Snells Law

Posted: August 29th, 2013

VERIFYING SNELL’S LAW

Aim

The aim of carrying out these experiments is to investigate how light travels, investigate reflection, refraction, and total internal refraction to find the critical angle – to ultimately verify Snell’s law.

Introduction

Willebrod Snell was a Dutch mathematician and astronomer, who derived a law concerning the refraction of light in 1621, famously known as Snell’s Law (Beech 2011 p38).

The refraction of light rays is this invention, known as Snell’s law, it shows that when a beam of light passes from a thinner component such as air, into a denser component, such as water or glass, the angle of the ray bends to the vertical.

Snell found the characteristic ratio between the angle of incidence and the angle of refraction. This shows that all substances have a bending ratio, the formula for this is:

Mr. Snell was also a professor at Leiden University were he was a teacher for mathematics

Mr. Snell was born in Leiden, Netherlands year 1580; he died October 30th, 1626. He had lived a short forty-seven years.

Leiden University, where Willebrord attended Leiden University as a student, he did not initially attend Leiden for mathematics, but he attended it to study law. In some of his earlier times at the University they had allowed Mr. Snell to make unique arithmetical lectures.

Even though Snell revealed the law of refraction, he did not make it public.. Light traveling perpendicular to the glass will not bend if the light travels at an angle into the glass it will bend to a degree proportional to the angle of inclination. Archimedes to Hawking:

laws of science and the great minds behind them, Oxford University Press, 16 Apr 2008 – Biography & Autobiography – 514 pages, Clifford A. Pickover
After studying the concept of Snell’s Law, an experiment was devised to try and prove Snell’s Theory. Using the foundations of Snell’s Law, it could be predicted before the experiment took place that, the light would react in certain ways throughout the experiment.

Risk Assessment

Under the Health and Safety at Work Act, a risk assessment should be carried out before procedures are undertaken (Health and Safety Executive, 1974). Firstly, any hazards (Anything that can cause harm) were identified and suitable precautions suggested.

The experiment was conducted under the supervision of an appropriately qualified physics teacher, with an adequate knowledge of physics and all equipment used, in an appropriately equipped and maintained science laboratory. All equipment was inspected to ascertain whether it was going to be suitable to use in the experiment, i.e. all equipment is intact and in full working order. The science laboratory dress code was implemented, which states that non slip, flat footwear should be worn, along with adequate eye protection.

It was important, that all participants in the experiment were briefed and given adequate instructions on how to conduct the experiment, and it was important to consider the

competence of the participants at this time. If the participants are not deemed competent or have misunderstood the instructions, then the level of risk is significantly increased to

that group of people. Furthermore, participants had to be aware of any person who could come into the area whilst the experiment was taking place, i.e. laboratory assistants, other students.

All electrical equipment should be checked before use to ensure there is no damage, and that there are no exposed wires, any broken glass or broken mirror should be swept up immediately and placed in the glass disposal bin and not general waste. The pins are to be kept safe and returned when not in use, all participants should be aware of these objects so that injury is not caused to themselves or others. Appropriate Personal Protection Equipment (PPE) should be worn during this experiment including safety glasses.

Apparatus

Plane mirror, ray box, glass block, semi-circular Perspex block, optical pins, plain paper, polystyrene tile.

Method

Firstly, the apparatus (as detailed above) was collected together, and set up as instructed depending on the experiment. The basic set up was a power box set at 12v  with ray box attached, then the out line of the required medium was drawn on to a piece of plain A4 paper. The ray box was then directed into the designated medium whether it was a plain mirror, glass block or semi-circular Perspex block for each experiment at the instructed angle. The results were then recorded on the piece of paper whether it was the reflective or refractive ray (as seen below).

Results

Experiment 1

1.         During the experiment, the light propagated in a single ray. This indicates that light normally travels in straight line. Another aspect to note is that light travels only from a source. Another aspect is that light is dependent on the medium of propagation. With this regard, the single ray was propagated only through air, vacuum, transparent and translucent objects. Opaque objects failed to propagate the single ray (Khare, & Swarup, 2010).

2.         The human eye can only perceive illuminated objects. In the darkened room, the objects that did not fall on the path of the light ray could not be perceived with the naked eye. With this regard, light mainly from the sun or any other light source bounces off the object and into the human eye thereby rendering the object visible.

