If the prism is surrounded by a fluid, what is the maximum index of refraction of the fluid that will still cause total internal reflection

n₁ > n₂.

prisms are made of glass with refractive index n₂ = 1.50, so the fluid that surrounds the prism must have an index n₁> 1.50

Explanation:

Total internal reflection occurs when the refractive index of the incident medium the light is greater than the medium to which the light is refracted, let's use the refraction equation

                 n₁ sin θ₁ = n₂ sin  θ₂

the incident medium is 1, at the limit point where refraction occurs is when the angle in the refracted medium is 90º, so sin θ₂ = 1

                 n₁ sin θ₁ = n₂

                 sin θ₁ = n₂ / n₁

We mean that this equation is defined only for n₁ > n₂.

In our case, for the total internal reflection to occur, the refractive incidence of the medium must be greater than the index of refraction of the prism.

In general, prisms are made of glass with refractive index n₂ = 1.50, so the fluid that surrounds the prism must have an index n₁> 1.50