# Relation Between Critical Angle and Refractive Index

## Introduction

The refractive index is proportional in nature to the critical angle. In a situation, when a light ray is traveling from a single medium to another medium, a critical angle is found to be created. This type of angle strikes the main boundary that is situated between the lower index and the medium. At that time, the ray does not reflect in the first medium of traveling. The limit of the critical angle can be measured by implementing a particular formula.

## Features of Critical angle

This angle is highly affected by the changes within a refractive index.

The refractive index may vary from the first medium to the second medium.

The wavelength of the ray plays an important role in changing the nature of the angle (Shahsafi et al. 2018).

In the case of a higher wave length, the critical angle also increases accordingly.

## Required conditions of a critical angle and refractive index

 Components Required conditions Critical angle The incidence angle needs to be greater and higher than the other angleThe ray needs to move forward from a dense medium to a low dense medium. Refractive index The density of the optical base needs to be appropriateThe temperature of the medium needs to be proper so that the value of the index can change accordinglyThe wavelength of the light is to be proportional

Table 1: Important conditions for critical index and refractive index

## Features of refractive Index

Figure 1: Refractive Index

This index is an important material property.

The Refractive index helps to describe the affecting procedure of material at the speed of light.

The index is mainly presented by the symbol n (Grebenikova et al. 2018).

The symbol μ is also used sometimes to present the value of this index.

The symbol v is representative of the light's speed in which it travels through a material.

## Application of critical angle and refractive index

In daily life, the refractive index is widely used to measure the value of gases, solids, and liquids as well. A Refractive index is also used to measure a solute's concentration. Some users also find it useful in differentiating gemstones.

The refractive index possesses significant and unique chatoyance (Danny et al. 2019). These characteristics help the user to properly differentiate various gemstones. The two most important factors, associated with the refractive index are the medium's type and nature.

The value of the refractive index changes with the nature of the medium. In a vacuum medium, the value of the refractive index is estimated as 1 whereas, in helium, the value increases to 1.000036 (Mammothmemory.net, 2022).

Water, as a medium, presents the value of 1.30 in the refractive medium. The value of sugar solution and glass increases from water accordingly from 1.38 to 1.5 as the density increases (Koutserimpas & Fleury, 2018).

• Diamond is the highest dense medium in which the value presents 2.4. Based on these values the changes within the refractive index according to the changes in the medium are estimated.

The critical angle is widely used in making optical fiber communication. The application of critical angle is also important in the case of spatial filtering of light (Niskanen et al. 2019). In real life, the knowledge of critical angles is significant and relevant as helps in understanding the possibility of reflection occurrence. In relation to the water-air boundaries, the value of the critical angle can be 48.6 degrees.

In relation to the glass-water boundaries, the value of the critical angle is estimated at 61.0 degrees. An important real-life application of critical angles is its usage in collecting electrical signals. Computer users also use critical angles for transmitting signals (Maurya et al. 2018). This helps electrical devices to stay connected as the light rays change their direction while changing their travelling medium.

Figure 2: Critical Angle

The SI unit of the critical angle is degree whereas the refractive index does not possess any SI unit. Applying the Snells law is a significant part to understand the changes within the critical angle and refractive index.

## The formula of refractive index and Critical angle

This formula is θcrit = sin-1(nr/ni). The result of that formula can be presented as sin-1(1/1.67) = 1.064rad.

This angle is related to the angle of incidence. The direction of light changes as it enters into a denser medium from a less dense medium (Liu et al. 2019). The light of the ray is also found to be bent to the normal angle. Refractive index (n)= 1/(Sin C)

Figure 3: Relation between Refractive index and Critical Angle

## Conclusion

Derivation of refractive index and critical angle is a significant part so that the relation between these two components can be analyzed. The consideration of light and rays is integrally connected to the concept of the critical angle. Based on the value of the angle of incidence, the value of the critical angle can be determined.

## FAQs

Q1. Which are the factors on which the critical angle is dependent?

The wavelength of the light, the value of the refractive index and medium temperature are these factors, based on which the value of the critical angle differs. Internal reflection can be measured by applying features of a critical angle to the fluorescence microscope.

Q2. What is the indication symbol of the refractive medium's components?

The denser medium of the refractive index is presented by μb and with μa, the rarer medium of this index is presented. The value of refraction is 900 in which the impact of a rarer medium is also included.

Q3. What is represented by C in the refractive index?

The refractive index C is representative of the speed at which the light travels in a vacuum place. The physical condition of the medium's structure is also an important part.

Q4. What is the relation of temperature with critical angle?

The value of the critical angle increases with the increase of the surrounding temperature. This relation also impacts the value of the refractive index.

## References

### Journals

Danny, C. G., Raj, M. D., & Sai, V. V. R. (2019). Investigating the refractive index sensitivity of U-bent fiber optic sensors using ray optics. Journal of Lightwave Technology, 38(6), 1580-1588. Retrieved from: https://opg.optica.org

Grebenikova, N. M., Myazin, N. S., Rud, V. Y., & Davydov, R. V. (2018, October). Monitoring of flowing media state by refraction phenomenon. In 2018 IEEE International Conference on Electrical Engineering and Photonics (EExPolytech) (pp. 295-297). IEEE. Retrieved from: https://www.researchgate.net

Koutserimpas, T. T., & Fleury, R. (2018). Electromagnetic waves in a time-periodic medium with step-varying refractive index. IEEE Transactions on Antennas and Propagation, 66(10), 5300-5307. Retrieved from: https://ieeexplore.ieee.org

Liu, S., Deng, Z., Li, J., Wang, J., Huang, N., Cui, R., ... & Tian, J. (2019). Measurement of the refractive index of whole blood and its components for a continuous spectral region. Journal of biomedical optics, 24(3), 035003. Retrieved from: https://www.spiedigitallibrary.org

Maurya, J. B., François, A., & Prajapati, Y. K. (2018). Two-dimensional layered nanomaterial-based one-dimensional photonic crystal refractive index sensor. Sensors, 18(3), 857. Retrieved from: https://www.mdpi.com

Niskanen, I., Suopajärvi, T., Liimatainen, H., Fabritius, T., Heikkilä, R., & Thungström, G. (2019). Determining the complex refractive index of cellulose nanocrystals by the combination of Beer-Lambert and immersion matching methods. Journal of Quantitative Spectroscopy and Radiative Transfer, 235, 1-6. Retrieved from: http://jultika.oulu.fi

Shahsafi, A., Xiao, Y., Salman, J., Gundlach, B. S., Wan, C., Roney, P. J., & Kats, M. A. (2018). Mid-infrared optics using dielectrics with refractive indices below unity. Physical Review Applied, 10(3), 034019. Retrieved from: https://arxiv.org