Reflection, Refraction, and Total Internal Reflection

Maxwell's Equation

The experiment is all about the reflection and refraction of light, a property of light as a wave and particle. On nineteenth century, James Clark Maxwell argued that light is a traveling wave of electric and magnetic fields, or simply an Electromagnetic Wave with a speed of c= 299792458 m/s in vacuum through his four famous equations, or also known as Maxwell's Equation (Albert Einstein popularizes the name "Maxwell's Equation", in his monograph Considerations Concerning the Fundamentals of Theoretical Physics). The four equations described all electric and magnetic phenomenon and a breakthrough in the understanding of light.

In this experiment, we will study the properties of light waves -- reflection, refraction & total internal reflection -- through approximate treatment of light in which light waves are represented in straight-line rays, which is called geometrical optics.

This experiment aims to investigate reflection and refraction of light using optical disk. It also aims to know the measurement of the index of refraction of a material using the optics set-up. And lastly, the experiment wants to trace the path of light as it emerges from optical materials of different geometries.

To be able to perform the experiment, this materials are needed:

We will start the experiment by building the main set-up that will be use in the whole experiment. First, The light source and the optical disk will be mounted on the optical bench, with slit plate and parallel ray lens between them. The slit plate will produce the multiple rays and the parallel ray lens will make the multiple rays parallel. The slit plate and parallel ray lens location will adjusted in able to coincide the parallel rays with the grid of the optical disk.

In the first part of the experiment, we will do the reflection of light by plane and spherical mirror. We need a slit mask that will produce single ray and let it coincide 0°-0° axis of the optical disk. Next, the plane and spherical mirror will place on the disk such that it will coincide 90°-90° of the optical disk. Then, we will rotate the optical disk in able to have different angle of incidence.

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Basically, in this part we will measure the the reflection of light in plane and spherical mirrors considering different angle of incidence. Also, we will verify if the plane and spherical mirrors obey the Law of Reflection, which state that the angle of incidence and angle of reflection are equal (θi=θr).

So I set 20, 50, and 80 degrees with respect to the normal line as my angle of incidence. The angle where the light was reflected were obtained and recorded in Table W1. The same procedure was done with convex and concave mirror.

We can see that the angle of incidence and the angle of reflection with respect to the normal line are equal. Therefore, we can conclude that the plane and spherical mirror obey the Law of Reflection.

In the second part of the experiment we will observe the reflection and refraction of light when it hit a transparent material and compute for index of refraction of the material. So first, we will replace the mirror with semicircular glass. Then, we will coincide the flat surface of the glass with the component axis of the optical disk and we will make sure that the center of the glass and the optical disk also coincide.

 

The optical disk will be rotated to set the needed angle of incidence. And lastly, the angle of reflection and refraction were obtained and recorded in Table W2.

As we can see in the data in Table W2, the angle of incidence and angle of reflection of the light with respect to the normal are equal. Therefore, we can say that glass also follows the Law of Reflection.

Comparing the data of angle of incidence and angle of refraction in Table W2, the angle of incidence is greater than the angle of refraction. Based on the data, we can say that the light bend towards to the normal line when it strike the flat surface of the cylindrical lens. This phenomenon is mathematically explains by Snell's Law:

where θ1 is the angle of incidence, θ2 is the angle of refraction and n1 and n2 is a dimensionless constant, called Index of Refraction, that is associated with a medium involved in the refraction.

In this part of the experiment we need to solve the index of refraction of the cylindrical lens using the data obtained. The data were plotted with sin θ2 vs sin θ1:

Looking at the graph, it shows that the linear equation produce by linearization is y = 0.689x that we can relate to Snell's Law in able to find and solve the index of refraction of the cylindrical lens.

Based on the computation, the index of refraction of the cylindrical lens is 1.46. Since the index of refraction of air is less than the index of refraction of the cylindrical lens, indeed the light ray bend toward the normal line.

The third part of the experiment is the somehow the same with part two. But in this part the incident ray will strike the curve surface of the cylindrical lens instead the flat surface. 

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Based on the ray diagram, the two parts differ in the which medium they refracted. In the part two of the experiment, our n1 is the air because after light ray strike the flat surface immediately the light refracted. While in this part of the experiment, the light ray go inside the glass before it refracted. In simple words, our n1 and n2 in part two is air and cylindrical lens respectively, while in the third part our n1 is the cylindrical lens and n2 is the air.

The angle of reflection and angle of refraction in this part were obtained and recorded in Table W3:

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The data on angle of incidence and angle of reflection show that even the incident ray strike the flat or curved surface of the cylindrical lens it will still obey the law of reflection.

Looking to the data of angle of incidence versus angle of refraction, the angle of refraction is greater than the angle of incidence. We can say that the light bend away the normal line.

In order to solve again the index of refraction of the material used. We need to plot and linearize the data. It was plotted with sin(θ2) versus sin(θ1):

Linearizing the data, it gives as a linear equation y = 1.4596x that we can relate to Snell's Law to solve for the index of refraction of the cylindrical lens.

The computed index of refraction of the cylindrical lens is 1.46, which is the same in part two. The computed index of refraction is the same because the same cylindrical lens. Since the index of refraction of glass is greater than the index of refraction of air, indeed the light ray bend away the normal line.

The last part of the experiment dealt with the total internal reflection of light. This phenomenon mostly happens when the light travel from higher index of refraction to lower index of refraction. In this part we only need to find the critical angle. We will find the critical angle by rotating the optical disk and observing the refracted ray, if the refracted ray become parallel to the flat surface of the cylindrical lens then that angle will be obtained and recorded to Table W4:

We found that the critical angle of the cylindrical lens to be 45 degrees. Using the critical angle we can solve for the index of refraction of the glass using Snell's Law:

In able to solve for the speed of light inside the semicircular glass we will use the notation of "Index of Refraction", which is needed concept to state the Snell's Law.

The computed velocity of the light inside the semicircular glass is 2.13E8 m/s. So the light slowdown inside the semicircular glass. Therefore, the higher the index of refraction the slower the speed of light inside that medium.

Conclusion:
 The data are precise, since the theoretical value is not given the percent error cannot be computed. Also, the data can't be verify if its accurate or not. Summary, the data are good and precise and there is a small discrepancy and error due to human error and machine error.

Ray tracing for plane and spherical mirror

Figure 1. Plane Mirror

Figure 2. Concave Mirror

Figure 3. Convex Mirror

 Ray tracing for different refracting media

Figure 4. Converging Lens

Figure 5. Diverging Lens

Figure 6.  Refraction of Light

Figure 7. Refraction of Light and Total Internal Reflection

References:

“Experiment 1 Reflection and Refraction,” Laboratory Manual for Physics (Physics 72.1), (2013).

"Introductory Optics System." Instruction Manual and Experiment Guide for the PASCO Scientific Model OS 850. PASCO Scientific. Web. 5 Dec. 2011.

Tipler, P., Mosca, G. Physics for Scientists and Engineers. Chapter 25. W. H. Freeman and Company, New York, 2008.

Walker, J., Halliday, D., & Resnick, R. (2011). Fundamentals of physics. Hoboken, NJ: Wiley.

Young, H., Freedman, R., University Physics with Modern Physics. Chapter . Pearson Inc. San Francisco, 2012,