Mastering Physics Solutions: Total Internal Reflection Conceptual Question

Total Internal Reflection Conceptual Question

Part A = BCEF
Part B = E, B, F, C

Solution Below:

Consider scenarios A to F in which a ray of light traveling in material 1 is incident onto the interface with material 2.

Part A

For which of these scenarios is total internal reflection possible?

In order for total internal reflection to be possible, the source must have a greater index of refraction than the destination medium.

BCEF

Part B

For the scenarios in which total internal reflection is possible, rank the scenarios on the basis of the critical angle, the angle above which total internal reflection occurs. At this angle, the refracted ray is at 90 from the normal.

You can use Snell’s law for this:

n1 * sin(θ1) = n2 * sin(90)

Or:

n1 * sin(θ1) = n2 * 1

So:

n1 * sin(θ1) = n2

For example, scenario B (water to air):

n1 * sin(θ1) = n2
1.33 * sin(θ1) = 1.00
sin(θ1) = 0.752
sin^-1(0.752) = 48.76°

You should notice that the reason scenarios like A are impossible is because you’d have to take the inverse sin of something greater than 1. This is why, in order for total internal reflection to be possible, the refractive index of the source must be greater than that of the destination.

For the different mediums, you get:

B = 48.76°
C = 24.41°
E = 62.46°
F = 33.34°

So the order from largest to smallest is:

E, B, F, C

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