Deriving an expression from geometry

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Homework Help Overview

The discussion revolves around deriving an expression for the displacement of light as it passes through a glass slab, specifically focusing on the relationship between the thickness of the glass and the angles involved. The problem is situated within the context of geometric optics and involves the application of Snell's law.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to use Snell's law to relate the angles of incidence and refraction. Some participants suggest analyzing the geometry of the situation by identifying right triangles and their relationships to the thickness of the slab and the angles involved. Questions are raised about the specific geometric relationships and how to express the displacement in terms of the given variables.

Discussion Status

Participants are actively engaging with the problem, with some offering guidance on how to approach the geometric aspects. There is an acknowledgment of the challenges faced by the original poster, particularly regarding geometric intuition and understanding. Multiple interpretations of the problem are being explored, but no consensus has been reached yet.

Contextual Notes

The original poster mentions difficulties with geometry and expresses a lack of foundational understanding, which may influence their approach to the problem. There is also a reference to an external document containing relevant formulas, indicating that the problem may involve specific constraints or assumptions not fully detailed in the thread.

Levi Tate
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Homework Statement



I need to derive an expression for the displacement of light as a function of thickness of glass and the angles.

I will post a screen shot of the formula to be derived but it can also be found here

http://clas.wayne.edu/multimedia/usercontent/File/Physics%20and%20Astronomy/Labs/PHY5341/Lab4%20Brewsters%20Angle.pdf

(pg 3)

Homework Equations



The equation is given as the solution. I am not very good with geometry so I don't really even know where to begin.

The Attempt at a Solution



Using Snell's law,

n1sinθ1=n2sinθ2

Solving for θ2 = Arcsin[(n1/n2)sinθ1]

So then I just have θ2.

Help, please?
 
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See attachment. You have to find the expression for the distance (d) between the original ray (1) and the displaced one (2). t is the thickness of the slab. There are two right triangles in the picture, with common hypotenuse (s ). Find s in terms of t and θ2, find d in terms of s and θ21. Eliminate θ2.

ehild
 

Attachments

  • displacement.JPG
    displacement.JPG
    12.2 KB · Views: 484
Thanks a lot for your help mate. I tried this problem for about an hour and I'm completely stuck. I never went to high school to get that Euclidian intuition and I'm dyslexic so I don't have a good geometric intuition. I'm just stuck, I can't see the solution in sight.

But I thank you for your assistance very much.
 
Do you see the right triangles in the picture? What is the relation between t, s and θ2?

What is the angle of the blue triangle between side s and the hypotenuse?


ehild
 

Attachments

  • displacement.JPG
    displacement.JPG
    12.4 KB · Views: 476

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