Question

Please help ASAP. I don't understand: Consider a light ray traveling from medium 1 to medium 2 with medium 2 extending downward indefinitely. Let the index of refraction of medium 1 be 1.0...?

Now suppose the index of refraction of
medium 2 is 1.06. What will be the maximum value of θ1 that will have total internal reflection? Answer in units of ◦

Answer 1

Work Backwards.

Explanation:

Find `theta_2` that will result in Total Internal Reflection . By

Snell's Law, TIR results in refracted angle to be `90^.` as light leaves medium 2 to 1.

Thus `sin(theta_2) * RIndex_(Medium2) = sin(90^.) * 1.00`

`sin(theta_2) * 1.06 = sin(90^.) * 1.00`

`sin(theta_2)` = `0.943`

`theta_2 = sin^-1(0.943)`

`theta_2 = 70.6^.`

Hence using this we can determine the angle of refraction as light enters medium 2 from medium 1. Since angles `sum_angle = 180` in a triangle, the angle of refraction is `19.4^.` Now using Snell's Law we can determine `theta_1`.

`sin(19.4) * 1.06 = sin(theta_1) * 1.00`
`sin(theta_1) =0.352`
`theta_1 = sin^-1(0.352)`
`theta_1 = 20.6^.`