A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is θc and the Brewster's angle of incidence is θb, such that sinθc/sinθb = n = 1.28. The relative refractive index of the two media is:

Let θc be the critical angle.
n1sinθc = n2sin90
sinθc = n2/n1
Brewster's angle
tanθb = n2/n1
sinθb = n2/√(n1² + n2²)
Given, sinθc/sinθb = 1.28
(n2/n1) / (n2/√(n1² + n2²)) = 1.28
√(1 + (n2/n1)²) = 1.28
1 + (n2/n1)² = 1.28² = 1.6384
(n2/n1)² = 0.6384
n2/n1 = √0.6384 ≈ 0.799
Solving the above equation, we get,
n2/n1 = 0.8