Snell's+Law+and+Index+of+Refraction

= Snell's Law and Index of Refraction =

Purpose
==== The purpose of this project is to approximate the indices of refraction for three different materials: acrylic, glass, and water. In doing this we tested and proved Snell’s Law. ==== ====We were hoping to see if the principles of physics that had been studied and figured out years before us still held for today’s world. Throughout our experimentation, we put our materials through multiple trials to ensure that none of our results were outliers or mistakes. In doing this we determine that the indices of refraction for these materials do not vary between angles and that Snell’s law remains true and factual. ====

Procedures and Required Materials
Place the protractor with the base line on top of the normal line, then find  of the entrance and exit angles. If the angle is greater than ninety degrees then subtract it from one hundred eighty.
 * 1) ==== Gather Required Materials ====
 * 2) ==== Point light source with focusing slits to give straight line of light for testing ====
 * 3) ==== Different transparent materials to measure angles of; in this testing we used glass, acrylic, and water in a plastic container of negligible thickness ====
 * 4) ==== Protractor ====
 * 5) ==== Ruler ====
 * 6) ==== Paper and pencil to trace size and angles of light and objects onto for documentation ====
 * 7) ==== Set up apparatus for testing ====
 * 8) ==== Place point light source on flat surface for testing ====
 * 9) ==== Choose one of the materials to test first ====
 * 10) ==== Place the material on top of a sheet of paper in front of light source ====
 * 11) ==== Turn on light source and trace line of light entering and exiting materials as well as the shape of the material on the paper ====
 * 12) ==== This will allow for one to measure the angles of light and draw the normal line later ====
 * 13) ==== Repeat all parts of step two four more times, each time repositioning the material at a different angle to get differing paths ====
 * 14) ==== Once steps two through three have been completed, repeat them both for each material being tested. This will allow for one to calculate different indices of refraction for each material and in this wayobserve if or if not Snell's law applies for multiple materials or simply some of them ====
 * 15) ==== Once all of the materials have been tested and traced at least five times each take out the protractor and ruler as well as the pencil. ====
 * 16) ==== Draw a perpendicular line to the surface of the material that the light struck. This line will be the "normal line," and will be the base line that the entrance and exit angles will be measured from ====
 * 1) ==== Once the angles are calculated for each material then apply Snell's law to find the unknown index of refraction for the material ====
 * 2) ==== Since index of refraction for air will always equal one, simply divide the sine of the angle entering by the sine of the angle of the light within the material. ====
 * 3) ==== Therefore, the slope of the graph of the sine of the incident angle versus the sine of the refracted angle will be that material's index of refraction. ====
 * 4) ==== Then graph the points with sine of the angle refracted along the horizontal axis and the sine of the incident angle along the vertical axis ====
 * 5) ==== Next draw a linear line of best fit to find the slope by picking two points from the line of best fit, and subtract the vertical components from each other and the horizontal components from each other ====
 * 6) ==== Divide the vertical components' difference by the horizontal components' difference to get an approximate index of refraction for each material ====
 * 7) ==== Establish the range of possibility error ====
 * 8) ==== Verify the calculated index of refraction with the other calculations to insure the viability of Snell's Law ====

[[image:columbusphysics/scan8.jpg width="438" height="608"]]
==== Shown above is an example of how the actual testing tracing should look. In the image above, the material tested was glass. The rays of light into and out of the material were traced and a normal line was drawn for reference. ====

==== In testing, the same set-up was used each time so as to avoid variations, issues, or errors in recording our data. The only error observed in each instance was due to human error in measuring angles or in tracing the lines of light and the materials. In this way our data is as close as possible to exact. ====

