The higher a gem's RI, the which of the following?

The higher a gem's RI, the which of the following?

• A. The Larger Its Critical Angle
• B. Does Not Affect the Critical Angle
• C. The Smaller Its Critical Angle
• D. Always Yields Zero Dispersion

Answer: (D)

Raising a gem’s refractive index changes the boundary conditions for light trying to exit the gem into air, which is governed by the critical angle for total internal reflection. The critical angle is defined by sin θ_c = n2/n1, where n1 is the gem’s refractive index and n2 is the outside medium’s index (air is about 1.0). As the gem’s RI (n1) increases, the ratio n2/n1 decreases, so sin θ_c becomes smaller and the actual critical angle θ_c becomes smaller as well. In other words, higher RI leads to a smaller critical angle. Dispersion, on the other hand, is about how refractive index changes with wavelength. Higher RI does not imply zero dispersion; it describes how much the rays bend, but dispersion depends on how the index varies with wavelength for that material. So the idea that higher RI always yields zero dispersion isn’t correct. Therefore, the correct takeaway is that the higher the gem’s RI, the smaller its critical angle.

Raising a gem’s refractive index changes the boundary conditions for light trying to exit the gem into air, which is governed by the critical angle for total internal reflection. The critical angle is defined by sin θ_c = n2/n1, where n1 is the gem’s refractive index and n2 is the outside medium’s index (air is about 1.0). As the gem’s RI (n1) increases, the ratio n2/n1 decreases, so sin θ_c becomes smaller and the actual critical angle θ_c becomes smaller as well. In other words, higher RI leads to a smaller critical angle.

Dispersion, on the other hand, is about how refractive index changes with wavelength. Higher RI does not imply zero dispersion; it describes how much the rays bend, but dispersion depends on how the index varies with wavelength for that material. So the idea that higher RI always yields zero dispersion isn’t correct.

Therefore, the correct takeaway is that the higher the gem’s RI, the smaller its critical angle.