You are running into pretty big conceptual issues here. Especially for a Hard Sci-Fi question, there simply is no correct answer.
General Relativity for instance, which is what all of modern physics is kind of based on, does not work the same way in higher dimensions. There are solutions to something like the Kerr Metric for rotating black holes, but all of these solutions make some pretty major assumptions to work.
We can make some very general assumptions. For instance, Euclidian distances;
$$l = \sqrt{(x_1-x_0)^2 + (y_1-y_0)^2 + (z_1-z_0)^2 + ... + (n_1-n_0)^2}$$
extend into any higher dimension. So this distance measurement between two points is correct for all higher dimensions assuming there is marginal curvature and the extra space dimensions behave the same way. Which is not a given. String Theory for instance has curled up dimensions

Which obviously do not support the notion of Euclidian distances anymore as the dimension is inherently non-Euclidian.
And this is what i mean, you don't provide any assumptions. So the answer is both yes and no. If the additional space dimensions are "flat" and simple extensions of 3+1 Space we live in, then all the math for Refraction, General Relativity and so on should translate. If however, the additional dimension is not "flat", all of that is thrown out the window.
Can we prove that ? Well we can prove case 1. Proving case 2 would involve making a new theory of spacetime.
For Case 1, the question is if the equations that describe Refraction hold up in higher dimensions. The first test we can do for this is a simple vector reflection. In R3 that looks like this;
$$r = d-2(d\cdot n)n$$
Where $r$ is the reflected vector, $d$ is the incoming vector and $n$ is the surface normal. We can be really lazy and just set the Normal to $n = (0,0,0,1)$ and the incoming to $d = (0,0,1,1)$. Solving for r we get $r = (0,0,1,-1)$. Which, just on a surface level, is correct. The Normal vector is the w direction, which used to be 1 and now it is -1 so the vector is properly reflected.
Ultimately, Refraction is just fancy reflection as a different commentor has written out. If we look at the refraction equation (Snells law of refraction);
$$\eta_1sin{\theta_1} = \eta_2sin{\theta_2}$$
we shall notice that the angle $\theta_1$ is what we are interested in. Since solving the equation means solving for $\theta_2$. What you conceptually do when performing refraction simulations is take your incoming vector $d$ and change its angle from $\theta_1$ to $\theta_2$

So what is $\theta_1$ ? Well, its an angle between the incoming $d$ and $n$. Equation for which is;
$$cos{\theta} = \frac{(d,n)}{||d||||n||}$$
Where $(d,n)$ is the inner product. This definition extends into n-dimensional space. So by definition, the refraction equation has solutions not just in 4+1 but n+1 spacetime.
Again provided those dimensions are "flat". The absolute nanosecond anything funky happens with the extra dimension, non of this works anymore.
But as long as this 4th dimension of yours is flat / behaves in the exact same way as the 3 we love, then the answer is "Yes, it is possible".