Reflection and Refraction
As air is the most essential resource for our survival, the light is the most important phenomenon for our perception. Although being a pretty complex phenomenon, the behavior of light in our everyday interactions can be simplified and approximated to the geometrical optics. In this field of physics, the light propagation is described in terms of rays. The rays come through the wave fronts (being tangent to them) and are an effective approximation because usually light moves in straight lines. The rays are linear in homogenous media; they can bend or be curved if the refractive index of the medium changes. Generally, the two most important phenomena described by the geometrical optics are reflection and refraction of light. In essence, these are the two phenomena with which we interact most frequently in our regular life: while looking into the mirror, watching the objects reflect in the calm water, observing fish in aquariums or our hands and feet while taking a bath.
When the light travels from one medium to another, on the interface between the media it can be: partly or totally reflected, transmitted through refraction to the second medium, partly or fully absorbed by either media (Roychoudhuri 79). Obviously, the reflection takes place if the second case. Depending on the character of the surface that the light reflects from, the reflection is classified into specular and diffuse.
Figure 1. (a) Specular and (b) Diffuse reflection (Roychoudhuri 79)
The specular reflection occurs when the light reflects from a smooth flat surface – in this case, both energy and information of the light is preserved because the pattern of the reflected light is the same as of the incident light. When the light is reflected from an uneven and jagged surface, the diffuse reflection takes place. The light gets scattered in different directions, so the energy of the light is conserved while the information is not preserved (as the pattern is broken) (Henderson “Specular vs. Diffuse Reflection”).
When a reflection takes place, the angle between the incident ray and the normal to the reflecting surface at the point of incidence is called the angle of incidence. The same angle between the reflected light and the normal is called the angle of reflection (as depicted in the Fig.2).
Figure 2. The Specular Reflection (Roychoudhuri 80)
The Laws or the Law of reflection can be stated as follows: when light reflects from a plane surface, the incident ray, normal, and reflected ray are coplanar, lie on the different sides from the normal, and the angle of incidence equals the angle of reflection (Tatum 1-2).
Most objects exhibit diffuse reflection with the mirrors being almost the only exception. The specular reflection is also exhibited by calm water and strongly polished surfaces (metallic, etc.) The Law of Reflection, however, applies to the diffuse reflection too. On the microscopic level, when the rays of light are reflected by the jagged surface each individual ray simply gets reflected from a different plane in accordance with the Law of Reflection (Henderson “Specular vs. Diffuse Reflection”). The information which the light carried (i.e. picture) is, however, lost, as the parallelism of the incident rays is disrupted.
When light strikes the boundary between two media that are optically transparent, then the light will proceed to a second medium while its path will be bend. The bending of the light path at the boundary is the refraction itself; it is caused by a change in the speed of light when crossing the boundary. The change itself is explained by the way by which light is transported through a medium. Light, essentially, is an electromagnetic wave, and it travels through the vacuum at a speed of c (3×108 m/s). When the wave interacts with the material, its energy is absorbed, and the electrons are set into vibrational motion. If the electromagnetic wave frequency does not match the electron resonant frequency of vibration then the energy in the form of electromagnetic wave is then reemitted by the particle, the emitted wave has the same frequency as the initial wave, and it also continues to move in the interatomic space with the same speed of c. Following this mechanism, the light ray or the electromagnetic wave energy is transferred through a medium While the speed with which the light travels between the atoms is the speed of c, the delay between absorbing and emitting the electromagnetic wave is responsible for the decrease in the overall speed of light (Henderson “Optical Density and Light Speed”). Quantitatively the change in the speed of life within the material compared to the speed of light in the vacuum is described by the refractive index n. It is the ratio of the speed of light in vacuum to the speed of light in a given medium:
where c is the speed of light in vacuum, n – refractive index of a medium, v – speed of light within this medium.
