Snell's Law Lab

NameSubjectDateCollege nameSubmitted toFinal lab report Title: Refraction through glass slab experiment and verification of Snell’s law. Abstract: The graph-1 shows a linear relationship; the greater the angle of incidence, the greater the angle of refraction. Although the refractive indices of all angles were nearly identical, I regret not trying more angles to see if this would have altered the refractive index. Nonetheless, I was able to achieve my goal since I was able to calculate the refractive index from this experiment using Snell's Law. The values can be rounded to a refractive index of 1.5 for all angles which is a constant according to Snell’s Law. The experiment has also proven that light bends/refracts when it enters a different medium. Measuring the accuracy of angles was a bit hard because if the mark was between one degree, it could have ranged anywhere from 0.1-0.9 degrees but I had to round it to 0.5 degrees. I also need to plot error bars the next time I draw a graph. I chose the thinnest beam but still it was rather thick, which made it difficult to determine the exact point at which the light entered the medium. Marking the exact point of the light beams, parallax errors, and determining where to draw the point are all areas where there are uncertainties. However, the results were quite accurate as it falls in close proximity to the expected result found in references. INTRODUCTION Light moves at certain speeds. However, when the speed changes, it causes the light to bend, the bending of light is called refraction which is quite apparent in everyday life. Dispersion through prism, twinkling of stars, sun dog effect or the illusion of multiple sun are all the examples of this phenomenon. Glass is a perfect everyday example of light refraction. If a slab of glass is placed over a piece of paper, then the words will look closer to the surface because of the different angle the light is bending. The bending causes the light ray to refract at some angle, this is how Snell's law came into effect. The law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index. In this experiment we can determine the bending of light rays owing to the change in refractive index and hence verifying the law. In optics, Snell's law describes the link between the route travelled by a beam of light as it crosses the boundary or separation surface between two interacting substances and their respective refractive indices. Willebrordus Snellius, a Dutch astronomer and mathematician, developed this law in 1621(also called Snellius). The account of Snell's law remained unpublished until Christiaan Huygens mentioned it in his dissertation on light. SNELL’S LAW. The ratio of the sine of angle of incidence to the sine of angle of refraction is a constant quantity for the two media. Only isotropic or specular media are subject to Snell's law (such as glass). Birefringence in anisotropic media, such as certain crystals, can split the refracted beam into two rays: the ordinary or o-ray, which follows Snell's law, and the extraordinary or e-beam, which is not always coplanar with the incident beam. Snell's law has numerous applications in physics, particularly in the field of optics e.g. optical fiber. It's found in things like eyeglasses, contact lenses, cameras, and rainbows. The refractive index of liquids is calculated using Snell's law by a device called a refractometer. It's frequently utilized in the candy-making sector. Hypothesis: we predicted that the difference in the refractive index of the media will cause bending of light and also predicted that the angle of incidence would be directly proportional to the angle of refraction. Objective: To study Refraction through glass slab experiment and verification of Snell's Law. METHODS Materials Required:         One drawing board or cardboard (A4) all pins white sheet of paper(A4) A rectangular glass slab protractor measuring scale(30cm) pencil 6-8 thumb pins. Theory: SOME IMPORTANT TERMS: Normal Ray: A ray of light which forms an angle of 90° with the refracting surface is said to be normal. When a ray of light travels along the normal, it does not suffer any refraction. Incident Ray: A ray of light that travels towards the refracting surface is called incident ray. Refracted Ray: A ray of light that changes its path when passes through a refracting surface is said to be refracted ray. Emergent Ray: A ray of light which emerges out into the original medium after refraction is said to be an emergent ray. Lateral Displacement: The perpendicular shift in the path of light, seen when it emerges out from the refracting medium is called lateral displacement. Angle of Incidence (i): The angle formed between the normal and incident ray is called angle of incidence. Angle of Refraction (r): The angle formed between the refracted and normal ray is called angle of refraction. Angle of Emergence (e): The angle formed