Total Internal Reflection: v1<v2, Angle of Incidence?

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Homework Help Overview

The discussion revolves around the concept of total internal reflection in the context of light traveling between two transparent media with different speeds of light, specifically when the speed in Medium 1 (v1) is less than that in Medium 2 (v2).

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the conditions under which total internal reflection occurs, questioning the implications of the relationship between v1 and v2. They discuss the application of Snell's Law and the correct interpretation of angles related to refractive indices.

Discussion Status

The conversation includes attempts to clarify the mathematical conditions for total internal reflection, with some participants questioning the validity of taking the arcsine of values greater than one. There is a recognition of the correct formulation of the angles involved, although no consensus on the implications has been reached.

Contextual Notes

Participants are navigating the constraints of the problem, particularly the implications of the speed of light in different media and the mathematical relationships that arise from Snell's Law.

jan2905
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Consider two adjacent transparent media. The speed of light through Medium 1 is v1, and the speed of light through Medium 2 is v2. If v1<v2, then total internal reflection will occur at the interface between these media if a beam of light is?



I said incident in Medium 1 and stikes the interface at an angle of incedence greater than arcsin (v2/v1). Is this correct?
 
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If v2 > v1 then v2/v1 is greater than 1. Does taking the arcsine of a number greater than 1 make sense? Use Snell's Law and n = c/v to derive the condition for total internal reflection.
 
Okay... that was dumb of me... so if I take n1=c/v1 and n2=c/v2, then i have arcsine(v1/v2) when i take n2/n1 right?
 
That's correct.
 

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