As the light travels through substance at a lower speed than through vacuum, the refractive index is higher than 1. It is closer to 1 in the gasses since the atoms are situated far apart from each other (1.00029 for the air, 1.00045 for the carbon dioxide). For practical purposes, the refractive index of the air is usually taken as 1. As the distance between the atoms decrease, the liquids possess higher refraction indices (1.333 for water, 1.473 for glycerine, 1.361 for ethanol (Urone et al. 988)). The solids accordingly have the highest refraction indices (1.31 for ice, 1.52 for crown glass, 2.419 for diamond, and 3.50 for the gallium phosphide which is the highest refractive index). When the refractive index of a medium is known, the speed of light in this medium can be found using the refractive index’s definition (Tatum 5):
v=cn
So, if the light is bend when passing through a boundary between two media with different refractive indices, this change it its path can be described mathematically. This was first performed by the Dutch mathematician Willebrord Snell in 1621. The Law of Refraction was named after him and is typically known as the Snell's Law (Urone et al. 987). In much the same way as in the Law of Reflection, the angles between the light rays and the normal are called the incident angle and the angle of refraction. The refraction is illustrated in the Fig. 3.
Figure 3. Refraction (Tatum 5)
The mathematical formulation of the Snell’s Law goes as follows:
n1sinθ1=n2sinθ2,
where n1 and n2 are the refractive indices of the media, θ1 is the angle of incidence, θ1 is the angle of refraction (Urone et al. 989).
The Fig. 3 illustrates the case when light travels from the medium with lower optical density to a medium which is optically denser. In this case, the angle of refraction is actually lower than the angle of incidence (the light bends closer to the normal). This case takes place when the light travels from air to glass or water. It might be easily found out that in the case when the second medium is less optically dense than the one from which the light moves then the angle of reflection will be greater than the angle of incidence (the light will bend farther from the normal). This is the opposite of the previously described phenomenon; it takes place when light travels from water or glass to air.
When light crosses the boundary between two media with different refractive indices and is refracted, a portion of it is always reflected. However, when traveling from a more optically dense medium to a less optically dense, at some angles of incidence, the light might not pass through the boundary at all and get fully reflected from the intermediary plane. As discussed before, the angle of reflection for this case is greater than the angle of incidence, so when the angle of incidence is increased, at some point, the angle of reflection will be right. Such angle of incidence is called a critic angle, and if the angle of incidence is further increased, the light will get fully reflected from the boundary as the refraction becomes impossible. If the Snell's Law is applied to this case, the formula for the critical angle can be derived (Urone et al. 992):
θC=sin-1n2n1, if n1>n2
where θC is the critical angle, n1 and n2 – refractive indices of the media. The critical angle is different for each pair of media, the most common values are 48.6 degrees for a water-air boundary, 41.1 degrees for crown glass-air, 24.4 degrees for diamond-air (Henderson “Total Internal Reflection”). It is important to note that if the good mirrors reflect up to 90% of the light energy (10% is absorbed), in the case of total internal reflection, the reflection is indeed total. Total internal reflection is widely used in modern technological applications. The fiber optics are based on this phenomenon. Light reflects inside the fibers of glass making possible to transmit information and images through the set of fibers.
Works Cited
Henderson, Tom. "Optical Density And Light Speed". Physicsclassroom.com. N.p., 2016. Web. 26 Feb. 2016.
Henderson, Tom. "Specular Vs. Diffuse Reflection". Physicsclassroom.com. N.p., 2016. Web. 26 Feb. 2016.
Henderson, Tom. "Total Internal Reflection". Physicsclassroom.com. N.p., 2016. Web. 26 Feb. 2016.
Roychoudhuri, Chandrasekhar. Fundamentals Of Photonics. [Bellingham, Wash.]: SPIE, 2008. Print.
Tatum, J. B. Physics: Geometrical Optics. 1st ed. 2013. Web. 26 Feb. 2016.
Urone, Paul Peter et al. College Physics. Houston, Texas: OpenStax College, Rice University, 2013. Print.
