# How to find the probability reflection at a liquid-air interface for a surface which reflects diffusely according to Lambert's law? The smooth surface is air-liquid interface and the rough surface is let's say a t-shirt.

The image above shows the probability of each reflection, and the $$p$$ value is the probability of the light rays totally reflected by the air-liquid interface. So this means $$p$$ represents the fraction of light rays that goes in an angle greater than the critical angle and we are after the intensity (or amount I don't really know how I should call it) of light in the yellow shaded area: The article I am reading estimates $$p$$ in the following way. However, after this estimation it makes more calculations to find the exact value of $$p$$. It calculates the reflected light incidents which enter with an angle smaller than the critical angle but I do not understand how it does this.

This is the article and it would be very helpful if someone explained all the steps clearly, because I am a high school student and literally have no idea.

Note: I am sorry if the post looks very ugly, I am not sure if I should remove the images. Sorry about that, I will edit according to your warnings.