Experiment 2 (fig 1)

3.         From the experiment, placing an object in the path of the ray of light interferes with the original direction of the ray. The incident light seemed to bounce of the obst6ractign white card. This interference is dependent on the colour of the material used. The interference with the path of the ray of light ranged from the use of white card to that of a black card. This bouncing off the ray of light off objects placed on its path is what is referred to as reflection. The white card reflected most of the light unlike the use of a black card (Young, 2000).

4.         This observation indicates that when light falls on a book. All or part of the incident light is usually reflected away depending on the colour of its cover.

5.         When a flat mirror was placed on the path of the ray of light, the incident ray was reflected back. The direction of the reflected ray varied with the change in angles of incidence to the mirror.

6.         After calculation, the sine of the angle of the reflected ray is directly proportional to the sine of the angle of the incident ray. The sine of the angle of refracted ray is also directly proportional to the sine of the angle of the incident ray.

7.         When light is transmitted through the air, it travels in a straight line until is reaches something on its path, say a mirror or a white card. This causes the ray of light to undergo reflection, refraction or polarization. This is highly dependent on the material being hit by the ray of light. Some objects absorb all the light, others reflect it while others allow most or part of it to pass through. In this case, the mirror absorbs very little of the light’s energy and thereby reflecting most of it in comparison to the white card. With this regard, the reflected light has more intensity in the case of a mirror or any polished surface as opposed to a white card.

Experiment 3 (fig 2)

8.         When the incident ray was at zero degrees to the normal, the ray was not refracted since it continued at the same zero degrees to the normal. However, when the set was change with the incident ray taking up angles greater than zero degrees, the light ray changes direction and hence refraction occurs.

9.

10. From the experiment, a comparison of the angle of incidence to the angle of refraction indicates that the angle of incidence is always greater to that of the refracted ray (Khare, & Swarup, 2007).

11.       The analysis of the data from the above experiment fails to reveal a clear relationship between the angle of incidence and the angle of refraction of the light ray. As an illustration, doubling the angel of incidence from twenty degrees to forty degrees does not lead to a doubling in the angle of refraction from twelve degrees to twenty-four degrees. Performing other simple mathematical applications such as addition or division also fails to reveal a relationship between the angle of incidence and the refracted ray. This indicates that when this data is plotted on a plane, a straight line would not result. However, when the sines of the angles were taken into account, a linear relationship is obtained.

Plotting a graph of the sine of the angle of incidence against the sine of the angle of the refracted ray results in a straight line. This indicates a linear relationship between the two angles. When straight line is obtained from two quantities plotted on a graph, then a mathematical relationship can be deduced from this information in the form of Y = MX + C. Where C is the Y- intercept, M is the gradient of the straight line and Y and X are the (y) and (x) coordinates respectively. From the graph, the line intercepts the Y-axis at zero. Therefore, Y/X is equal to M and sine incident divide by sine of the refracted ray is equal to a constant (Institution of Electrical Engineers, 2000).

Experiment 4 (fig 3)

12.       During the experiment, light was emitted from a denser medium that is the glass block to a less dense medium, air. In the beginning, some of the rays are refracted as the pass through the glass block into the air surface while some is reflected back into the water. When the angle of incidence increases, more of the ray is reflected while less of it is refracted through the glass block into the air. When the angle of incidence is increased to an angle greater than the critical angle, none of the rays is refracted across the air as all the rays are reflected into the glass block. This critical angle is defined as the ratio of the two indexes of refraction. With this regard, increasing the incident angle to angle greater than that of the critical angle results in total internal reflection (Laufer, 2000).

13.

14.       This idea can be harnessed for practical purposes by sending light rays down a cable. In order to achieve this, the cable is first designed using two materials that allow light to pass through but having different densities in relations to light propagation. These two regions are known as the core and cladding. The material having the denser index of refraction is used as the inner covering while the material with the lesser index of refraction is placed on top. The outer material is later covered with a  protective covering to prevent damage. Calculating the ratio of the two indexes of refraction enables in finding the critical angle where total internal reflection occurs. A ray of light can then be illuminated inside the pipe at angle slightly greater than the critical angle and this ray of light will be propagated to the end of the pipe under total internal reflection. The ability of converting print, voices, music, and images into pulses of laser light leads to the latter being used as the incident ray in the above pipe and propagating it through long distances (Agrawal, 2004).

