What is the derivation of this equation: d = t sin θ [ 1 - (n cosθ / n' cosθ)]

[Rosella Lin]

Hi,

Could someone please tell me how to derive this formula by using Wave Phenomenon

d = t sin θ [ 1 - (n cosθ / n' cosθ)]
I think some of it is derived using Brewster's Principle and the Refractive Index but I cannot tell how?

Thanks.

 

[Nugatory]

You'll have to tell us more. What is this formula for, what is the physical significance of the variables it used, where did you come across, and what does that source say about the derivation?

 

[Rosella Lin]

Right! so I am trying to find the Refractive Index of liquids using a laser and diffraction grating.

So under by using this formula and deriving it further from here we can measure the RI.

Here is the image for that. This it where it comes from.

t = thickness of container (constant)
cos θ = angle of incidence and cos θ' = angle of refraction

n = RI of air and n' = R I of medium 2

There is nothing of how to derive it from the source but I have to understand how this came. If we further carry on this equation we end up here :

Thanks !