i derived the formula for the critical angle of a medium? Is it correct?

Answer is correct. But please check the derivation given below, since it's not n₁/n₂ but n₂/n₁.

n_i = Refractive index of medium i with respect to air or vaccum = Speed of light in air/Speed in Medium i

n₁sinθi = n₂sinθr

For critical angle of medium, θr = 90

n₁sinθi = n₂

sinθi = n₂/n₁

If you have to find the critical angle for a medium say Diamond and into air.

n₁ = 2.42

n₂ = 1

sinθi = 1/2.42

θi = sin^-1(1/2.42) = 24^o

Regards,

Team,

TopperLearning.