15.       Reflection is referred to as the bouncing off of light rays when they meet a different medium or object. In order for there to be a bouncing off or reflection, then two mediums are required. Another requirement for total internal reflection to occur is the presence of two mediums having different refractive indexes. The two materials therefore provide the two mediums. In normal circumstances, the most commonly used material used in the making of fibre optics is silicon dioxide. The advantage of using this is that its refractive index can be varied by doping it with compounds such as GeO2, P2O5, F and B2O3 (Hunt, 1982).

17.       Man’s ability in the realm of light technology to convert print, voices, music, and images into pulses of laser light has immensely revolutionized the application of the fibre optic cable. The demand for fiber optic cable has been on an exponential increase over the years. This is because of the numerous applications of the fiber optic cable. The uses of telecommunications are wide ranging from global networks to personal computers. These applications employ the transmission of print, voices, music, and images over both less and large distances covering hundreds of miles while utilizing a single standard fiber optic cable design out of various cable designs (Isaacs, 2000).

Carriers utilize optical fiber networks in transmitting plain old telephone service (POTS) along their national networks. Many offices also utilize fiber optics while using local exchange carriers in the transmission of information between main office switches at the regional areas or to the neighborhood or personal homes during fiber to the home ( FTTH). Data transmission also utilizes optical fiber technology.

Multinational firms use optical fibers in the transmission of vital information and data between its regional and international offices. This is because of the optical fiber’s ability to transmit vital information and data safely and securely over both short and long distances. Cable television companies also utilize optical fiber networks in the transmission of digital video and data services to both its offices and the clients. This is mainly because of the optical fiber’s ability offer high bandwidth in the transmission of broadband signals such as the latest high-definition telecast ( HD).

Optical fibers are also utilized in the realms of intelligent transportation systems. Super highways with automated traffic light systems, tollbooths and transforming message boards use fiber optics that is mainly based on telemetry systems. In the biomedical industry, the fiber optics are used are used in modern health facilities in the transmission of digital diagnostic images. Most of the developed nations and some of the developing nations have a global interconnected fiber optic system mainly in the provision of high-speed internet (Foot, 2005).

Experiment 5 (fig 4 & fig 5)

From studying the results above, they show that there is no clear linear relationship between the angle of incidence and the angle of refraction. For example, a doubling of the angle of incidence from 40 degrees to 80 degrees does not result in a doubling of the angle of refraction. Thus, a plot of this data would not yield a straight line. If however, the sine of the angle of incidence and the sine of the angle of refraction were plotted, the plot would be a straight line, indicating a linear relationship between the sines of the important angles.

These results have been plotted on a graph (appendix 2) which shows sin i against sin r  to Verify Snell’s law.

Analysis

As the speed of light is measured at 3.00 x 108 ms-1 in a vacuum and travels at 2.00 x 108 ms-1 in glass then this allows us to work out the absolute refractive index. This equation is written as follows,    Speed of light in medium 1  .

Speed of light in medium 2

=   3.00 x 108 ms-1 .   =    3.00  .   =   1.50

2.00 x 108 ms-1            2.00

This can also be worked out from the gradient of the graph by dividing the value of sin i by the value of sin r. The value at sin i is divided by sin r to give the gradient, from the graph the sin i value is 0.60 and the sin r value is 0.40. When these are divided the answer is 1.50.

0.60 = 1.50

                                                               0.40

Discussion

This experiment did follow Snell’s Law, ……………………………….

It was felt that when the experiments were carried out, the data should be collected as slowly and as accurately as possible, continuously double checking the results. Additional experiments would liked to have been carried out so that as much data could be collected. With more data this would make the experiment more accurate and make the results more generalisable to the Snell’s Law theory.

Finally, this experiment has confirmed that the theory of Snell’s Law does apply to the experiments carried out. As investigated, more experiments could be conducted on a variety of different materials, to ascertain whether Snell’s Law can be proved or disproved for these materials, …………………………….