Physics
Physics
Problem
A light ray enters a solid glass sphere of refractive index at an angle of incidence . The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is ____.Intuitive explanation
The key is tracking how the refracted ray travels through the sphere and then applying Snell's law in reverse at the exit point. When light hits the back surface from inside, you'll have both a reflected ray (bouncing back into the glass) and a refracted ray (escaping into air). The angle between them depends on the geometry of incidence at that back surface and how Snell's law bends the exiting ray. Find the refraction angle at entry using Snell's law, trace the ray's path to the back surface, then use geometry and Snell's law again to find where each ray actually goes.
Intuitive explanation
The key is tracking how the refracted ray travels through the sphere and then applying Snell's law in reverse at the exit point. When light hits the back surface from inside, you'll have both a reflected ray (bouncing back into the glass) and a refracted ray (escaping into air). The angle between them depends on the geometry of incidence at that back surface and how Snell's law bends the exiting ray. Find the refraction angle at entry using Snell's law, trace the ray's path to the back surface, then use geometry and Snell's law again to find where each ray actually goes.