Light enters a solid tube made of plastic having an index of...

Light enters a solid tube made of plastic having an index of refraction of $1.60 .$ The light travels parallel to the upper part of the tube. (See Figure $23.55 .)$ You want to cut the face $A B$ so that all the light will reflect back into the tube after it first strikes that face. (a) What is the largest that $\theta$ can be if the tube is in air? (b) If the tube is immersed in water of refractive index $1.33,$ what is the largest that $\theta$ can be?

Light enters a solid tube made of plastic having an index of refraction of $1.60 .$ The light travels parallel to the upper part of the tube. (See Figure $23.55 .)$ You want to cut the face $A B$ so that all the light will reflect back into the tube after it first strikes that face.
(a) What is the largest that $\theta$ can be if the tube is in air? (b) If the tube is immersed in water of refractive index $1.33,$ what is the largest that $\theta$ can be?

Key Concepts

Total Internal Reflection

Total internal reflection is the phenomenon where light, traveling in a medium with a higher refractive index, reflects completely at the boundary with a medium of lower refractive index when the angle of incidence exceeds a certain threshold. This concept is crucial in determining the conditions under which light is confined within a medium, which is the principle being applied in the problem to ensure that all the light reflects back into the tube.

Critical Angle

The critical angle is the minimum angle of incidence in the denser medium for which light, upon reaching the boundary with a less dense medium, is refracted along the boundary. It is derived using the indices of refraction of the two media and is the key threshold in scenarios involving total internal reflection.

Snell's Law

Snell's Law relates the angles of incidence and refraction to the refractive indices of the two involved media. It is essential for calculating the critical angle as well as understanding how light bends when it enters or exits different materials.

Refractive Index

The refractive index is a measure of how much a medium slows down light compared to its speed in vacuum. It plays a fundamental role in the behavior of light at interfaces, influencing both the bending of light via refraction and the conditions necessary for total internal reflection.

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