A relação entre a Irradiância ( E ) e a Radiância (L) de uma superfície plana infini ta e isotrópica (Lambertiana) é dada pela seguinte equação:

Let's analyze the given equations and understand the relationship between irradiance ($E$) and radiance ($L$) of an infinite, isotropic, and Lambertian surface.

The first equation, $E = e^{-iL}$, doesn't seem to make sense in the context of radiometry. Irradiance is typically denoted by $E$ and is measured in units of power per unit area (W/m²), while radiance is denoted by $L$ and is measured in units of power per unit area per unit solid angle (W/m²sr).

The second equation, $E = frac{dl}{dx}$, also doesn't seem to be a valid relationship between irradiance and radiance. The derivative of radiance with respect to distance ($x$) doesn't have any physical meaning in this context.

The third equation, $E = pi L E$, is also incorrect. The correct relationship between irradiance and radiance for a Lambertian surface is $E = pi L$, which states that the irradiance is equal to the radiance multiplied by $pi$.

The fourth equation, $E = 2 pi sqrt{L}$, is not a valid relationship between irradiance and radiance either.

Since this question was annulled, it doesn't have a correct answer. However, I've explained the correct relationships between irradiance and radiance for a Lambertian surface and pointed out the mistakes in the given equations.