Bailey, The Spectrometer, Strandquist, Tuesday 3:00
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The Spectrometer
Author: Quinn Bailey, Lab Partners: Conner Vannocker, Mason Charvat
Date Due: Apr. 30, 2024, Date Submitted: Apr. 29, 2024
Lab Section: Tuesday 3:00 - 5:00 PM, Instructor: Mr. Strandquist
ABSTRACT: Refraction and reflection are some of the most basic concepts in optics. The
purpose of this lab was to study these effects. To do this, a device called a spectrometer was used
to measure the path of refracted and reflected light. For the first part, the apex angle of a prism
was determined to be 56.66 degrees. For the second part, the index of refraction of said prism
was found to be 1.585±0.009. For the third part, the wavelengths of blue, green, and yellow light
were calculated to be 353.3 nm, 548.0 nm, and 578.6 nm respectively.
I. DATA
Part 1:
Angle (degrees)
1
174.83
2
174.75
3
174.55
Avg.
174.71
Std. Dev.
0.28
Table 1: The results from measuring the straight-through angle.
Left
(Degrees)
Right
(Degrees)
Difference
(Degrees)
Apex
(Difference/2)
1
123.05
232.68
109.63
54.82
2
125.42
236.23
110.82
55.41
3
116.43
235.92
119.4
59.74
Avg.
56.66
Max. Dev.
4.93
Table 2: The results from measuring the apex angle.
Bailey, The Spectrometer, Strandquist, Tuesday 3:00
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Part 2:
Color
Dm (Degrees)
Yellow
41.66
Green
39.94
Blue
41.18
Table 3: The results for the angle of minimum deviation
Part 3:
Color
θL (Degrees)
θR (Degrees)
Blue
198.5
156.58
Green
205.73
139.27
Yellow
207.92
137.22
Table 4: The results from measuring the mercury spectrum.
II. ANALYSIS
For part 2, the index of refraction for the yellow light trial can be calculated as
𝑛=
𝑠𝑖𝑛(0.5(𝐷𝑚+𝐴))
𝑠𝑖𝑛(𝐴/2)
=
𝑠𝑖𝑛(0.5(41.66+56.66))
𝑠𝑖𝑛(56.66/2)
= 1. 59
Note here that A is the apex angle which was experimentally found in part 1. This process can be
repeated for the rest of the data.
Color
n
Yellow
1.594
Green
1.573
Blue
1.588
Avg.
1.585
Std. Dev.
0.009
Table 5: The value of n for part 3.
Bailey, The Spectrometer, Strandquist, Tuesday 3:00
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For part three, the diffraction angle of the blue light can be calculated as
θ = 0. 5(θ𝐿 − θ𝑅) = 0. 5(198. 5 − 156. 58) = 20. 96 degrees
This value can then be used to calculate the wavelength of blue light as
λ=
𝑑𝑠𝑖𝑛(θ)
𝑚
−6
=
1×10 𝑠𝑖𝑛(20.96)
1
= 353. 5 nm
The discrepancy between this value and the accepted value of 436 nm can be calculated as
353.5−436
436
× 100% =− 18. 92%
These steps can be repeated for the rest of part 3
Color
Accepted λ (nm)
θ (degrees)
λ (nm)
Discrepancy
Blue
436
20.96
353.5
-18.92%
Green
546
33.23
548.0
0.37%
Yellow
578
35.35
578.6
0.10%
Table 6: The calculated results from part 3.
III. DISCUSSION
In this lab, a spectrometer was used to observe the properties of diffraction and reflection.
For part 1, the apex angle was measured as 56.66 degrees. This is close to the expected value of
around 60 degrees, meaning the measurements were fairly accurate. However, they were not
super precise, as the maximum deviation was 4.93. For part 2, the index of refraction was
calculated using data collected from all three colors. This led to a value of 1.58, with a low
standard deviation of 0.009. For part 3, the wavelengths of light were calculated. The green and
yellow values were close to the accepted values, with discrepancies of 0.37% and 0.10%
respectively. However, the blue light value had a larger discrepancy of -18.92%. This can most
likely be attributed to human error. If this lab were to be repeated, error could be reduced if the
prism used was affixed to the turntable in some way. The prism moved easily, which could lead
to large errors in results.
IV. CONCLUSION
In this lab, the phenomena of diffraction and reflection were studied using a spectrometer.
For part 1, the apex angle of a prism was determined to be 56.66 degrees. In part 2, the index of
Bailey, The Spectrometer, Strandquist, Tuesday 3:00
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refraction of the prism was calculated to be 1.585±0.009. For part three, the wavelengths of blue,
green, and yellow light were calculated to be 353.3 nm, 548.0 nm, and 578.6 nm respectively.