Electromagnetic Radiation Lab

Objective
For this lab, the purpose is finding the behavior of electromagnetic radiation due to a simple antenna.

Data

Graph:

Data Analysis

Graph

UNCERTAINTY ANALYSIS:

The uncertainty values for the peak to peak voltage are as follows:

±12 for V= (50 mV, 90 mV)

±6 for V= (19 mV, 28 mV)

±3 for V= (7.5 mV, 15.5mV)

The quantization uncertainty in the measurements of the distance z was set to ±0.01 cm. However, this uncertainty distance that was measured may have been calculated to the base of the prong. Consequently , an additional uncertainty, ±.02cm, needs to be added making it a total ∆z uncertainty of ±0.03cm.

Z minimum	Z maximum	Vmax	Vmin	Vuncertainty
0.02	0.08	144.1614372	65.30877	39.42633133
0.07	0.13	71.97213324	44.16668	13.90272463
0.12	0.18	47.28534799	33.06248	7.111432949
0.17	0.23	34.83099292	26.31653	4.257233117
0.22	0.28	27.44228895	21.81686	2.812715339
0.27	0.33	22.59180341	18.61364	1.989079353
0.32	0.38	19.17788295	16.22204	1.477923748
0.37	0.43	16.65045626	14.37048	1.13998933
0.42	0.48	14.706491	12.8957	0.905395224
0.47	0.53	13.16610911	11.6939	0.736106122

Conclusion

Based on the results we got, we verified the concept of EM waves. There were many assumptions that were in constructing the model of the theoretical voltage. The charge, Q, was considered to being a constant value throughout was one assumption that led to a comparable theoretical set of data numbers. The range of error between the two could be explained by discussing the simplifications made in order to keep this experiment simple. The data between the experimental and the theoretical were all in the range of uncertainty. 

Lenses (Converging)

Objective
Use thin a lenses to verify the equation 1/p + 1/q =1/f

Procedure

Observe and measure the focal length by putting the lenses under the sunshine.

Set up the equipments: put the lenses on a ruler and project the light through the lenses on a piece of 

paper

The image on the paper (when focus)

measure the distance from the light source to the lenses (p), and from the lenses to the image (q)

Data

Data Analysis

Since 1/p + 1/ q = 1/ f

1/p = -1/q + 1/f
if we graph 1/p vs 1/q, the slope should be about 1, and the x intersection should be 1/f.

Graph

From the graph, we calculate that f=1/0.1653=6.05 cm. And the focal length we measured in the beginning of the lab is 5.85. The percent error is 3.42%.

Conclusion

We are surprised that the error is only about 3% because when we measured the focal length by eyes, it seemed to have a big error. In this lab, we observed that when the object distance is more greater than f, the imagines are always inverted and smaller than the object. However, when the object distance is smaller than the focal length, we can see upright images and they are larger than the objective. We also verified the equation 1/p +1/q =1/f 

Convex and Concave Mirrors

Objective
Study the difference between convex and concave mirror and the way images are created by them.

Convex mirror

1. The image is upright, smaller than the object, and the image distance is closer to the mirror than the object.

2. When the object moves closer to the mirror, the image gets larger (but still small than the object). And the image is still upright. Object distance become less larger than the image distance.

3. When the object moves further from the mirror, the image gets smaller, and it is still upright. Object distance becomes much larger than the image distance.

Concave mirror

Example

p>f

 

p<f

1. The image is smaller than the object, and it is inverted. The distance between object and the mirror is greater than the distance between image and the mirror.

2. The image becomes upright and the size is larger than the object. Image is closer to the mirror than the object.

3.Image is still smaller than the object and inverted. The difference of distance become lager.

Conclusion

convex mirror

The image is always upright and smaller than the object.

convave mirror

 When the object is close to the mirror, the image is upright and larger than the object, while the image is inverted and smaller than the object when the object is far from the mirror.

Introduction to Reflection and Refraction

Objective
Experience the light travels between two materials and verify the Snell's Law.

Procedure
part 1: light travels from air to glass

 Put the circular protractor under the glass, and set up the light source.

Measure the angles between the incident, and refractive lights to the normal line.

Data for part 1

θ1	θ2	sin θ1	sin θ2
0	0	0	0
10	5	0.17	0.09
15	11	0.26	0.18
20	12	0.34	0.21
25	17	0.42	0.29
30	19	0.5	0.33
40	23	0.64	0.39
50	27	0.77	0.45
60	35	0.87	0.57
70	39	0.94	0.63

part 2: light travels from glass to air

Set up the equipment as showed and measure the angles just like we did for part1

Data for part 2

θ1	θ2	sin θ1	sin θ2
0	9.5	0	0
5	9.5	0.09	0.17
10	16.5	0.17	0.28
15	24.5	0.26	0.41
20	30	0.34	0.5
25	44	0.42	0.69
30	51.5	0.50	0.78
35	64.5	0.57	0.90
40	80	0.64	0.98

Conclusion

By graphing the sin θ1 _vs sin θ2 ,  we found the ratio of the index of refraction n2/n1. (n1sin θ1=n2sin θ2) For air, n1 is 1, so the slope of the graph should be the index of refraction of the glass, which is close to 1.5. In part 2, we found out that we can't get any refraction anymore after going up to some certain angle. The critical angle we found was about 43 degree. To calculate the theoretical value, we say, n2*sinθ2=1*1 (because the max of sin is 1)  Solve for θ2 and we found that θ=41.8 degree, which is very close to the measured value.

Introduction to Sound

Objective
Use sound sensor, logger pro, and tuning fork to study sound waves.

Procedure

Let first person say "AAAAAAA" into the microphone and collect the data

 

 Let another person do the same thing and record the data.

 

Strike the tuning fork and record the data

 



Data

 

First Person

 

 

Second Person

 

 



Stuck the tuning fork hardly

 

 

Struck the tuning fork softly

 Questions

1
a) Yes, it is repeating.
b) We observed 4 waves. We determined waves by group
c) Prob time is 0.03 seconds. It is about a blink of an eye.
d) The period of the waves is 0.0075 seconds
e) Frequency is 133Hz
f) Lambda =2.55m. It is about the height of the classroom
g) Amplitude is about 0.6115 (no unit)
h) There would be more waves, but the frequency, lambda, amplitude will stay the same
    test results: there are 38 waves, period become 0.00789, lambda becomes 2.68, Amplitude becomes 0.602

 

 

2
 18 waves, T=0.00167s, A=0.234, lambda=0.566m

3
8 waves, T=0.00375, A=0.0695, lambda=1.275

4
We expect to have the same frequency, wave length, sahpe, but different amplitudes.

    Struck softly


   Struck hardly