3/20 Elecrtromagnetic Radiation

Purpose
The purpose of this experiment was to investigate the behavior of EM radiation due to a simple antenna.

Experiment

 

Set up

 

 

Three ways to verify the signal on the oscilloscope is generated by the transmitting antenna:

1. Move the wire back and forth to see if there's a change in wave shown in the oscilloscope
2. Unplug the detector
3. Turn off the function generator

Data:We are measuring the peak to peak amplitude of the received EM wave as a function of the distance from transmitter.

Distance (m)	# of divisions peak to peak	Vertical scale(mV)	Peak to peak amplitude (mV)
0 ± 0.02	3.5 ± 0.1	50	175 ± 5
0.05 ± 0.02	1.2 ± 0.1	50	60 ± 5
0.10 ± 0.02	3.2 ± 0.1	20	64 ± 5
0.15 ± 0.02	2.9 ± 0.1	20	58 ± 5
0.20 ± 0.02	2.8 ± 0.1	20	56 ± 5
0.25 ± 0.02	2.4 ± 0.1	20	48 ± 5
0.30 ± 0.02	2.2 ± 0.1	20	44 ± 5
0.35 ± 0.02	1.9 ± 0.1	20	38 ± 5
0.40 ± 0.02	2.0 ± 0.1	20	40 ± 5
0.45 ± 0.02	1.5 ± 0.1	20	30 ± 5
0.50 ± 0.02	3.8 ± 0.1	10	38 ± 5
0.55 ± 0.02	3.6 ± 0.1	10	36 ± 5

A/r + b plot:



A/r^2 +b plot:



 A/r^3 + b plot:



A/r +b plot best fits our data, but our data differed from a 1/r function by a b component because of the approximation used when calculating field near the transmitter. The near field is a function of A/r^3 and far field is a function of A/r.

Theoretical Ananlysis

From the calc variant,

where:

L = 0.1 m

k = 9 * 10^9 N^2 * m^2 / C^2
Q = 1.24 * 10^(-10) C
V_0 = 40.29 mV

Therefore,

Distance (m)	Theoretical Amplitude (mV)
0.05	59.99751
0.1	51.0499
0.15	47.61179
0.2	45.82335
0.25	44.73271
0.3	43.99963
0.35	43.47352
0.4	43.07777
0.45	42.76936
0.5	42.52229
0.55	42.31994

 

The experimental and theoretical data have the same trend, but the experimental fluctuate within the theoretical data plot.

Uncertainty Analysis:

Voltage uncertainty: ΔV = ± 10 mV (for a scale of 50mV)

                                        = ± 4 mV (for a scale of 20mV)
                                        = ± 2 mV (for a scale of 10mV)

Distance uncertainty: Δz = ± 0.001 m (uncertainty of the ruler)

                                        = + 0.02 m (detector is not a point and has length involved in measurement )

Total distance uncertainty: Δz_total = + 0.021 m / - 0.001 m

Using the uncertainty in distance, we can calculate the theoretical Vmax and Vmin

Distance (m)	Voltage max (mV)	Voltage min (mV)
0.05 (+0.021/-0.001)	60.32	54.96
0.1 (+0.021/-0.001)	51.15	49.29
0.15 (+0.021/-0.001)	47.66	46.74
0.2 (+0.021/-0.001)	45.85	45.31
0.25 (+0.021/-0.001)	44.75	44.39
0.3 (+0.021/-0.001)	44.01	43.76
0.35 (+0.021/-0.001)	43.48	43.29
0.4 (+0.021/-0.001)	43.08	42.94
0.45 (+0.021/-0.001)	42.77	42.66
0.5 (+0.021/-0.001)	42.53	42.43
0.55 (+0.021/-0.001)	42.32	42.25

The experimental graphs does not lie within theoretical with uncertainty.

Discussion:

1. The simplification we made in our model is treating the antenna as a point source but it actually not and it has some length with it. Also, we assume our detector is a point detector but it actually has some length involved in our measurement, too. For example, when we measure the distance from the antenna to the detector is 5 cm, it actually less than 5 cm because of the length of the detector.

2. Maybe improving the model by increasing the distance from the antenna to the detector, so both the antenna ans detector can be treated as a point source.

4/1 Lenses

Purpose

     The purpose of this experiment was to observe characteristics of a converging lens when the object is placed on one side of the lens and the real inverted image is placed on the other side of the lens.

Experiment

 

Measuring the focal length: 5.0 ± 0.5 cm

 

 

Set up

 

Data and Analysis

 

d0(cm)	di±0.2(cm)	h0±0.2(cm)	hi±0.2(cm)	Md	Mh	Type of image
5f=25±2.5	7.4	8.8	2.3	0.296±0.042	0.261±0.030	inverted and real
4f=20±2.0	8.4	8.8	3.4	0.42±0.058	0.386±0.033	inverted and real
3f=15±1.5	8.9	4	2.6	0.593±0.081	0.65±0.087	inverted and real
2f=10±1.0	11.8	4	4.5	1.18±0.153	1.125±0.112	inverted and real
1.5f=7.5±0.75	18.3	1.1	2.8	2.44±0.301	2.545±0.789	inverted and real

 

When object distance is 0.5f, the light rays could not form image on white board (virtual image). If look through the lens, we observed a bigger and upright image.

