The Fiber Optic Temperature Sensor · AI Generator #GEN-FA2A9E74
Physics · optics
Problem
A fiber optic temperature sensor uses a small air gap at the tip of an optical fiber to measure temperature changes. The sensor works by detecting changes in the critical angle for total internal reflection as the air gap's refractive index changes with temperature.
The optical fiber has a core with refractive index ncore=1.46 and is initially surrounded by air at 20°C where nair=1.000. As temperature increases, the refractive index of air decreases according to nair(T)=1.000−2.7×10−6(T−20), where T is in Celsius.
Light rays in the fiber core undergo total internal reflection at the core-air interface when their angle of incidence exceeds the critical angle. (a) What is the critical angle at 20°C? (b) At what temperature will the critical angle decrease by exactly 1.0° from its value at 20°C?