A Ray of Light and Total Internal Reflection

A ray of light originates in medium A and is incident upon medium B. For which one of the following pairs of indices of refraction for A and B is total internal reflection NOT Possible?

Options:

a. nA = 2.54, nB = 1.63

b. nA = 1.36, nB = 1.00

c. nA = 1.12, nB = 1.06

d. nA = 1.26, nB = 1.15

e. nA = 1.28, nB = 1.36

Answer:

Based on this condition, we can identify the pair where total internal reflection is NOT possible: options a, b, c, and d. Because the index of refraction of medium B is greater than or equal to the index of refraction of medium A, so total internal reflection is not possible.

The value of nA: In this case, nA is lower than nB, so total internal reflection cannot occur. Total internal reflection occurs when light travels from a medium with a higher index of refraction (nA) to a medium with a lower index of refraction (nB) and the angle of incidence is greater than the critical angle.

Total internal reflection occurs when the angle of incidence of a ray of light is greater than the critical angle, which is determined by the indices of refraction of the two media. The critical angle can be calculated using Snell's law, but in this case, calculation is not needed to answer the question. The condition for total internal reflection is that the index of refraction of medium A is greater than the index of refraction of medium B.

Therefore, option e (nA = 1.28, nB = 1.36) is the only pair of indices of refraction for which total internal reflection is possible.

Do you understand why total internal reflection is not possible for certain pairs of indices of refraction?

Yes, total internal reflection is not possible when the index of refraction of the medium the light is traveling into is greater than or equal to the index of refraction of the medium the light is coming from. This is because the critical angle required for total internal reflection cannot be reached in such cases.