The index of refraction of the core of a typical fiber optic is ncore = 1.46; the cladding has nclad = 1.4. Calculate the critical angles for the total internal reflection i crit and α crit.

Question

I have verified the answer for i crit is 74, but I cannot for the life of me figure out what α crit is. I've tried using the formula:
sin α crit = √(n^2core - n^2clad)
sin α crit = .4142463035
then α crit = sin^-1 = 24.5 degrees

but 24.5 is not the correct answer...

i crit = 74 degrees
α crit = ?

Can someone please help me out? What's the correct answer and what formula am I supposed to be using?

Answer 1

Thank you!