Part A

$($Figure $1)$shows a light ray traveling within a cable bent to its critical extent, beyond which light will leak out of the core. The radius of curvature of the center of the core is R$.$Derive an expression for the angle of incidence at which the indicated light ray strikes the outer edge of the core. $($Hint: Construct a right triangle with vertices a$,$b$,$and c as in the figure.$)$

Part B

Determine the critical radius R$.$

Express your answer in terms of $11,$z$,$and d$.$