How Does Refractive Index Relate to Trigonometric Identities?

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Homework Help Overview

The discussion revolves around the relationship between refractive index and trigonometric identities, particularly in the context of angles and their mathematical properties. Participants are exploring how these concepts interrelate, especially through calculus and trigonometric functions.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are considering relationships between angles, specifically theta and phi, and how to eliminate one variable. There is also discussion on the implications of a function reaching a maximum and the application of differentiation. Some participants suggest using trigonometric identities and double angle formulas as potential strategies.

Discussion Status

The discussion is active, with participants sharing their attempts and seeking clarification on differentiation techniques. There is a recognition of the complexity involved in the calculations, and suggestions for alternative approaches are being explored.

Contextual Notes

Some participants express frustration with the differentiation process, indicating that previous attempts have led to complicated results. There is an underlying assumption that knowledge of calculus and trigonometric identities is necessary for progressing in the problem.

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please help...
 
Try to think of a relationship between theta and phi that will get rid of one of the variables.

Then, what do you think happens when a function is at a maximum? (think calculus)
 
sin theta = n sin phi ?

the differential equals 0?
 
Yeah

so differentiate.
 
i already tried that - i will scan in what i did
 
but how do you differentiate that - i tried but came up with an absolute mess!
 
Hmm, maybe try using trig identities?

double angle formulas?
 

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