The Fiber Optic Light Fountain · AI Generator #GEN-F6A0B7E7
Physics · optics
Problem
A decorative water fountain uses fiber optic cables to create illuminated water streams. Light from an LED enters a curved optical fiber at point A with an incident angle of 30° to the normal of the fiber's entrance face. The fiber has a circular cross-section with radius r=0.5mm and is made of glass with refractive index n1=1.52. The fiber is surrounded by air with refractive index n2=1.00.
After entering the fiber, the light ray travels through the curved section and eventually strikes the cylindrical side wall of the fiber at point B. At point B, the ray makes an angle θ with the normal to the curved surface (pointing radially inward).
(a) What is the angle of refraction when light enters the fiber at point A?
(b) For total internal reflection to occur at point B, what is the minimum value of the angle θ?
(c) In this particular fiber design, the light ray strikes the side wall at point B with θ=75°. Will total internal reflection occur, and if so, what fraction of the incident light intensity is reflected?