In this case, the loop parallel to the interface passes through the medium unrefracted (there is no refraction due to the boundary conditions on \(B\), but the ray is still refracted due to a change in velocity of the ray). The other loop is reflected and the center line of this ray intersects the interface behind the point of reflection and
\(d\lt0\)
\(d\), the lateral shift is negative.
When \(\theta=\alpha\),
One loop passes perpendicularly into the less dense medium at the point of reflection and is refracted in the less dense medium as the result of an increase in velocity. The other is reflected when the incident angle \(\alpha\gt\) critical angle.
Notice that as the right loop enters into the less dense medium, the particle has a parallel velocity component that is opposite to the parallel velocity component of the ray. The particle is travelling in the reverse direction to the ray, along the interface. And the adjusted angle that the loop makes with the normal is,
\(\alpha_{adj}=-\left( 90^{ o }-\alpha -\theta \right) \)
this suggest that the ray is refracted back into the same side of the normal as the incident ray,
which would be very odd indeed.
This approach is flawed as the underlying mechanism of total internal reflection possibly as the result of applying boundary conditions on the ray's \(B\) field has not been explored yet. Previously, there is a change in direction in the ray, as its normal and parallel \(B\) field components are effected differently at the boundary.
Note: If, however changes in speed alone can provide for total internal reflection (post "No \(B\), Speed Alone" dated 25 Aug 2015), then the above can be superimposed onto the results for total internal reflection as before.
