Refraction

Lab 10

Mohamed Adnan

Partners: John Daniel

Objective: To study refraction of light at plane surfaces and to determine the index of refraction of Lucite glass and water using the laws of reflection and refraction.

Theory: When light moves in a vacuum its speed is equal to C (3.00 x 10^8 m/s). However, when light passes through a medium, such as air, water, or glass, then the speed of light decreases due to the optical density property of the medium. The optical density is how well electromagnetic waves move inside a medium. The greater the optical density, the slower the speed of light will be in the medium. One way to compare the speed of light in vacuum to the speed of light in a media is by using the index of refraction. Refraction is when the direction of light is altered from one medium to another by the relationship of the index of refraction of each medium. The index of refraction is the ratio of speed of light to the speed of light in a specific medium. Hence, each medium has its own index of refraction. To calculate the index of refraction, the angle of the incident ray and the angle of the refraction ray are needed. The incident ray is the ray of light from the initial medium from which it is coming from. The refracting ray is when the light enters the second medium and changes direction. From this information, the index of refraction can be calculated.

Materials:Glass Prism, Pins, Paper, Tube with water, Laser, Metal frame with sliders.

Data:

Calculations:

1) nglass = sini /sinr = sin43.0/sin28.5 = 1.42nglass = sinr /sini = sin44.5/sin27.0 = 1.54nglass = sin((Dm + A)/2)/sin(A/2) = sin((45.0 + 75.0)/2)/sin(75.0/2) = 1.42Average nglass = 1.462) Deviation Angle in Procedure 3A: 56 degreesDeviation Angle in Procedure 3B: 60 degrees These deviation angles are both greater than the deviation angle in Procedure (2).3) 12.3 cm/6.5 cm = 1.9 Se

4) Velocity of light in water:

Velocity of light in glass:

5) Index of refraction of the glass plate relative to water:

DiscussionIn Part 1, a pentagon shaped Lucite glass was traced and a laser was used to determine the angle of incidence and the angle of refraction from the parallel-sided portion of the plate about 1/2 cm from the corner. The incident ray, i1, has an angle measured to be approximately 45 degrees, and r1 was measured to be approximately 28 degrees. The angles for i2 and r2 were also 45 degrees and 28 degrees, respectively. The index of refraction was calculated using the experimental values of the incidence ray and the refracted ray. The index of refraction of glass was determined to be 1.51. This value is relatively close to the theoretical value of the index of refraction of glass, which is 1.50. Therefore, there is a percent error of 0.67%. This percent error is quite low and further shows that the experimental index of refraction beam of light is quite accurate.In Part 2 of the experiment, the glass pentagon was used again and the ray of light was passed through four centimeters down from the apex of the triangular part of the pentagon. The incident ray, emerging ray and the refracted ray are made. The incidence angles, i1 and i2, were about twice the amount of the reflected angles r1 and r2. When a ray of light is passed through a prism at angle A, it is deviated from its original direction by an angle D, which has a minimum value of Dm. The incident and emergent rays are extended to find the angle of deviation, which is 58 degrees. The apex has an angle of approximately 74 degrees. The index of refraction of glass was calculated to be 1.52, while the theoretical index of refraction of glass is 1.50. This gives a percent error of 1.33%. The experimental index of refraction is relatively close the theoretical index of refraction of glass. In Part 3, the jar of water and the water refraction apparatus was used. The apparatus for water refraction had four brass sliders and were placed into the slots by the corresponding numbers and with their arrows pointing upwards. The apparatus is placed onto the jar and slider 4 is pushed all the way down. Sliders 2 and 3 are pushed as close as to the surface as possible, without touching the water. By looking from the side of the jar, slider 1 is adjusted, so that it appears to be in line with slider 2 and slider 4. The sliders were then taken out, and the appropriate measurements were marked. Sliders 2 and 3 were marked for being the x-axis (water level). Slider 2 mark was used as the center of the axis, from where the normal is created to the x-axis. Slider 1 was marked to be the incident ray. And slider 4 was marked as the refracted ray. The experimental values of i and r were used to calculate the index of refraction of water, which was calculated to be 1.27. The theoretical value of the index of refraction of water is 1.33, which gives a percent error of 4.7%. This percent error may be due to an incorrect set up of the sliders. Furthermore, sighting was used to determine the alignment of sliders 1 to sliders 2 and 4, which is an unreliable and inaccurate method.

Conclusion:Many sources of error in this experiment may have affected the interpretation of the results. An important source of error is human error, such as inaccurate calculations as well as inaccurate reading of the measurements using the ruler or protractor. Therefore, there is an uncertainty in all the degree values i1, i2, r1, r2, A, Dm of 1 degree. There is also an uncertainty in the calculated values of index of refraction 0.01 for all the parts of the experiment. Another important source of error is the equipment used during the experiment. The laser beam may not have been used correctly and cracks or chips in the lucite glass may have provided emergent rays that were going in a different direction. An incorrect alignment of the sliders in part 3 of the experiment may have resulted in a higher percentage of error. The results illustrate that light traveled faster in water than in glass, because water has a lower index of refraction. Through these experiments, refraction measurements could be obtained. By analyzing incident and emergent rays of a laser through glass and water, the indices of refraction of the two materials were obtained. Through these measurements, we are able to ascertain that glass refracts light more than water, as light travels slower in glass.

Questions: 1. What cause, other than experiment error, will make the emergent ray not parallel to the incident ray, in Part (1)?Besides experimental error, the emergent ray will not be parallel to the incident ray if the sides of the glass are not parallel and entirely uniform. So any changes in the parallelism of both sides of the glass, such as cracks, broken edges and corners will cause the emergent ray not to be parallel to the incident ray.

2. In which part of the experiment were the images of the pins colored? Explain.In part 1 of the experiment, the images of the pins were colored, because when the light was pointed through the incident angle on one side of the glass, they exited through the other side where the images of the pins were.

3. Show by a geometrical proof that for small angles of incidence the ratio of computation 3 should equal n. Show also in which direction this ratio should deviate from n for large angles of incidence.nglass = sini /sinrFor small angles sinr = tanr and sini = taninglass = tani /tanrtani = A/Dr tanr = A/Da nglass = Dr/DaWhere Dr = real depth, Da = apparent depthFor larger angles, the ratio will be higher.

4. If a hunter desired to shoot a fish whose image could be seen in clear water, should he aim above or below the fish? Explain by the aid of a diagram.If a hunter desired to shoot a fish whose image could be seen in clear water, he should aim below where he sees the fish because the light emergent from the fish bends farther away from the normal as it hits the air.

AirWater(1)(2)(2) < (1)

5. Compute the displacement of the incident ray in Part (1).44.5 27.0 = 17.5 degrees