Why does incident ray, refracted ray and normal lie in the same plane? (looking for physical reasons) If we have a ray striking a plane then the unit vector in direction of the incident ray can be thought of as rotating in a plane that contains the normal to interface and the part of the unit vector along the plane of the interface.
However, I can not understand why this unit vector is not rotated around lines parallel to the plane of the interface which it strikes. To summarize, why does normal, incident and refracted ray lie in the same plane? I am asking for a physical answer, not a mathematical one.
I have already seen a mathematical answer here in this post but I don't think it really explained anything of 'why' it happens and, even if it does, uses some strange operations which I have not heard of it.
I seek either a less mathematically sophisticated answer/ one that directly explains the reasoning for this physical phenomenon happens. Also, I already know of snell's law of refraction, I'm asking for the intuition for why it should be true.
An afterthought: If light travels as a wave then shouldn't It technically refract in a lot of directions when it hits a surface?
 A: Why ... because of the equations. That is the best answer there can be, IMHO. Maths is the pure logic
One short-hand I would use it to point out that Maxwell's equations are invariant under rotations, i.e. Maxwell's equations have no preferred direction. In the problem with refraction you have:
(1) Plane of your surface, which is fully characterized by the normal in 3d space
(2) Direction of the incident light
These two vectors fix the situation, i.e. I would expect all refraction-related phenomena to be describable in terms of these two vectors, since there is no third preferred vector in the setting of the problem.
You could also play it this way. Say refracted ray was to be refracted out of the normal-incident plane. Which way would it go, out of the page or into the page? There is no information in Maxwell's equations to give this answer.
Final note. This only applies in case of isotropic dielectrics of course. Once you have crystalline solids, which do have special directions, the situation can change. I am sure one could then come up with configuration where light would be refracted in the off-plane direction.
A: The shorthand answer is this: Due to boundary conditions on the oscillating electric and magnetic fields of the incident and reflected light on both sides of the reflecting surface.
