Critical Angle and Refractive Index: Understanding Light’s Behavior

by Yuvi K - January 7, 2024

What is Critical Angle?

Critical angle, also known as the limit of total internal reflection, is the point where the light ray is bent back and no longer is able to pass through the medium. It happens in a certain angle when the light changes its speed due to changing the medium. This angle is called the critical angle, expressed through the Greek letter Θ (theta). It is the angle at which light changes from an optically dense to an optically rarer medium.

The Critical Angle is given an algebraic expression which is determined as a function of the refractive indices of the two media. It is derived from Snell’s Law and is calculated by ‘sin 𝚽c = n2/n1’ and ‘𝚽c’ is the critical angle.

The critical angle is the angle of incidence at which the angle of refraction equals 90°, and is the value of angle beyond which light is totally reflected from the boundary of two optically different materials. Reflection can either be regular or exhausted.

Critical angle formula holds true when the incident light beam hits the boundary of two media of different indices of refraction. When the incident light beam has a greater angle than the critical angle of the medium, the angle of incidence will exceed the angle of refraction and no refraction or transmission can be observed. In this case the angle is so great, that the ray is totally internally reflected. In this case, the only partially reflected beam is called an evanescent wave which dies rapidly because of its size and wave length.

What is Refractive Index?

The refractive index (n) is a numerical value which is used to describe how light behaves as it passes through a material. The greater the refractive index, the more the light is bent as it passes through the material. This is why materials such as glass, which has a higher refractive index than air, are used for lenses. The refractive index of any material is fixed and is determined by the speed of light in the material and the speed of light in a vacuum (in a vacuum the speed of light is a constant, regardless of the material). This means that the refractive index of a material can be used to determine its speed.

The refractive index of a material is expressed in terms of a wavelength, which affects the amount of refraction that will be observed. The wavelength is measured as the distance between successive wave crests (or troughs). This distance is known as the wavelength and is measured in nanometers (nm).

There are two types of refractive index – the index of refraction (n) and the index of dispersion (γ). The index of refraction is the ratio of the speed of light in vacuum (c) to the speed of light in the material (v) – n = c/v. The index of dispersion is the difference in the refractive index of the material at different wavelengths. The index of dispersion can be used to determine the materials ability to refract light of different wavelengths in different directions, such as in optical fibers. It is calculated as the ratio of the refractive index of the material at one wavelength to the refractive index at a different wavelength – 𝛾 = n1/n2.

Difference Between Critical Angle and Refractive Index

Critical angle and refractive index are two key words that are related to light. The critical angle of a medium is the maximum angle of incidence for which light is totally internally reflected, while the refractive index of a material is a numerical value that measures how light is bent as it passes through the material.

The critical angle is the angle of incidence between two media of different refractive indices which results in a total internal reflection. As the angle of incidence increases, the ratio of the speed of light in the denser medium to the speed of light in the rarer medium will increase. When this ratio reaches 1, the angle of incidence is said to be the critical angle, and complete internal reflection will occur.

Refractive index, on the other hand, is expressed as the ratio of the speed of light in a vacuum to the speed of light in the material. It is determined by the material’s composition and physical properties. To measure refractive index, the speed of light must be measured in the two different media, and the speed of light in a vacuum must be known. Higher refractive indices indicate that light is bent more upon entering the material, while lower refractive indices indicate less bending.

Both critical angle and refractive index are important concepts when considering the behavior of light. Critical angle is needed to determine the maximum angle of incidence for total internal reflection and refractive index is needed to determine the speed of light in a material. When understanding the behavior of light, it is important to keep both terms in mind.

Conclusion

Critical angle and refractive index are two important concepts when considering the behavior of light. Critical angle is the maximum angle of incidence for total internal reflection, while refractive index is a numerical value that can be used to understand the speed of light in a material. Both concepts are used to understand how light interacts with different materials, and by understanding both terms, one can gain a better grasp of the behavior of light.