between the normal and emergent ray is called angle of emergence. During Refraction: (i) Angle of incidence = Angle of emergence. (ii) Incident ray and emergent ray are parallel. VARIABLES INVOLVED: Constant variable- refractive index of glass, position of glass slab, the colour of light ray. Independent variable- angle of incidence(i) of the light ray nor al to the glass slab. Dependant variable- angle of refraction(r) of the light ray normal to the glass slab. Experimental set-up: In order to maximize the relative intensity of the light ray, it is required to turn off the lights and close the curtains and the same glass slab should be used through the experiment to ascertain constant refractive index. White plain sheet is used to ensure the clarity of observations. During the projection of light ray, it is needed to make sure that the ray is always at the centre of and parallel to the respective radial line so that the angle made by ray to the normal is same as that by the radial line. PROCEDURE: 1. A sheet of white paper was fixed on the cardboard with the help of the pins and the glass slab was placed in the middle of the sheet. 2. The boundary of the slab was marked with a sharp pencil and was labelled as ABCD once the slab glass slab was removed. 3. On the line AB mark a point E and draw a normal at it. A line is drawn making an angle i with the normal, the angle should be neither too small nor too large. 4. The slab was again placed on the boundary ABCD and two pins were fixed vertically about 3-4 cm apart on the line AE. 5. Looked through the glass slab along the plane of paper from the CD side and head was moved until the images of the two pins were seen clearly. Closing one eye, the position is adjusted such that the images of the pins lie in the same straight line. 6. Other two pins were fixed vertically such that the images of all the four pins lie in the same straight line. 7. The slab and the pins were removed and points were encircled with the help of pencil. 8. The points were joined and produced towards the slab so that it meets the boundary line CD. Thus, the incident ray, refracted ray and emergent ray was obtained respectively. 9. The angles were measure with the help of the protractor and labelled as < i , < r and < e. 10. The process was repeated for different angles of incidence i to get a verified result. OBSERVATION AND RESULTS: TABLE 1- EXPERIMENTAL DATA (taking the value of angle up to one decimal places) S.n o 1 Angle of incidence(i) {In degrees} 10 Angle of refraction(r) {In degrees} 6.5 2 20 13 3 30 19.5 4 40 25 5 50 31 6 60 35 For 7 70 39 i=10 degrees 8 80 39.5 CALCULATION: r=6.5 degrees Sin(i)=0.173 sin(r)=0.113 n=sin(i)/sin(r) n=0.173/0.113 n= 1.53 (calculated value of refractive index from the experimental data) Similarly for the rest of the values of i and r we can calculate the value of n. Average value = (sum of all he values of n)/number of n values = (1.53+1.52+1.49+1.52+1.48+1.51+1.49+1.54)/8 =1.52 TABLE 2- CALCULATED VALUES s.no Sin(i) Sin(r) n=sin(i)/sin(r) 1 0.173 0.113 1.53 2 0.342 0.224 1.52 3 0.500 0.334 1.49 4 0.642 0.422 1.52 5 0.766 0.515 1.48 6 0.866 0.573 1.51 7 0.939 0.629 1.49 8 0.984 0.636 1.54 Average(n) 1.51 sin(i) vs sin(r) 0.7 0.6 sin(i) 0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 sin(r) GRAPH1 Slope of the above graph will give the value of n Slope =sin(i)/sin(r)=n n=refractive index of glass slab        Here calculated slope from the graph= 1.513 Greater the angle of incidence results in greater the angle of refraction (maximum value of angle of incidence <90 degrees) The path of the incident ray, the refracted ray and the emergence ray when light passes through a rectangular slab is shown in experimental setup picture Within the experimental error, < i = < e. It implies that the incident ray and the emergent ray are parallel to each other. It is clear that though the emergent ray us parallel to the incident ray but it is laterally displaced from the incident ray. From the observation it is clear that < i is greater than < r, implying that a ray of light bends towards normal while passing from air to glass. On plotting a graph, sin(i) vs sin(r) a straight-line curve is obtained. DISCUSSION: There were some aspects of the experiment that could have been improved. The experiment should ideally be carried out in a single day, and the same glass slab should be used throughout. The angles were measured with a protractor to the nearest degree, which meant the angle could only be measured to 0.5 precision. It would be more accurate to use a protractor with measurements down to the minute of arc. However, to guarantee that the measurements were more exact, the same protractor was utilised throughout the experiment. Another flaw was that the light source chosen created a wide beam of light, making it difficult to consistently measure the light's centre. If this experiment is replicated, a light source that