Is there a limit to how steep the refractive index gradient can be

[Antonij]

Is there a limit to how steep a refractive index gradient can be before ray optics are no longer able to predict the path of the light? How is it related to wavelength? Under what conditions the light will be able to travel perpendicular to the gradient
In a straight line? (having diffrent index to the sides of the beam)

 

[sophiecentaur]

Is there a limit to how steep a refractive index gradient can be before ray optics are no longer able to predict the path of the light? How is it related to wavelength? Under what conditions the light will be able to travel perpendicular to the gradient
In a straight line? (having diffrent index to the sides of the beam)

The refractive index is, of course, related to the wavelength but there would be no angular dispersion along a Normal Path. Perhaps you could describe in more detail what the context is of your question.

 

[Antonij]

The refractive index is, of course, related to the wavelength but there would be no angular dispersion along a Normal Path. Perhaps you could describe in more detail what the context is of your question.

A ray is coming at a grazing angle (above critical angle) from the optically denser material through the gradient. Will the ray be bent perpendicularily from the normal, traveling in straight line perpendicular to the normal no mayter how steep is the gradient?

 

[DaveC426913]

I assume he's asking this:
1] If you have a ray impinging on an interface between two materials, is it possible to have a refractive index so high that the emergent ray is effectively 0 degrees - parallel to the interface?

[ EDIT ] Nope. The more times I read the OP the less sense it makes - esp. the very last phrase in parentheses.

 

[Tom.G]

Maybe this?
https://web.stanford.edu/~ajlucas/Evanescent Waves.pdf

 

[Antonij]

I assume he's asking this:
1] If you have a ray impinging on an interface between two materials, is it possible to have a refractive index so high that the emergent ray is effectively 0 degrees - parallel to the interface?

View attachment 226807

[ EDIT ] Nope. The more times I read the OP the less sense it makes - esp. the very last phrase in parentheses.

Your picture is accurate to what i was asking about, except there is a smooth transition between high and low index, not an interface. I know that for a sufficiently "slow changing" gradient this is possible. The question is if there's a limit to how "fast changing" gradient can be so that it behaves the same way

 

[DrDu]

A systematic way to derive ray optics as a limit of wave optics is the so called eiconal approximation. It also allows to estimate the errors neglected due to the change of the refractive index. The book by Born and Wolf is certainly a good starting point.