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

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SUMMARY

The exitant radiance from a Lambertian plate measuring 0.5 meters by 0.5 meters on a cloudy day with a uniform sky radiance of 1000 W/m² sr is calculated to be 400π W/m² in both a 45-degree direction and normal to the surface. This result is derived from the plate's uniform Lambertian reflectance of 0.4, which, when multiplied by the irradiance of 1000π W/m², yields a reflected radiosity of 400π W/m² in all directions. The Lambertian nature of the surface ensures that the exitant radiance remains consistent regardless of the angle of observation.

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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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