How to Apply Snell's Law Without Knowing the Index of Refraction?

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To apply Snell's Law without knowing the index of refraction, one must first determine the angles using geometric relationships from the given depths. By drawing right triangles based on the real and apparent depths, trigonometric functions such as sine, cosine, and tangent can be utilized to find the incident and refracted angles. Once the angles are established, Snell's Law can be applied to derive the index of refraction. The discussion emphasizes the importance of geometry in solving the problem before applying Snell's Law. Understanding these geometric principles is crucial for successfully navigating the problem.
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Homework Statement


[/B]
I know that the depth is 30 cm , the apprared depth to the observer is 15 cm. But how am i going to use snells law to get the refracted and incident angle when i have no idea what the index of refraction is for n2 liquid? ?

Homework Equations


N1sin1=n2sin2

The Attempt at a Solution


Im trying to use smells law to figure out both angles but I am missing the index of refraction and i don't know how to compute it using the depth and length givenhttps://www.physicsforums.com/attachments/93432
 
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Hello2016 said:

Homework Statement



I know that the depth is 30 cm , the apprared depth to the observer is 15 cm. But how am i going to use snells law to get the refracted and incident angle when i have no idea what the index of refraction is for n2 liquid? ?[/B]

Homework Equations


N1sin1=n2sin2

The Attempt at a Solution


Im trying to use smells law to figure out both angles but I am missing the index of refraction and i don't know how to compute it using the depth and length givenhttps://www.physicsforums.com/attachments/93432
You need to figure out the angles using geometry, from the figure drawn. Only after that do you use Snell's law to find the index of refraction.
 
nrqed said:
You need to figure out the angles using geometry, from the figure drawn. Only after that do you use Snell's law to find the index of refraction.
Oh so like tan sin and cos?
 
Hello2016 said:
Oh so like tan sin and cos?
Yes, draw right angle triangles, use the apparent and real depths to get the sides of some triangles and then use trigonometry to find the angles.
 
Hey I am not sure how i should use x in the geometry
 

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