What is the Exitant Radiance from a Lambertian Plate on a Cloudy Day?

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The exercise involves calculating the exitant radiance from a horizontal Lambertian plate on a cloudy day with uniform sky radiance of 1000 W/m^2 sr. The plate has a reflectance of 0.4, leading to an irradiance of 1000(pi) W/m^2 on its surface. The reflected radiosity is calculated as 400(pi) W/m^2, which remains consistent in all directions due to the Lambertian nature of the surface. Therefore, the exitant radiance at both 45 degrees and normal to the surface is confirmed to be 400(pi) W/m^2. This conclusion aligns with the properties of Lambertian reflectance.
Hodranoel
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The exercise i have is as follows:

A flat plate (measuring 0.5 meter by 0.5 meter) is placed on the highest mountain in the landscape, exactly horizontal. It is a cloudy day, such that the sky has a uniform radiance of 1000 W/ m^2 sr.
The plate has a uniform Lambertian reflectance p=0.4.
What is the exitant radiance leaving the center point of the plate in a direction 45 degrees from the normal? In a direction normal to the surface?

Would you help me please?
Thank you in advance!

Boulayo
 
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Ok... maybe I've solved it but i still have some doubt.

The answer should be: It's 400(pi) W/m^2 in both cases of 45° and 0° because the surface is Lambertian.
The irradiance on a point of the surface is 1000(pi) W/m^2, then the reflected radiosity is 400(pi) in every direction because it's multiplied with the reflectance.

Can you confirm it? Thanks! :-)
 
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