Lab 5 Analysis Worksheet
1. Include a photo of your raw data, including your TA’s signature. Failure to include this
data will result in a grade of zero for the entire lab report.
2. Show a sample calculation for the slope, x-intercept and y-intercept for one of your
labeled points from your data.
3. Include both tables of values for your two different lenses. You do not need uncertainties
for the values in these tables.
29.22mm thickness lens
Label
X1 (mm)
1
2
3
X2 (mm)
Y1 (mm)
125
119
99
2
5
9
Y2 (mm)
91
95
70
D (mm)
3
6
10
slope
5
10
15
-0.029
-0.042
-0.034
Yintercept(mm)
5.68
9.96
12.41
4
5
6
7
8
9
92
75
64
47
34
80
11
15
19
24
27
8
61
51
39
27
17
11
14
17
23
28
32
35
20
25
30
35
40
45
-0.097
-0.083
-0.160
-0.200
-0.294
-0.391
19.90
21.25
29.24
33.40
37.00
39.30
22.06 mm thickness lens
Label
X1 (mm)
1
2
3
4
5
6
7
8
9
10
Y1 (mm)
22
17
5
10
11
15
15
23
26
25
35
40
72
56
43
57
46
72
30
10
YX2 (mm)
Y1 (mm)
intercept(mm)
D (mm)
slope
102
3
5
-0.025
5.55
112
5
10
-0.053
10.89
142
6
15
-0.071
16.14
114
10
20
-0.086
19.83
112
13
25
-0.029
16.25
82
10
30
-0.520
52.64
63
23
35
-0.176
34.12
97
20
40
-0.200
39.40
48
31
45
-0.222
41.67
27
37
50
-0.176
41.76
4. Include both graphs of your values (two different images), along with the plotted second
order polynomial trend line that is forecast backwards and includes the equation on the
graph. You do not need uncertainties on your datapoints.
X-intercept(mm vs Distance (29.22mm
lens)
X-intercept(mm)
400
300
200
100
y = -0.2229x2 + 7.416x + 194.25
0
0
10
20
30
D (mm)
40
50
X-intercept(mm vs Distance (22.06mm lens)
600
X-intercept(mm)
500
400
300
200
100
y = -0.121x2 + 5.7865x + 193.51
0
0
10
20
30
40
50
60
D (mm)
5. Include a screenshot or table of the six cells of LINEST values produced from the second
order polynomial fit for both graphs. Use this information to explicitly state the idealized
focal length of your lenses, along with the uncertainty, with proper significant figures.
29.22mm lens
-0.2229021 7.41597619 194.249339
0.11957829 6.13045278 66.7571071
29.22 mm lens ideal focal length = 190 ± 60mm
22.06mm lens
-0.121049 5.78645688 193.505128
0.23162236 13.0717942 156.495147
22.06mm lens ideal focal length 190 ± 160mm
6. Show a sample calculation of determining the radius of curvature and its uncertainty for
one of the lenses, and then include statements of both radii and their uncertainties.
7. Show a sample calculation of determining the index of refraction of the lens from the
radii and the focal length for one of the lenses, and then include statements of both
indices of refraction and their uncertainties.
8. Perform a statistical comparison of the two indices of refraction that you calculated and
state your interpretation of the results of the comparison.
9. Respond to the following questions/instructions:
a) What are some of the assumptions and/or approximations that you used in
performing your analysis? Discuss their implications.
For this lab we assume the lens has imperfections or defects meaning it refracts light
perfectly without distortions. However, the lens may have had scratches or dirt which
could cause light to be refracted at an incorrect angle. This affects my data points which
affects slope and the intercepts in my chart.
I’m also assuming that the lens was in the same position on the graph paper for all of
the data collection. However, it could have very likely moved or not have been perfectly
aligned with the graph paper. This could screw up my intercepts as well as make the
relation between data points and their distance from the center of the lens inaccurate.
In addition to this, I’m assuming there was little human error in the measurements
made. If there were large human errors, the intercepts, and focal length would be
affected.
b) Given that the theoretical relationship between the data points is not a quadratic
func- tion, why do you think a second order polynomial fit used? Why isn’t a higher
order polynomial used? Discuss. (It may be useful to play around with the Trendline
feature in Excel to explore what the other fitting functions look like as compared to
your data.)
Higher order trend lines have more curves and less accurately represent the data.
The second order polynomial trendline fits the best to my data compared to the
others. A 3rd or 4th order trendline over complicates things and the 2 nd order line fits
in a simple way.
c) Using your polynomial fit equation, how far from the optical axis could light enter
the lens and focus no more than 5% from the ideal focal length? In other words, for
what value of x (the distance from the optical axis) would your laser light focus on
the optical axis no more than 0.05f away from f? (You do not need to calculate
uncertainties for this.)
d) Given that the two lenses are made of the exact same material (cut from a single
piece), what would be the scientific implication if your statistical comparison of the
indices of refraction showed that they were not statistically the same (regardless of
the values you got)? In other words, discuss the implication of such a result in terms
of the analysis you performed.
If indices of refraction were not statistically the same, that could mean that one of the lens’
had been damaged or scratched which could have affected the measurements taken. It
could also mean that a major error was made on my part, either when collecting data or
doing calculations.