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

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SUMMARY

The equation d = t sin θ [ 1 - (n cosθ / n' cosθ)] is derived using principles from wave phenomena, specifically Brewster's Principle and the concept of refractive index. The variables represent the thickness of the container (t), the angle of incidence (θ), the refractive index of air (n), and the refractive index of the medium (n'). This formula is essential for measuring the refractive index of liquids using a laser and diffraction grating. Understanding this derivation is crucial for accurate optical measurements in various scientific applications.

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Rosella Lin
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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.
 
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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?
 
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.

upload_2016-9-25_23-47-42.png

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 :

upload_2016-9-25_23-49-55.png


Thanks !
 

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