Difference Between Angle of Incidence and Angle of Refraction

Key Difference – Angle of Incidence vs Angle of Refraction
 

The key difference between the angle of incidence and angle of refraction is the sequential order of the two angles, made at a media interface by a wave.

Refraction is a property of waves. A wave can have different velocities for different mediums. The change of velocity at a boundary of a medium causes a wave to refract. This article is particularly focused in light rays, for the sake of simplicity.

Definition of Angle of Incidence and Angle of Refraction

Angle of incidence is the angle between the normal at the interface and incident ray.

Angle of refraction is defined as the angle between the normal at the interface and refracted ray. Angles can be measured by any unit, but here, degrees are used. Let us first have a glance at laws of refraction.

1. Incident ray, refracted ray and the normal at the interface lie in the same plane.
2. Sine of the angle of incidence(i) to that of the angle of refraction(r) at the interface remains in constant relation. This constant is called the refractive index of the second medium relative to the first medium.

Keep in mind the property of the reversibility of light. If we simply reverse the direction of the light ray by considering the present end as the start and the present start as the end, the light ray will trace the same path.

Formation of Angle of Incidence and Angle of Refraction

The difference between incident and refracted ray depends on the fact whether the light ray comes to the interface or leaves the interface. Picture a light ray as a stream of photons. The stream of particles hit the interface making a certain angle with the normal, then sink into the other medium essentially making a different angle with the normal.

The angle of incidence can be varied manually since it is independent of the medium. But the angle of refraction is defined by the refractive indices of the media. More the difference between refractive indices, more the difference between angles.

Location of Angle of Incidence and Angle of Refraction relative to the interface

If a light ray goes from medium1 to medium2, the angle of incidence lies in the medium1 and the angle of refraction lies in the medium2 and vice versa for interchanging of the mediums.

Both of the angles are made with the normal at the interface of mediums. Depending on the relative refractive index, the refracted light ray may make an angle greater than or less than that of incident light ray.

Values of Angle of Incidence and Angle of Refraction

Refracting from a rarer to denser medium

Any value between 0 to 90 degrees can be assigned as the angle of incidence, but the refracted ray cannot be taken any value if the light ray comes from the rarer medium. For the entire range of the incident angle, the angle of refraction reaches a maximum value which is exactly the same as the critical angle described next.

Refracting from a denser to rarer medium

The above is not valid for a situation where the light ray comes from a denser medium. When we increase the incident angle gradually, we shall see the angle of refraction also increases rapidly until a certain value of the incident angle is reached. At this critical angle(c) of the incident ray, refracted light ray achieves its maximum value, 90 degrees (refracted ray goes along the interface) and vanishes for a moment. If we try to increase the incident angle further, there we shall see a sudden appearance of a reflected ray in the denser medium, making the same angle according to the laws of reflection. The incident angle at this point is called the critical angle, and there will be no more refraction.

As a summary, one could see, though categorized differently, both these phenomena are just a result of the reversibility of light.

Key difference

The key difference between the angle of incidence and angle of refraction is the sequential order of the two angles, made at a media interface by a wave.

Image Courtesy:

“Snells law2” by Oleg Alexandrov — I just tweaked the original – Rotated and tweaked version of en:Image:Snells law.svg, same license. (Public Domain) via Commons

“RefractionReflextion” by Josell7 – Own work. (CC BY-SA 3.0) via Commons