# Geology Paper on Total Internal Reflection: Laboratory Exercise

Geology Paper on Total Internal Reflection: Laboratory Exercise

Introduction

Total internal reflection is one of the concepts of physics that finds wide application in the modern times. The term is used to describe a phenomenon in which a ray of light passed through a transparent medium is completely reflected back through the medium at the interface with a separate medium. This phenomenon however, occurs only when the angle of incidence at the interface between the two media is greater than a given critical angle. Evidence of such is seen through various occurrences such as disappearance of images in water, the silvery appearance of a glass prism in water and many others. Various factors have also been cited to influence the probability of occurrence of total internal reflection. In particular, refractive indices of the materials involved and the thicknesses of the material layers are the key factors that play crucial roles in the occurrence of total internal reflection (Otsuki & Ishikawa, 2010)

Background Information

The concept of total internal reflection cannot be discussed without mentioning refraction. This is defined as the bending of a ray of light when it passes through an interface from one transparent material to another. When a ray of light strikes the interface between two materials say water and air, the ray is observed to bend depending on the angle with which it strikes the interface. The two materials have different refractive indices resulting in the potential for light refraction. According to Ribeiro (2014), refraction follows Snell’s law which asserts that when two materials with refractive indices n1 and n2 respectively are in contact and n2 is greater than n1, then:

Sin L = n1/ n2

In this equation, L is the critical angle at which total internal reflection occurs. When the incidence angle is less than or equal to the critical angle, refraction occurs. At the critical angle, refraction occurs along the interfacial line. However, when the angle of incidence is slightly higher than the critical angle, total internal reflection occurs. This implies that the mirror effect that is total internal reflection only occurs on condition that the incident light is not refracted through the second medium. Various phenomena can be linked to the concept of total internal reflection. For instance, Lee et al (2016) describes various experiments that have been used in the past to demonstrate total internal reflection. For instance, placing marbles in water and observing their disappearance is an indication of total internal reflection. Similarly, when objects are placed under water and they are partially or wholly modified, total internal reflection and refraction are the main concepts that could be used to explain this.

The concept of total internal reflection finds use in various principles of the contemporary times. Moreno et al (2005) describe some of the applications of this phenomenon. For instance, it is the key principle underlying the functioning of optical fibers which are used in the production of endoscopes. Similarly, automotive rain sensors use the principle of total internal reflection in the operation of automatic wind screens. Optical fingerprinting also uses the same principle, albeit in a frustrated format. For folding optical paths, prisms in binoculars apply this principle instead of the normal reflective coatings. In medicine, gonioscopically images are created using the same principle to determine the angle between the iris and the cornea in the eye. Other areas in which total internal reflection finds application include: the operation of LED light panels, multi- torch screens, gait analysis and in the natural shine of diamonds.

The wide applicability of total internal reflection warrants an understanding of the concept in physics studies. Due to this, the laboratory exercise conducted was to help in developing an understanding of various features of total internal reflection and to provide an evidence of the same. The report attempts to answer some of the questions presented through the laboratory manual in order to create a deeper understanding of the concept.

Characteristics of Total Internal Reflection

A scenario could be demonstrated such that water streaming out through a black hole from a rectangular tank into a pan is illuminated by a laser beam through the black hole. When this is done with the objective of observing total internal reflection, any attempts to illuminate the place of contact between the water and the pan fails. This is because when light passes through water via an interface between water and air, the point of contact between the pan and the striking water is away from the interface where total internal reflection occurs and the laser cannot be used to illuminate this point. However, some rays of light are still observable within the water in spite of the fact that total internal reflection occurs at the interface between air and water. Yildiz and Vale (2015) describe a phenomenon that could best be used to explain this occurrence. The principle behind this occurrence is based on total internal reflection which occurs when the angle of incidence is at least 2⁰ greater than the critical angle between water and air. The beam travels through two media with different refractive indices hence follows Snell’s law. When the critical angle is superseded, total internal reflection occurs resulting in the generation of an evanescent field.

The evanescent field produced following TIR decays exponentially hence the brightness of the shone light is seen to reduce from the point of TIR into the sample. The point of contact between the water and the pan can thus not be illuminated since the light observed within the sample is a result of the evanescent field and it decays before reaching the end of the water stream. This phenomenon occurs in many other experiments including the watch glass experiment which appears like a reflecting surface.

Another alternative test to total internal reflection can be conducted by using a notched glass tube to direct the laser beam and to attempt to direct the line to the inside tube walls. In such a case, the interface between the glass and the air is where total internal reflection is supposed to occur. However, for the light rays to go through the glass and be observed within the internal tube walls, it implies that the incidence angle between the glass and the air is less than the critical angle and thus refraction occurs instead. In the experiment, it was observed that it was difficult to direct the rays inside the tube walls. The rationale for this finding is based on the refractive effects of the different materials. The glass has higher refractive index in comparison to the air (Whitehead, Mossman & Kushnir, 2008). As such, the direction followed by the light ray is dependent on the incident angle as well as the refractive index of glass relative to that of air. In addition to this, the notch makes it more difficult to accomplish the objective of the exercise due to its impacts on the angle of incidence. The notch either reduces or increases the angle of incidence depending on the position struck by the light rays. Moreover, the size of the notch also affects its impacts on total internal reflection or refraction.  A deeper notch reduces the angle of incidence hence reducing the potential for total internal reflection.

An optical fiber placed over a piece of paper and illuminated at one end using a laser beam also shows illumination on the end in contact with paper. This is because the optic fiber provides a good exemplification of total internal reflection limitations. The piece of paper at the end of the fiber is translucent hence does not refract light nor reflect the light internally. At the same time, the light absorptivity of the material is also very limited. This leads to an increased light intensity at the lower end of the fiber hence the observed illumination. On the other hand, if a transparent material such as glass, air or water would have been at the end of the fiber, refraction would have resulted where the incident angle is less than the critical angle as is probable when the thin optic fiber is used. Alternatively, total internal reflection could have occurred when a larger optic fiber is used and the incident angle becomes higher than the critical angle between the two. In each case, Snell’s law guides the direction taken by the light.

References

Lee, J., Cha, Y., Jung, Y., Oh, E., Moon, Y. and Kim, J.B. (2016). Revisiting a surprising demonstration of total internal reflection. The Physics Teacher, vol. 54, no. 410.

Otsuki, S. and Ishikawa, M. (2010). Internal reflection ellipsometry in air and water ambient. The Optical Society Journal, vol. 35, no. 4, pp. 4426- 8.

Moreno, I., Araiza, J., Avendano- Alejo, M. (2005). Thin film spatial filters. Optics Letters, vol. 30, no. 8, pp. 914-6.

Ribeiro, J.L. (2014). Internal reflection on a watch glass surrounded by water: A simple experiment and a variation. Revista Brasileira de Ensino de Fisica, vol. 36, no. 2, pp. 2501- 1 – 2501-3.

Whitehead, L., Mossman, M. and Kushnir, A. (2008). Observations of total internal reflection at a natural super- hydrophobic surface. La Physique Au Canada, vol. 64, no. 1, pp. 7- 12.

Yildiz, A. and Vale, R. (2015). Total internal reflection flourescence microscopy. Cold Spring Harbor Laboratory Press.