Experiment 7: Introduction to Reflection and Refraction

The equipment needed for this experiment is fairly limited considering other experiments which require many different objects, fluids, logger pro, etc. The only equipment needed for this experiment is a light box or laser, a semicircular plastic or glass prism, and a circular protractor. The semi circular prism is used for this laboratory because the shape provides a convenient mathematical purpose. A light ray traveling in the plastic which starts or ends at the midpoint of the flat side is traveling along the radius of the circle, which gives a constant continuous distance from the curved edge to the straight edge.



As can be seen, this lab is does not require a significant amount of work to setup, the only thing that may be of frustration is the fact that the protractor may move when the light box is placed over it. However, this can be corrected by simply putting any form of tape on the sides to allow it to not move.


This is the result for the first trial which gives angles of incidence at intervals of exactly ten degrees each time. The maximum angle of incidence in this trial is 80 degrees because 90 degrees will give an angle of refraction of zero because it will be vertical to the glass prism. The graph of this trial using the angle of incidence and the angle of refraction is:

As it can be seen, the relationship is nearly linear, but obviously it is not perfectly linear due to several slight errors, one of which may be human errors and inability to decipher exactly which angle the light is passing through. The uncertainty for each of the angles is probably +- 2 degrees or so at maximum. There are also other errors that may be difficult to determine such as the error on the protractor. Every ruler and protractor will have some uncertainty on it just like the volume labels in a volumetric flask. These however are fairly minimal, and may only alter the results only slightly.

Normally the angle of incidence should keep increasing by ten degrees until the 80th degree. However the angle could not reach that degree because there will be no more light shining through for refraction. The light could not be seen and therefore the angle will stop at that point. The refraction cannot be seen because it is too refracted. All in all the experiment was a success and gives many details about the properties of light. The slope of the graph of the first trial was .648 when using the linear fit line for the graph. The angle of incidence when hitting a reflective device such as a mirror equals the angle of reflection but the angle of refraction is given by a different formula which depends on the index of refraction of the material and also the index of refraction of the air, or whichever outer substance is outside.

Experiment 4: Standing Waves

The objective of this experiment is to gain knowledge and understanding of standing waves driven by an external force. There are several items that must be obtained before the experiment may be executed. These such items are a Pasco Variable Frequency Wave Driver, a weight which will be calculated using the mass, a meter stick for measuring the length of the string, a pulley and a pendulum clamp.

The main idea behind this entire lab is to find a relationship between the amount of nodes and antinodes, and as well as the frequency given by these nodes. It is clear to see that a higher frequency will create more nodes and antinodes.




Nodes Hz
2 17
3 32
4 51
5 71
6 86
7 104
8 122
9 140
10 158
11 177

This was used with a 123 centimeter string and clearly shows that the frequency increases as the nodes and anti nodes increase. There will always be one more node than antinode on any given wave.

Velocity = Frequency X Wavelength

Wavelength = 2(Length) / n

Velocity = sqrt(Tension / mass per unit length)

The tension in the string was calculated by simply determining the weight on it which in this case was 200.2 grams multiplied by the downward force of gravity at 9.8 m/s^2. The weight of the rope was determined by putting a set amount of length on the scale and then multiplying it by the length to determine how much the weight of the string was.

nodes

Experiment 2: Fluid Dynamics

A bucket filled with water to a height h has a blocked hole on the bottom. The measurements of both the height h and the height of the hole from the bottom of the bucket is measured. Taking th difference between these two measurements gives the height of the hole to the surface of water. Measuring as accurately as possible, the height h is 13.6 cm and the height from the bottom is 2.5 cm both with an uncertainty of +- .05 cm giving the height from the hole to the surface of the water as 11.1 cm +- .10 cm. The diameter of the hole is measured again as accurately as possible giving a value of .55 cm +- .05 cm. The area of that hole can then be calculated by taking half the diameter, squaring it, then multiplying by pi.

The volume emptied chosen was to 400 mL of water which was then measured by a beaker. 6 trials were done in measuring the time needed to empty the 400 mL of water and they came out to 15.9, 13.32, 12.45, 12.65, 12.61, and 13.39 seconds. Due to human errors and reaction time the uncertainty of each of these time intervals was +- 0.15 seconds. The average time of these six trials was calculated as 13.39 +- 2.02 seconds.

Using the volume emptied 400 mL, area of drain hole 2.38 * 10^-5 m/s, acceleration due to gravity 9.8 m/s/s, and height of water 11.1 cm, the theoretical time taken given by:

The theoretical time was calculated to be 11.41 seconds. The difference between actual and theoretical values were all between 1.20 and 4.49 seconds, but the 4.49 seconds deviates greatly from the rest and is an outlier. Calculating the percent errors on the times between actual and theoretical values came to be 39%, 16%, 9.1%, 10.8%, 10.5%, and 15.6%. This was given by the universal formula of error percent:


Even using the values of uncertainty, the experimental values did not agree with the theoretical values entirely. All the time difference errors were near 1 to 4 seconds uncertainty did not calculate to be that great. To correct this problem a greater value of uncertainty should be estimated. Fluid experiments seem to have larger uncertainty than some branches of physics because the exact volume measured is more difficult to catch precisely. Other main uncertainties come from reaction time of starting the stopwatch and stopping it since this requires two people. The biggest form of uncertainty comes from the inaccurate volume measurement since water is flowing fairly quickly and it is less obvious to tell what the volume is precisely. The beaker itself has an uncertainty when filling up because of how precise the beaker is constructed. Many beakers, graduated cylinders, and other glassware contain an uncertainty and it is printed on the glassware. For example 500 mL +-.5 mL.