r_k B C Radius(m) D E Radius (m^2) Co(1/m^2) го r 1 0.396 0.156816 6.3769 0.658 0.432964 2.309661 r 2 0.846 0.715716 1.397202 r_3 0.993 0.986049 1.014148 r4 1.122 1.258884 0.794354 Details For data analysis, please complete as follows: Given that, (R-R) f Eq. 1 where: R is the true value of the linear Radius of the kth ring .Ro is the true value of the linear radius of the innermost ring f-50 mm and is the listed value for the focal length of the camera lens k-1, 2, 3... and is the rings formed through constructive interference of light waves emitted by the mercury lamp light source A-546.1 nm and is the wavelength of the light emitted by the mercury lamp light source. d-1.995 mm and is the distance between the parallel plates of the Fabry Perot Interferometer It also should be noted that the observed values for the radii of the rings (innermost and kth rings) are not calibrated and, as such, have an unknown scale factor applied to them. The first portion of our analysis is to solve for this scale factor, considering the following. Rk=S.Tk Eq. 2 Eq. 3 Ro= S.To R-RS (-) Eq. 4 Where: .S is the scaling factor ⚫rk is the observed, scaled value of the linear Radius of the kth ring ⚫ro is the observed, scaled value of the linear radius of the innermost ring Combining Eq. 4 with Eq. 1 gives you: 5(1-7) f -k 44 -k Eq. 5a Eq. 5b where the difference of the squares of the observed scaled radii of the (kth and Oth) concentric rings form a linear relationship with the k. From this relationship, the scaled factor can be derived from the slope of the a graph of these values. Please plot a scatter plot graph and obtain an equation corresponding with a linear trend line to find the scale factor S. Once that S is obtained, please use that value to find Ro and R, the true values of ring radii (i.e. using Eqs. 2 and 3). Use this information to solve for the focal length of the camera by creating a second scatter plot graph that includes the value of the focal length in its slope. Please note that R,² forms a linear relationship with k in the following equation. R=k+ R Eq. 6 With the given values of X and d along with the nominal value of f, please provide a percentage difference between the nominal value of f and its experimental value. Also from this second graph, find the percentage difference between the previously calculated value of RO and the one that is indicated by the trendline of the second graph (via the y intercept).
r_k B C Radius(m) D E Radius (m^2) Co(1/m^2) го r 1 0.396 0.156816 6.3769 0.658 0.432964 2.309661 r 2 0.846 0.715716 1.397202 r_3 0.993 0.986049 1.014148 r4 1.122 1.258884 0.794354 Details For data analysis, please complete as follows: Given that, (R-R) f Eq. 1 where: R is the true value of the linear Radius of the kth ring .Ro is the true value of the linear radius of the innermost ring f-50 mm and is the listed value for the focal length of the camera lens k-1, 2, 3... and is the rings formed through constructive interference of light waves emitted by the mercury lamp light source A-546.1 nm and is the wavelength of the light emitted by the mercury lamp light source. d-1.995 mm and is the distance between the parallel plates of the Fabry Perot Interferometer It also should be noted that the observed values for the radii of the rings (innermost and kth rings) are not calibrated and, as such, have an unknown scale factor applied to them. The first portion of our analysis is to solve for this scale factor, considering the following. Rk=S.Tk Eq. 2 Eq. 3 Ro= S.To R-RS (-) Eq. 4 Where: .S is the scaling factor ⚫rk is the observed, scaled value of the linear Radius of the kth ring ⚫ro is the observed, scaled value of the linear radius of the innermost ring Combining Eq. 4 with Eq. 1 gives you: 5(1-7) f -k 44 -k Eq. 5a Eq. 5b where the difference of the squares of the observed scaled radii of the (kth and Oth) concentric rings form a linear relationship with the k. From this relationship, the scaled factor can be derived from the slope of the a graph of these values. Please plot a scatter plot graph and obtain an equation corresponding with a linear trend line to find the scale factor S. Once that S is obtained, please use that value to find Ro and R, the true values of ring radii (i.e. using Eqs. 2 and 3). Use this information to solve for the focal length of the camera by creating a second scatter plot graph that includes the value of the focal length in its slope. Please note that R,² forms a linear relationship with k in the following equation. R=k+ R Eq. 6 With the given values of X and d along with the nominal value of f, please provide a percentage difference between the nominal value of f and its experimental value. Also from this second graph, find the percentage difference between the previously calculated value of RO and the one that is indicated by the trendline of the second graph (via the y intercept).
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Need help on finding the values of R_k , R_0 and S . If you can show me how to solve it step by step , thanks in advance .
Transcribed Image Text:r_k
B
C
Radius(m)
D
E
Radius (m^2) Co(1/m^2)
го
r 1
0.396
0.156816 6.3769
0.658
0.432964 2.309661
r 2
0.846
0.715716 1.397202
r_3
0.993
0.986049 1.014148
r4
1.122
1.258884 0.794354
Transcribed Image Text:Details
For data analysis, please complete as follows:
Given that,
(R-R)
f
Eq. 1
where:
R is the true value of the linear Radius of the kth ring
.Ro is the true value of the linear radius of the innermost ring
f-50 mm and is the listed value for the focal length of the camera lens
k-1, 2, 3... and is the rings formed through constructive interference of light waves emitted by the mercury lamp light source
A-546.1 nm and is the wavelength of the light emitted by the mercury lamp light source.
d-1.995 mm and is the distance between the parallel plates of the Fabry Perot Interferometer
It also should be noted that the observed values for the radii of the rings (innermost and kth rings) are not calibrated and, as such, have an unknown scale factor applied to them. The first portion of our analysis is to solve for this scale factor, considering the following.
Rk=S.Tk
Eq. 2
Eq. 3
Ro= S.To
R-RS (-) Eq. 4
Where:
.S is the scaling factor
⚫rk is the observed, scaled value of the linear Radius of the kth ring
⚫ro is the observed, scaled value of the linear radius of the innermost ring
Combining Eq. 4 with Eq. 1 gives you:
5(1-7)
f
-k
44
-k
Eq. 5a
Eq. 5b
where the difference of the squares of the observed scaled radii of the (kth and Oth) concentric rings form a linear relationship with the k. From this relationship, the scaled factor can be derived from the slope of the a graph of these values.
Please plot a scatter plot graph and obtain an equation corresponding with a linear trend line to find the scale factor S. Once that S is obtained, please use that value to find Ro and R, the true values of ring radii (i.e. using Eqs. 2 and 3).
Use this information to solve for the focal length of the camera by creating a second scatter plot graph that includes the value of the focal length in its slope. Please note that R,² forms a linear relationship with k in the following equation.
R=k+ R
Eq. 6
With the given values of X and d along with the nominal value of f, please provide a percentage difference between the nominal value of f and its experimental value.
Also from this second graph, find the percentage difference between the previously calculated value of RO and the one that is indicated by the trendline of the second graph (via the y intercept).
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