The illustration shows total internal reflection taking place in apeice of glass. The index of refraction of this glass:
A) at least 2.0
B) at most 2.0
C) at least 1.15
D) at most 1.15
E) cannot be calculated from the given data

Question

The illustration shows total internal reflection taking place in apeice of glass. The index of refraction of this glass: 
A) at least 2.0 
B) at most 2.0 
C) at least 1.15 
D) at most 1.15 
E) cannot be calculated from the given data

Quizplus · Accepted Answer

Total internal reflection occurs when light travels from a medium with a higher index of refraction to a medium with a lower index of refraction, and the angle of incidence is greater than the critical angle.

In the illustration, the light is traveling from the glass to the air, which has a lower index of refraction. Therefore, the glass must have a higher index of refraction.

The critical angle is given by the equation sinθc = n2/n1, where θc is the critical angle, n1 is the index of refraction of the first medium (in this case, glass), and n2 is the index of refraction of the second medium (in this case, air).

We know that total internal reflection is occurring in the glass, which means that the angle of incidence is greater than the critical angle, so sinθ > sinθc.

This tells us that n2/n1 < 1, since sinθ = n2/n1 * sinθc, and sinθ is greater than sinθc.

Therefore, n1/n2 > 1, which means that the index of refraction of the glass is at least 1.15 (since that is the minimum value in the given answer choices). It could be larger than 1.15, but we cannot determine a specific value from the given data.

The Illustration Shows Total Internal Reflection Taking Place in Apeice