Answer
1.28
Work Step by Step
By using Snell's law,
$n_{a} sin \theta_{a}= n_{b} sin \theta_{b}$
where $n_{a}$= refractive index of glass=1.52
$\theta_{a}$= angle of incidence= 57.2$^{\circ}$
$\theta_{b}$= angle of refraction= 90$^{\circ}$ ( since ray is totally reflected)
Let $n_{b}$= $n_{oil}$
= 1.52$\times$ sin(57.2)= $n_{oil}$$\times$ sin(90)
=$n_{oil}$= $\frac{1.52sin(57.2)}{1}$= 1.28