does not accomplish this would be preferable. To improve accuracy, all data was collected quantitatively rather than qualitatively. To boost dependability, the experiment was repeated eight times with different angles to guarantee the relationship discovered was reliable. To avoid this variable, all lights were turned off and the room was made as dark as feasible. The same type of paper was used for each trial to keep this variable consistent and the same person measured all the angles to ensure it was measured consistently and the same person drew the path of the light beam to make sure there were no inconsistencies when drawing the light beam. All variables were kept consistent and the only variable being changed was the angle of incidence (independent variable) which caused the angle of reflection to change (dependent variable). Snell’s law of refraction was proved by this experiment as the sine of the incidence ray divided by the sine of the reflected ray created a straight increasing line when graphed. Snell's law of refraction can be used to a variety of items in society. Many people do this by utilising comprehensive internal reflection. Total internal reflection happens when the angle of incidence crosses the critical angle. Optical fibres are one example. Optical fibres are thin, high-quality glass rods that transfer information via complete internal reflection of visible or infrared light signals. When compared to an ordinary cable of the same thickness, optical fibres can transport more information and the signals do not degrade as much over long distances. The difference in the angle of incidence and the angle of reflection marks the bending of light that is refraction. This shows that the change in refractive index of the media cause the change in the path of the light. Thus, the part of our hypothesis found to be correct. Further the measurement of the angles shows that the angle of incidence always came to be greater than the angle of incidence implying that the ray of light bend towards normal when travels from rarer (air) to denser (glass) medium and vice versa. Lastly, when we plotted the graph between the angle of incidence and angle of refraction we obtained a linear graph passing through the origin, that is, Y = mx + c Where m = slope (this slope indicates refractive index(n) of glass slab) This linear graph implies that the angle of incidence is directly proportional to the angle of refraction. Thus, our hypothesis found to be true. CONCLUSION: The refractive index of glass is given by the ratio of the sine value of incident angle to the sine value of angle of refraction. The refractive index of glass slab holds a constant value that is equal to 1.50. While in our experiment, the value of the refractive index found to be 1.513. Therefore, Observed value of n = 1.50 Calculated value of n = 1.513 So, percentage error is, %Error = [(Calculated value - Observed value) / Observed value] x 100% = (1.513 - 1.50 / 1.50) 100 % = 0.86 % The results is acceptable since the result is within the range of accepted value and the error percentage is so less making the value in close proximity of the expected value. Also, the small value of the y- intercept in the graph shows that the systematic error is little in this experiment. Although further revisions on the methods for controlling variables is to be done to further increase the accuracy and precision and thus the reliability of this experiment. So, the experiment is needed to be repeated with suggestions mentioned above. In order to reduce percentage error, below are some considered limitations and suggested methods for improvement. EvaluationThe lines drawn on both sides of the glass slab create unnecessary uncertainty and inaccuracy in measuring (angle r) as it is necessary to make markings at the glass slab boundaries, which is difficult to do. So, we found that it is easier to produce accurate outcomes with a semicircular glass slab than using rectangular glass plate for refraction. Since a semi-circular ray passes across its curved frontier and centre point, which is at the linear frontier, as against its rectangular glass slab, it ensures that any light ray passes only once, because the first borders are at 90° angles towards the tangent line that reaches to the crossed border point. Hence more reliable markings (more accurate measurement of angle r) can be made far from the glass slab. As the traversed length increases, the light ray is dispersed and blurred and it becomes harder to detect the second bend of the ray. This leads to error. As the dispersion increases with travel, the length travelled before the second bend has to be reduced to a minimum. So, the light ray should be projected as close to the glass block as possible. When the corner I increases, the closer if the difference between the markings becomes. When very close, it is difficult to mark and use protractor to measure the angle.