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

• Antonij
In summary, when a refractive index gradient is too fast changing, the emergent ray is no longer able to follow the normal and instead follows the wave front. This can happen with waves of any wavelength.

#### 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)

Antonij said:
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.

sophiecentaur said:
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?

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.

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• refractive-index.png
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DaveC426913 said:
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

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.

## 1. What is a refractive index gradient?

A refractive index gradient is a measure of how quickly the refractive index changes with distance. It is used to describe how light is bent as it passes through a medium, such as air or water.

## 2. How is the refractive index gradient measured?

The refractive index gradient is typically measured using a technique called interferometry. This involves splitting a beam of light and then recombining the beams to create an interference pattern, which can be used to calculate the refractive index gradient.

## 3. Is there a limit to how steep the refractive index gradient can be?

Yes, there is a limit to how steep the refractive index gradient can be. This limit is known as the critical angle and it is determined by the properties of the medium through which the light is passing. Beyond the critical angle, the light will undergo total internal reflection instead of being refracted.

## 4. What factors affect the refractive index gradient?

The refractive index gradient is affected by several factors, including the properties of the medium (such as density and temperature), the wavelength of the light, and the angle at which the light enters the medium.

## 5. Why is the refractive index gradient important?

The refractive index gradient is important because it influences the behavior of light as it passes through a medium. This can have a significant impact on the performance of optical devices, such as lenses and prisms, and is also essential for understanding natural phenomena such as mirages and rainbows.

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