Reflection and Refraction

In this experiment, we begin looking at light waves and how they refract. We had a light box with a narrow slot to let a thin ray of light out, a protractor, and a semicircular clear plastic disk.

For the first set of data, we had the light entering the flat side of the disk, and exiting the curved side. We recorded the angles of incident and refraction as theta 1 and 2 respectively. 

Trial	ϴ_1	ϴ_2	sin(ϴ_1)	sin(ϴ_2)
1	5	4	0.087156	0.069756
2	10	7	0.173648	0.121869
3	15	10	0.258819	0.173648
4	20	12.5	0.34202	0.21644
5	25	16	0.422618	0.275637
6	30	19	0.5	0.325568
7	40	26.5	0.642788	0.446198
8	50	31	0.766044	0.515038
9	60	35	0.866025	0.573576
10	70	39	0.939693	0.62932

When we plotted the SINE of the angles against each other, we got a nearly perfectly linear trendline.

For our second data set, the incident ray entered on the curved side and exited on the flat side of the half-disk. At 45 degrees for the incident angle, no light exited the plastic disk.

Trial	ϴ_1	ϴ_2	sin(ϴ_1)	sin(ϴ_2)
1	0	0	0	0
2	5	7.5	0.087156	0.130526
3	10	16	0.173648	0.275637
4	15	23	0.258819	0.390731
5	20	32	0.34202	0.529919
6	30	48	0.5	0.743145
7	35	63	0.573576	0.891007
8	40	75	0.642788	0.965926
9	45	75	0.707107	0.965926

When the sin of these two angles were plotted against each other, the graph was exactly the same, except the axes were reversed.

The slope of theses lines must represent the ratio for the index of refraction of the materials. Since the index n for air is 1 we could easily figure out the refraction index for the plastic.

Standing Waves on a string

For this lab, our goal was to analyze mechanical waves on a string, specifically standing waves. We were given a frequency generator, a long string, a ruler, some weights, and a mechanical oscillator. This is a picture of our setup. Not visible is the hanging mass, which is over the opposite end of the table.

When a vibrating string produces standing waves, the number of nodes and antinodes that appear depend on the tension in the string, the length of the string, and the frequency of oscillations. By counting the n number of loops, we can easily come up with wavelength because wavelength is simply 2L/n
The velocity of a wave on a string is denoted by v = √(T/µ) where T is the tension in the string and µ is the mass per unit length of the string.

For our first set of data, the oscillating length of string was 133 cm with a hanging mass of 200g. Our velocity was therefore √(200g/1.38g/m) = 12 m/s

Freq.	Nodes	Wavelen
17Hz	2	2.66 m
32Hz	3	1.33 m
46Hz	4	88.7 cm
63Hz	5	66.5 cm
76Hz	6	53.2 cm
109Hz	8	38 cm

For data set 2, we reduced the tension to 100g

Freq	Nodes	Wavelen
27Hz	2	2.66 m
48Hz	3	1.33 m
71Hz	4	88.7 cm
88Hz	5	66.5 cm
113Hz	6	53.2 cm
134Hz	7	38 cm

Mechanical waves

For this lab, we were supposed to come up with an experiment to relate period to wavelength.
The materials we had to use were a stopwatch, a long spring, and a meter stick. 
We decided that we would hold the spring at a specific length, and then start a standing wave on it, and measure the time for 10 cycles and divide by 10 to get the period of oscillations.

By changing the distance between the 2 people holding it, and the number of nodes, we could determine the relationship between period and wavelength.

We got the following results:
8 meters 1.04 sec
4 meters .587 sec
2.66 met. .350 sec
2 meters .262 sec

When we plotted this on a graph, the curve was very linear which makes sense since 
T=1/f and f=v/λ so T = λ/v
Here is a video of our method.

Fluid dynamics lab

Our second lab we did was investigating fluid dynamics using Bernoulli's Equation. Our job was to calculate the amount of time it would take to empty a specific volume of water from a larger bucket with the setup as shown:

 Using a stopwatch, we measured how long it took to fill up a 200 mL beaker, and repeated the measurement to calculate error. Numbers are in seconds

1. 3.82
2: 4.75
3: 4.35
4: 4.30
5: 4.38
6: 4.52

Using error calculations, we came up with a average time of 4.35 +/- .31
The height of water in the bucket was 144.5 mm +/- 0.5mm
The area of the drain hole was 3.85e-5 m^2  +/-0.025e-5

Calculating the theoretical time with uncertainty yielded a time of 3.48s +/- .39
Comparing the theoretical with the actual value, we have a difference of 25% which is acceptable considering the amount of error introduced from drain hole inaccuracies, and delay in operating the stopwatch.
Calculating backwards, the actual drain hole diameter is 14% smaller than the measured 7mm hole at 5.99mm