What is the Difference Between Refractive Index and Critical Angle

The key difference between refractive index and critical angle is that refractive index is the ratio of the velocity of a light beam in the air to the velocities of the specific medium, whereas critical angle is the angle of incidence at which the angle of refraction is 90 degrees.

In optical mechanics, refractive index and critical angle are related terms. Generally, the critical angle is inversely proportional to the refractive index of an optical medium.

1. Overview and Key Difference
2. What is Refractive Index
3. What is Critical Angle
4. Relationship between Refractive Index and Critical Angle
5. Refractive Index vs Critical Angle in Tabular Form
6. Summary – Refractive Index vs Critical Angle

What is Refractive Index?

Refractive index is a dimensionless number that is used as an indication of the bending ability of light in an optical medium. It is also known as refraction index. This parameter determines the degree at which the light is bent or refracted upon the light entering a material.

We can describe the refractive index using Snell’s law of refraction.

n1 sin θ1 = n2 sin θ2

Here, θ1 and θ2 refer to the angle of incidence and angle of refraction, respectively. These two angles are applied for a ray that crosses the interface between two media with refractive indices given by n1 and n2. Moreover, the refractive indices determine the reflected amount of light upon reaching the interface. It is also the critical angle for total internal reflection.

$Refractive Index vs Critical Angle in Tabular Form$

Figure 01: A Light Ray Refraction

The refractive index typically varies with wavelength, which can cause white light to split into its component colors upon refraction. We call it dispersion. This can be observed in prisms and rainbows and chromatic aberration in lenses. Furthermore, we can describe the light propagation in absorbing materials with the use of a complex-valued refractive index.

What is Critical Angle?

The critical angle is the angle of incidence beyond which rays of light passing through a denser medium to the surface of a less dense medium are no longer refracted but totally reflected. With respect to optical fibers, the critical angle is the least angle of incidence at which total internal reflection takes place. Furthermore, if a light ray exceeds the critical angle, the light is totally reflected back to the direction where it came (into the denser medium).

$Refractive Index and Critical Angle - Side by Side Comparison$

Figure 02: Behavior of a Ray Incident from a Medium of a High Refractive Index N1 to a Medium with a Low Refractive Index of N2

It is the smallest angle of incidence that can yield a total reflection. If not, it is equivalently the largest angle for a refracted ray that exists. If the single refractive index for light waves that are incident from an internal medium is n1, and the single refractive index for an external medium is n2, the critical angle is given by:

θc = arcsin(n2/n1), when n2 ≤ n1.

What is the Relationship between Refractive Index and Critical Angle?

Generally, the critical angle is inversely proportional to the refractive index of an optical medium.

What is the Difference Between Refractive Index and Critical Angle?

Refractive index and critical angle are two related terms in optical mechanics. The key difference between refractive index and critical angle is that refractive index is the ratio of the velocity of a light beam in the air to the velocities of the specific medium, whereas critical angle is the angle of incidence at which the angle of refraction is 90 degrees.

The following table summarizes the difference between refractive index and critical angle.

Summary – Refractive Index vs Critical Angle

Refractive index can be described as a dimensionless number that is used as an indication of the bending ability of light in an optical medium, while critical angle is the angle of incidence beyond which rays of light that pass through a denser medium to the surface of a less dense medium are no longer refracted but totally reflected. The key difference between refractive index and critical angle is that refractive index is the ratio of the velocity of a light beam in the air to the velocities of the specific medium, whereas the critical angle is the angle of incidence at which the angle of refraction is 90 degrees.

Reference:

1. “Physics Tutorial: The Critical Angle.” The Physics Classroom.

Image Courtesy:

1. “Refraction at interface” By Ulflund – Own work (CC0) via Commons Wikimedia
2. “ReflexionTotal en” By Jfmelero (adapted by Gavin R Putland). – File:ReflexionTotal.svg — subsequently translated and retouched. (CC BY-SA 3.0) via Commons Wikimedia