 

 



 

1/q = -1/p + 1/f

1/q = -m/p + b

so, m should be 1 and b should be 1/f (0.2 ± 0.02 cm^-1)

However, the experimental m= 0.82 and experimental b= 0.165.

% difference of m= (1-0.82)/1 X 100% = 18%

% difference of b = (0.2-0.165)/0.2 X 100% = 17.5% ± 7.5%

 

Conclusion

     According to table 1 and graph 1, as the object distance decreased, the image distance increased. Therefore, the image and object distance had inverse relationship as shown in graph 1. Also, the images formed from a converging lens is always real and inverted. When half of the lens was covered, the image became dimmer since the light passed through the lens was decreased by a factor of 2. Besides, as the object distance became closer to the lens, the image size and distance became larger. At 0.5f, there was no image because the image was between the vertex and the focus; hence, the image became virtual.

      The experimental m was 0.82, with a percent error of 18%; percent difference of b (1/f) was 17.5% ± 7.5%. Therefore, the percent difference of b lies within a range of 10-20%, and 10% was within the allowable range. The 20% difference could be the focus was not as accurate as it should have been. Unclear images at small object distances also contributed to this error. This was because the image became dimmer and unclearer as the object distance decreased. Hence, uncertainty became greater since it became harder to see the actual height of the image.

 

 

 

3/27 Mirrors

Purpose

     The purpose of this experiment was to characterize the images formed by convex and concave mirrors.

Experiment

 

Convex mirror
The image is smaller than the object.
The image is upright.
when you move closer to the mirror, the image is getting bigger.

 

Concave mirror
when the object is very far from the mirror: the image is smaller than the object; the image is inverted; the object and image are on the same side of the mirror.
when the object is close to the mirror: the image is larger than the object; the image is upright and blurry; the object and images are on the different side of the mirror.

 

Diagrams

 

 

Image in convex mirror changes depending on the object distance

 

 

Image in concave mirror changes depending on the object distance

 

  

 

Compute magnification of the mirrors

 

Data

Magnification ratio	Magnification of the mirror
	Convex	Concave
hi/h0	0.318 ± 0.024		-0.339 ± 0.009
di/d0	-0.304 ± 0.023		0.297 ± 0.008

 

Conclusion

 

     The magnifications for the convex mirror were determined to be 0.314 from the ratio of image height and object height and 0.304 from the ration of the image distance and object distance. The maginifications for the concave mirror were determined to be -0.339 from the ratio of image height and object height and -0.297 from the ratio of the image distance and object distance. The uncertainty was 0.029, so all of the magnifications determined lied within this uncertainty range.





3/25 Introduction to Reflection and Refraction

Purpose

The purpose of this experiment was to explore the law of reflection, refraction, and total internal reflection.

Part A

 

Light ray box faced to the flat side of the len

 

 

Trial	θ1 (±1)	θ2 (±1)	sin θ1 (±0.02)	sin θ2 (±0.02)
1	0	0	0	0
2	5	3	0.09	0.05
3	10	6	0.17	0.10
4	15	8	0.26	0.14
5	20	13	0.34	0.23
6	25	14	0.42	0.24
7	30	18	0.50	0.31
8	35	22	0.57	0.37
9	40	26	0.64	0.44
10	45	27	0.71	0.45
11	50	28	0.77	0.47
12	55	31	0.82	0.52
13	60	33	0.87	0.55
14	65	35	0.91	0.57
15	70	36	0.94	0.59

 

 

 

The slope of this graph is the index of refractive glass, which is 1.56.

n₁sinθ₁= n₂sinθ₂

sinθ1_/ sinθ2 _{= n2/n1 = n glass/ n air= n glass.}

 

Part B

 

 

Light ray box faced to the curve side of the len

 

 

Trial	θ1 (±1)	θ2 (±1)	sin θ1 (±0.02)	sin θ2 (±0.02)
1	0	0	0	0
2	5	9	0.09	0.160
3	10	17	0.17	0.292
4	15	24	0.26	0.407
5	20	34	0.34	0.560
6	25	40	0.42	0.643
7	30	51	0.50	0.778
8	35	60	0.57	0.867
9	40	77	0.64	0.974

 

The slope of this graph is the reciprocal value of the index of refrative glass, which is 0.67.

n₁sinθ₁= n₂sinθ₂

sinθ1_/ sinθ2 _{= n2/n1 = n air/ n glass= 1/ n glass}

n₁sinθ_critical= n₂sin90

θ_{critical = asin(n2}sin90_{/n1) = 42 degress}

Conclusion

 

      The index of refrative of glass was determined to be 1.6, and product of the slope in case 1 and 2 was 1 because their relationship is inversed. In case 2, we could not get a refraction when the incident angle was larger than 40 degress because it reached to the critial angle for a total internal reflection, which means there is only reflection and no refraction once the incident angle is greater and equal to the critical angle, and the critical angle was calculated to be 42 degress for this glass.