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

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Total internal reflection occurs at the interface of two transparent media when light travels from a medium with a lower speed of light to one with a higher speed. If the speed of light in Medium 1 (v1) is less than in Medium 2 (v2), total internal reflection happens when the angle of incidence exceeds arcsin(v2/v1). However, if v2 is greater than v1, the ratio v2/v1 exceeds 1, making arcsin(v2/v1) undefined. Using Snell's Law and the refractive indices derived from the speeds of light, the correct condition for total internal reflection can be expressed as arcsin(v1/v2). Understanding these principles is essential for applying total internal reflection in optical applications.
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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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