# Angle of incidence and index refraction relationship

### optics - Does the angle of incidence change the refractive index? - Physics Stack Exchange The index of refraction can also be stated in terms of wavelength: into the second medium is related to the angle of incidence by Snell's law. Like with reflection, refraction also involves the angles that the incident ray and the This dependence is made explicit in Snell's Law via refractive indices. This relationship between the angles of incidence and refraction and the indices of refraction of the two media is known as Snell's Law. Snell's law applies to the.

Assuming that the air on both sides of your window have the same refractive indices, we have the following situation: We find that the incoming and outgoing light beams are actually parallel.

### Snell's law - Wikipedia

When light travels from an area of lower index to an area of higher index, the ratio is less than one, and the refracted ray is smaller than the incident one; hence the incident ray is bent toward the normal as it hits the boundary. Of course, refraction can also occur in a non-rectangular object indeed, the objects that we are interested in, lenses, are not rectangular at all.

The calculation of the normal direction is harder under these circumstances, but the behaviour is still predicted by Snell's Law. Calculating n Given a transparent substance, we can always find its index of refraction by using a setup like the example above. Surrounding the substance of unknown index n with a material with a known index of refraction, we can find the unknown n by measuring angles and applying Snell's Law. However, calculating ns in this way, an obvious question arises. How did the first index get calculated? We could always choose an arbitrary substance as a meterstick, and calculate all other indices in terms of this base.

However, indices of refraction arise in Maxwell's equations for electromagnetic waves; that, in fact, is how they are defined. If light is travelling from medium 1 into medium 2, and angles are measured from the normal to the interface, the angle of transmission of the light into the second medium is related to the angle of incidence by Snell's law: When light crosses an interface into a medium with a higher index of refraction, the light bends towards the normal.

Conversely, light traveling across an interface from higher n to lower n will bend away from the normal. This has an interesting implication: If the light hits the interface at any angle larger than this critical angle, it will not pass through to the second medium at all. Instead, all of it will be reflected back into the first medium, a process known as total internal reflection.

## Refraction of light

For any angle of incidence larger than the critical angle, Snell's law will not be able to be solved for the angle of refraction, because it will show that the refracted angle has a sine larger than 1, which is not possible.

In that case all the light is totally reflected off the interface, obeying the law of reflection. Optical fibers are based entirely on this principle of total internal reflection. An optical fiber is a flexible strand of glass. A fiber optic cable is usually made up of many of these strands, each carrying a signal made up of pulses of laser light. The light travels along the optical fiber, reflecting off the walls of the fiber.

## Snell's Law

With a straight or smoothly bending fiber, the light will hit the wall at an angle higher than the critical angle and will all be reflected back into the fiber. Even though the light undergoes a large number of reflections when traveling along a fiber, no light is lost.

Depth perception Because light is refracted at interfaces, objects you see across an interface appear to be shifted relative to where they really are. If you look straight down at an object at the bottom of a glass of water, for example, it looks closer to you than it really is. Looking perpendicular to an interface, the apparent depth is related to the actual depth by: An example A beam of light travels from water into a piece of diamond in the shape of a triangle, as shown in the diagram.

Step-by-step, follow the beam until it emerges from the piece of diamond. The speed can be calculated from the index of refraction: