Snells Law Experiment Analysis - Report Example

A REPORT ON SNELL’S LAW EXPERIMENT Name Professor Institution Course Date TABLE OF CONTENTS Cover Page ................................................................................................................................1 Executive Summary ..................................................................................................................2 Introduction........................................................................................................................... 3 -5 Literature Review ................................................................................................................ 6-7 Tool, Materials and Procedure ........................................................................................... 8-10 Results and Discussion...................................................................................................... 11-13 Conclusions ........................................................................................................................... 14 References .............................................................................................................................. 15 Executive Summary The scope of this experiment is to investigate how light bends in salt (or sugar) water depending on its concentration. A laser pointer is used as the source of light. The protractor is used for measuring of the incident and refracted angles. Prior to the real experimental research, this report also considers some pertinent past literature about Snell’s law. This is then followed by the experiment itself, recording the results obtained, analyzing the experimental data, discussing the results, and concluding as to whether the experiment objectives have been realized. In the literature review section, past research about Snell’s law experiment has been highlighted. The experiment procedures that follow are more limited to salt water medium. The results are then recorded in a table for easy analysis. This report will employ analysis techniques such as the use of graphs and calculation of the slope. The use of graphs will help in showing how the incident ray angles are related to the corresponding angles for the refracted rays. Further, a plot of the graph for the sine of incident ray angles verses the sine of the refracted ray angles is very crucial because this will be used for finding the refractive index of the material under investigation, and in this case the salt water medium. The refractive index, which is the relationship between the sine of the angle of incidence and the angle of refraction, is given by finding the slope of the graph for the sine of the angle of incidence against the angle of refraction. For the results to be accurate, measurements and the calculations must be done appropriately. When a light passes through some medium, it is refracting. In order to ascertain this kind of refraction, Snell’s law must be investigated. The law shows the relationship between the angle of the incident ray and the angle of the refracted ray. Some of the materials which allow the refraction of light include water, glass, and air. Worth noting, materials have different physical properties. That is why the values obtained will vary considerably from one media to another. However, in this experiment, the salt water medium is used. Introduction The Snell’s law is very useful in most science studies for investigation of refraction on different media. Most studies on refraction of light incorporate this law in order to comprehend how the incident angle and the refracted angle are related according to this law. Although a lot of experiments have been performed, primarily involving different media, this particular experiment involves the use of the salt water medium. Salt water has got a higher density than the distilled water. The ocean water is mostly the source of salt water or if distilled water is mixed with some salt, its density will certainly change. As a result of the changed density, salt water will be considered as a completely different medium while investigating Snell’s law. The aim of this experiment is to investigate and measure the refraction of light while it passes through a salt water medium. In other words, the results obtained must be used in verifying Snell’s law. Snell’s Law is used to determine the refraction index, say , of a piece of material, such as water, and use it to determine the speed of light through that material. The results obtained will be used in determining the refraction index of water. The refraction index is defined as the relationship between the average speed of light via a medium (e.g. water) and the speed of light via a vacuum. This is expressed as: Where the refraction index the average speed of light via a medium the speed of light via a vacuum. Light has got a speed of in a vacuum. In optics, all angles must be measured with respect to a line that is normal to its surface. The light ray which hits the surface is known as the incident ray while the ray which bounces off a given surface is known as a refracted ray. The angle between the normal line and the incident ray forms the incident angle. Refraction simply means bending, and the line separating the two medium is known as the boundary. A medium is also used to refer to the material, for example, water, through which the laser ray travels. Fig 1 shows how different media are related through a common interface which is known as the boundary. From the Fig 1, Snell law can be stated mathematically as: Where: and are refraction indices in the second and first medium respectively. Therefore, this experiment provides means of determining Snell’s law from the fundamental principles. Literature Review Snell’s law, also known as the law of refraction or Snell-Descartes law, is used to show the relationship that exists between the incident angle and the angle of refraction when waves or light passes through the boundary of two media, such as glass and water (Cyril & Chomet (1996). This relationship was discovered in 1621 by the Dutch scientist Willebrod Snell (1591 - 1626). Snell’s law is used in optics for tracing of rays so as to compute the angle of incidence and the angle of refraction (6). The results obtained can also be used to calculate the refractive index. This law is only true for isotropic medium, such as some crystals or liquids. Further, when the conditions are identical and light is propagated from the opposite direction, the ray will trace the same path. If light is travelling from a medium whose refractive index is higher to another medium whose refractive index is lower, then according the Snell’s law, the value of the refractive index obtained will be more than one. This case leads to what is called total internal refraction. The angle of incident light at which total internal reflection takes place is known as the critical angle. When this angle is reached, the refracted ray will travel along the interface of the two media. In the investigations involving refraction of light, total internal refraction and the critical angle must be explained. Total internal refraction is a situation where the entire light wave that was intended to be refracted in the second medium is entirely reflected on the boundary of the two media but does not pass through to that medium. Such a phenomenon only happens when light is travelling from a medium whose refractive index is more than the medium after the boundary line and also when the incident angle has exceeded the critical angle. The critical angle is also defined as the incident angle above which total internal refraction will result. Other proves that have been highlighted through Snell’s law include the fact that: light bends when it travels between the media-it bends towards the normal when it enters, that it bends away from the normal line when it leaves. Diagram Showing the Critical Angle Condition A Diagram Showing the Condition for Total Internal Refraction It is crucial to understand what brings about refraction. When light crosses the boundary between two materials whose refractive index is different, then this material will be refracted at the surface of the boundaries. Further, refraction index largely depends on the wavelength of the light. The refraction index for red light is smaller as compared to the refractive index for blue light. In other words, the blue light bends more than the red light. However, in terms of wavelength, the red light has got a larger wavelength than the blue light. Material, Tools and Produce for Determining Snell’s law In order to perform Snell’s experiment, the following materials and tools are used: Laser, Protractor, Water Thin and rectangular or square glass Pencil Data Sheet White Sheet of paper Experimental Procedure The following are the steps that can be used in verification of Snell’s law using the water medium. 1. Put a white sheet of paper on a surface that is flat. 2. Mount a laser pointer in such a way that its ray is horizontal to the sheet of paper, travels as close to the surface as possible, and leaves a red line or streak of light on the surface of the paper. Both practice and adjustments are necessary at this step. 3. Once uninterrupted streak or line of light has been obtained, place a square or rectangular glass (half full of water) on the surface of the paper so that the ray from the laser is incident to it and exits on the opposite side. 4. Using a sharp pen or pencil, draw straight lines all around the glass full of water. This is meant to register where the slab is located on the paper. Mark the corners as A, B, C and D as shown in Fig 2. Note: The laser ray is incident on one side, AA, and makes an angle of with the normal line and enters the water through an angle. The ray leaves the glass on side where it is refracted back into the air at an angle . 5. Using a sharpened pencil, mark 2-3 points on the incoming laser ray and 2-3 points on the outgoing laser ray. This helps to register the location of the ray path on the paper. 6. Lift the glass containing water, turn off the laser and connect all the marked points so as to get a trace of the laser ray. 7. Draw two lines for (normal) as shown in Fig 2. 8. Using a protractor, measure angles ii , r1, i2 and r2 and record the results in Table 1. 9. Repeat the same procedures above for different angles of incidence. 10. Applying Snell’s law, use both ii and r1, to measure the refractive index of water and tabulate the results in Table 1. The layout showing incident angle and refraction angle Fig 2: The Layout Showing Different Angles and the Normal Pictures showing Different Materials and Tools Used Fig 3: Protractor Fig 4: Glass Containing Water A Natural Case where Refraction can be Witnessed is Shown in Fig 5 Fig 5: Refraction in Real Life Results and Discussion Table 1 shows the typical results of this experiment 5° 3° 0.08715 0.0523 10° 6° 0.1736 0.1045 15° 9° 0.2588 0.1564 20° 12° 0.3420 0.2079 25° 16° 0.4226 0.2756 30° 19° 0.5 0.3256 35° 22° 0.5735 0.3746 Table 1 A Plot of against is as Shown in Fig 4 Fig 5: A Plot of against Fig 6: A Plot of and A Plot of and is as shown in Fig The gradient of the graph in Fig 5 = Thus, the gradient of Vs is . This shows the trend with the ray tracings. The gradient gives the speeds of light air and water. Mathematically, when the data gives a relationship that is liner, such a relationship can be expressed as . In order to calculate the average refractive index of water, Table 2 can be used Angle of Incidence Angle of Refraction Constant Refractive Index Sin 10°=0.1736 Conclusions The results obtained from this experiment shows how Snell’s law works. For example, a plot of the sine of the incident angles against the sine of the refracted angle indicates a relationship that is linear. The accuracy of the results depends on how accurate measurements and calculations are carried out. Thus, the refractive index of water as per this experiment is . The accuracy of this experiment is much limited to precision, especially where the points are marked. The calculations must also be done in the correct way, and with a lot of accuracy since any single error can distort the results. Therefore, in order to increase accuracy, patience is crucial when marking the angles and setting the ray from the laser in a straight line. References Cyril, Isenberg, and Seweryn, Chomet. Physics Experiments and Projects for Students. New York: Wiley & Sons Ltd, 1996. Print. Snell's Law and the Index of Refraction. Retrieved from http://www.colorado.edu/physics/phys1140/phys1140_fa01/Experiments/O3/O3.html on 1/04/2013. Read More

The ocean water is mostly the source of salt water or if distilled water is mixed with some salt, its density will certainly change. As a result of the changed density, salt water will be considered as a completely different medium while investigating Snell’s law. The aim of this experiment is to investigate and measure the refraction of light while it passes through a salt water medium. In other words, the results obtained must be used in verifying Snell’s law. Snell’s Law is used to determine the refraction index, say , of a piece of material, such as water, and use it to determine the speed of light through that material.

The results obtained will be used in determining the refraction index of water. The refraction index is defined as the relationship between the average speed of light via a medium (e.g. water) and the speed of light via a vacuum. This is expressed as: Where the refraction index the average speed of light via a medium the speed of light via a vacuum. Light has got a speed of in a vacuum. In optics, all angles must be measured with respect to a line that is normal to its surface. The light ray which hits the surface is known as the incident ray while the ray which bounces off a given surface is known as a refracted ray.

The angle between the normal line and the incident ray forms the incident angle. Refraction simply means bending, and the line separating the two medium is known as the boundary. A medium is also used to refer to the material, for example, water, through which the laser ray travels. Fig 1 shows how different media are related through a common interface which is known as the boundary. From the Fig 1, Snell law can be stated mathematically as: Where: and are refraction indices in the second and first medium respectively.

Therefore, this experiment provides means of determining Snell’s law from the fundamental principles. Literature Review Snell’s law, also known as the law of refraction or Snell-Descartes law, is used to show the relationship that exists between the incident angle and the angle of refraction when waves or light passes through the boundary of two media, such as glass and water (Cyril & Chomet (1996). This relationship was discovered in 1621 by the Dutch scientist Willebrod Snell (1591 - 1626).

Snell’s law is used in optics for tracing of rays so as to compute the angle of incidence and the angle of refraction (6). The results obtained can also be used to calculate the refractive index. This law is only true for isotropic medium, such as some crystals or liquids. Further, when the conditions are identical and light is propagated from the opposite direction, the ray will trace the same path. If light is travelling from a medium whose refractive index is higher to another medium whose refractive index is lower, then according the Snell’s law, the value of the refractive index obtained will be more than one.

This case leads to what is called total internal refraction. The angle of incident light at which total internal reflection takes place is known as the critical angle. When this angle is reached, the refracted ray will travel along the interface of the two media. In the investigations involving refraction of light, total internal refraction and the critical angle must be explained. Total internal refraction is a situation where the entire light wave that was intended to be refracted in the second medium is entirely reflected on the boundary of the two media but does not pass through to that medium.

Such a phenomenon only happens when light is travelling from a medium whose refractive index is more than the medium after the boundary line and also when the incident angle has exceeded the critical angle. The critical angle is also defined as the incident angle above which total internal refraction will result. Other proves that have been highlighted through Snell’s law include the fact that: light bends when it travels between the media-it bends towards the normal when it enters, that it bends away from the normal line when it leaves.

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