Tables and Data

 * ~ === Acrylic === ||~  ||~   ||
 * ==== Angle of Incidence ==== || ==== Angle of Refraction ==== || ==== Sine of Angle of Incidence ==== || ==== Sine of Angle of Refraction ==== || ==== Index of Refraction ==== ||
 * ==== 38 ==== || ==== 24 ==== || ==== .616 ==== || ==== .407 ==== || ==== 1.51 ==== ||
 * ==== 58 ==== || ==== 33 ==== || ==== .848 ==== || ==== .545 ==== || ==== 1.56 ==== ||
 * ==== 49 ==== || ==== 29 ==== || ==== .752 ==== || ==== .485 ==== || ==== 1.56 ==== ||
 * ==== 66 ==== || ==== 38 ==== || ==== .914 ==== || ==== .616 ==== || ==== 1.48 ==== ||
 * ==== 17 ==== || ==== 11 ==== || ==== .292 ==== || ==== .191 ==== || ==== 1.53 ==== ||


 * ~ === Glass === ||~  ||~   ||
 * ==== Angle of Incidence ==== || ==== Angle of Refraction ==== || ==== Sine of Angle of Incidence ==== || ==== Sine of Angle of Refraction ==== || ==== Index of Refraction ==== ||
 * ==== 40 ==== || ==== 24 ==== || ==== .643 ==== || ==== .404 ==== || ==== 1.58 ==== ||
 * ==== 42 ==== || ==== 26 ==== || ==== .609 ==== || ==== .438 ==== || ==== 1.53 ==== ||
 * ==== 70 ==== || ==== 40 ==== || ==== .940 ==== || ==== .643 ==== || ==== 1.46 ==== ||
 * ==== 57 ==== || ==== 33 ==== || ==== .839 ==== || ==== .545 ==== || ==== 1.54 ==== ||
 * ==== 38 ==== || ==== 25 ==== || ==== .616 ==== || ==== .423 ==== || ==== 1.46 ==== ||


 * ~ === Water === ||~  ||~   ||
 * ==== Angle of Incidence ==== || ==== Angle of Refraction ==== || ==== Sine of Angle of Incidence ==== || ==== Sine of Angle of Refraction ==== || ==== Index of Refraction ==== ||
 * ==== 16 ==== || ==== 13 ==== || ==== .276 ==== || ==== .225 ==== || ==== 1.23 ==== ||
 * ==== 34 ==== || ==== 26 ==== || ==== .559 ==== || ==== .438 ==== || ==== 1.28 ==== ||
 * ==== 18 ==== || ==== 14 ==== || ==== .309 ==== || ==== .242 ==== || ==== 1.28 ==== ||
 * ==== 15 ==== || ==== 12 ==== || ==== .259 ==== || ==== .208 ==== || ==== 1.24 ==== ||
 * ==== 49 ==== || ==== 38 ==== || ==== .755 ==== || ==== .616 ==== || ==== 1.23 ==== ||

This is generally consistent with our results, so we will accept this as a rough estimate of the index of refraction for acrylic.
==== The slope of the line of best fit shown above in this case gives an index of refraction of 1.451 for glass. This is generally consistent with our results, so we will accept this as a rough estimate of the index of refraction for glass. ====

**Results**
====We concluded that Snell’s law is indeed a correct way to equivocate the incident and refracted angles. We were able to effectively calculate the indices of refraction of glass, water, and acrylic, and when we compared them with other experimental results to conclude that Snell’s law is consistently correct. We were also able to conclude that light bends when entering a material with a higher index of refraction. This explains why a pencil partially immersed in water will appear to be broken or bent at an angle. This happens because light travels differently in water than in air. We tested this idea through the measuring of angles of light both within and without certain materials. Afterwards, we took the angles and applied Snell’s law of optics, taking the sine of each angle and then dividing them. This allowed for us to get an approximate value for n, the indices of refraction, for each trial. These were generally within 7 tenths of each other and this error was attributed to the human error that went in to measuring and calculating. To get a more general number for the index of refraction we graphed the sine of the angle of the glass within the material along the horizontal axis against the sine of the angle outside the material along the vertical axis. In this way we could draw a line of best fit on the graph. We took the slope of this line and the slope was then the index of refraction. This gave us a much more consistent and general index of refraction that fit for most every trial of each material respectively. The graphs of each materials show a reasonably consistent positive slope, with a fairly low margin of error. Therefore, we believe the concluded indices of refraction were both accurate and precise. ====