Question

A fiber-optic rod consists of a central strand of material surrounded by an outer coating. The interior portion of the rod has an index of refraction of 1.97. If all rays striking the interior walls of the rod with incident angles greater than 50.4° are subject to total internal reflection, what is the index of refraction of the coating?

Answer 1

Answer:

The refractive index of the outer coating is 1.52.

Explanation:

Refractive index of interior part, n' = 1.97

critical angle, C = 50.4°

Let the refractive index of the coating is n.

Use the Snell's law,  

$n\times sin r = n'\times sinC\\\\n\times sin 90 = 1.97 \times sin 50.4\\\\n = 1.52$