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## Homework Statement

In the figure shown below, a light ray enters a glass slab (with index of refraction nglass = 1.65 ) at point A

and then undergoes total internal reflection at point B. The medium that surrounds the glass slab is a liquid whose

index of refraction, nliquid = 1.30. Find the value of the initial angle of incidence i for which total internal reflection

can take place.

## Homework Equations

Snell's Law At point A: n (liquid) sin [tex]\Theta[/tex] i = n (glass) sin [tex]\Theta[/tex] 2

At Point B: n (liquid) sin [tex]\Theta[/tex] 3 = n (liquid) sin 90

[tex]\Theta[/tex]3=90-[tex]\Theta2[/tex]

## The Attempt at a Solution

Using the above equations I got the [tex]\Theta[/tex]i=15.5, [tex]\Theta[/tex]2=12.12, and [tex]\Theta[/tex]3=77.88

Now what has thrown me off is the HINT the professor gave , which was tan[tex]\Theta[/tex]=sin [tex]\Theta[/tex]/cos[tex]\Theta[/tex].

What is this equation for? I can't seem to find the relevance in my text or notes. AND what value would I use for [tex]\Theta[/tex], the [tex]\Theta[/tex] for i ????