The Fiber Optic Periscope · AI Generator #GEN-30A1D010
Physics · optics
Problem
A submarine designer wants to create a compact periscope using a bent optical fiber instead of traditional mirrors. The fiber has a core with refractive index nc=1.46 and is surrounded by cladding with refractive index ncl=1.44. The fiber is bent into a quarter-circle arc with radius of curvature R=15.0cm.
For the periscope to work properly, light entering the fiber horizontally must undergo total internal reflection at every point along the curved section, even at the point where the bending is most severe.
(a) What is the critical angle θc for total internal reflection at the core-cladding interface?
(b) At the point of maximum curvature, what is the minimum angle θmin that a light ray makes with the normal to the core-cladding interface?
(c) Will total internal reflection occur throughout the bent section? Justify your answer quantitatively.
(d) If the fiber core has diameter d=50μm, what is the minimum radius of curvature Rmin that would still allow total internal reflection for all rays?