The index of refraction n in a medium is equal to c/v, where c is the vacuum speed of light, and v is the speed of light in the medium. That gives the plastic an index of n = 3.00/1.90.
By Snell's law, n2/n1 is also the ratio (sin θ₁)/(sin θ₂), where θ₁ is the angle of incidence in the medium with index n1 and θ₂ is the angle of incidence in the medium with index n2. So:
θ₂ = arcsin(n1*(sin θ₁)/n2)
You have n1 = 1.00 for air and n2 = 3.00/.190 for the plastic and the rest is easy.
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