$[-/3$ Points$]$

$$

$n_{\text{m}\text{i}\text{n}}=$

$($Why is this the minimum $n$ value?$)$

$$

$[-/3$ Points$]$

The figure below shows a ray of light entering one end of an optical fiber at an angle of incidence ${}_1=53\mathrm{.}0.$ The index of refraction of the fiber is $1\mathrm{.}46.$

$($a$)$ Find the angle $$ the ray makes with the normal when it reaches the curved surface of the fiber.

$($b$)$ Calculate the critical angle ${}_c$ for the optical fiber.

$q,$ Explain how this indicates that the internal reflection from the curved surface is total.