound like a fair argument?
anybody care to correct me?

Callisto

No, the surface is an isotropic radiator. The cos law means the projected
area of the surface is being reduced. Any deviation from the cos variation
means it's not an isotropic radiator.