final draft

1

Introduction

Part 1:

There are several goals for this lab. The first is to gain an understanding of light by studying the

diffraction pattern of a laser light. By taking the distance the grating was from our target sheet,

we can use equations found in the lab manual to calculate the number of gratings in the

diffraction grating. By doing this, we can show that the number of lines per millimeter that we

calculated and the number provided by the manufacturer are not significantly different. What we

learn from this part of the lab will be applied to the second part of the lab.

Part 2:

In the second part we will determine an unknown light source's identity by analyzing its emission

spectrum. By straining a light through the diffraction grating and looking through the

spectrometer, we can look at the visible spectrum of the unknown light source. By taking the

angles between the different color emissions we can calculate the wavelengths of the colors.

Using these wavelengths, we can compare them against known elements and their emission

spectrums to determine what the unknown light source. We will also use a digital spectrometer to

compare our calculated wavelengths against.

2

Equipment used (both parts):

Equipment Used Serial # (where applicable)

Sight Saver N/A

Laser N/A

Optical bench 1667

Diffraction Grating SE-9357

Caliper N/A

Flashlight N/A

Clamp N/A

Data Collector (For Logger Pro) RT SPECT 26 (or USB 2G25336)

Optic Wire VIS-NIR

Computer 65KQ4M1

Unknown Bulb Bulb #6

Spectrometer PHY 242-S9

Meetings:

4/22/14 - 1:50 -2:00 pm. Group met to sign the draft cover.

4/24/14 1:30 -3:00 pm. Group met to finish draft so we would not have to work on it on Friday.

References:

PHY 242 Lab Manual by Steve Ellis

HyperPhysics website (hyperphysics.phy-astr.gsu.edu/hbase/quantum/atspect.html)

Appendix B Errors and Uncertainty Limits. Blackboard.

3

Procedure:

Part 1:

1. The laser was set a little more than 1 meter away from the clipboard that had the white

paper attached to it. A pen was used to help clip the paper to the clipboard.

2. Next, the research team aimed the laser through the 100 lines/mm diffraction grating.

Researcher Ryan Samons, marked and labeled the first and second orders. This

information was recorded in Data Table 1.

3. This procedure was repeated five different times at five different differences. The data

was recorded in Data Table 1.

4. This procedure was repeated for the 300 lines/mm. Each of the first and second orders

were marked and labeled accordingly on the white paper. All data was recorded in Data

Table 1.

5. This procedure was also repeated for the 600 lines/mm diffraction plates. Each of the

first and second orders were marked and labeled accordingly on the white paper. All data

was recorded in Data Table 1

6. The average distances and average distances over the two values were also recorded in

Data Table 1. The number of experimentally derived lines/mm for each diffraction plate

were calculated as well.

Part 2:

1. The spectrometer (which consists of a collimator and telescope) was set up according to

Figure 3 in the lab manual.

4

2. Then the unknown light source was placed shinning into the collimator through the slit on

the end. Then looking through the telescope and the collimator the slit was moved until

the proper amount of light was entering the collimator unimpeded.

3. The telescope was focused by aiming across the room to the adjacent wall and focusing

the image. Then the lab lights were turned out.

4. Once the lights were off we checked to make sure there were three visible orders to the

left and the right of our zero point (the white light in the middle). Making sure we picked

three colors to analyze that appeared in all three orders.

5. The colors we identified were purple, green, and orange.

6. The angle between the orange light was measured for left and right, 1st, 2nd, and 3rd

order. This process was repeated for the green and purple light as well.

7. While measuring the angles Ryan Samons was lining up the telescope with the color

spectrums and Logan Murphy was using the magnifier in order to properly read the angle

using the vernier readings.

8. We also measured the angles to the sides of the color spectrums as to account for the

error in the crosshairs.

9. A fiber optic cable was attached to the computer for Logger Pro to measure the relative

intensities for the light. This was while using the digital spectrometer and Loger Pro

which allowed us to take a screen shot of the spectrum for comparisons.

10. The wave lengths for each line and the respective order were calculated.

5

Data and Calculations:

Part 1:

Below is the table showing the results for the 100 lines/mm plate.

Table 1:

100 line/mm

h (m) s #lines(1/d)

First Order

(m=1) Second Order (m=2)

First Order


1

0.31

3 0.022 0.043 107.0451275 103.8945408

2

0.28

8 0.02 0.039 105.7673262 102.4365441

3

0.26

6 0.019 0.036 108.7741221 102.3783639

4

0.24

3 0.017 0.034 106.5469861 105.7770232

5

0.21

3 0.015 0.029 107.2497063 102.9813825

Average: 107.0766536 103.4935709

Average over 2 values: 105.2851123

The number of lines were calculated using the following equations derived from the lab manual:

N = number of lines =1

d (Equation 1)

= 2 + 2

(Equation 2)

6

Below is a sample calculation using h = 0.313m, s = 0.022m, m=1 and = 655 109m.

This was chosen because it is the midpoint of the laser's range.

N = ((1) (655 109m) 0.022m2 + 0.313m2

0.022m)

1

1m

1000mm

N = 107.05lines

mm

Using this formula in Excel, the values were quickly calculated for the remaining orders and as

well as the 300 line/mm and 600 line/mm plates. The averages for the 1st and 2nd order were

calculated and then the average of those averages was also calculated. An example of the average

for the 1st order:

Average =107.045 + 105.767 + 108.774 + 106.547 + 107.250

5= 107.077

This average and the 2nd order average were then averaged:

Average over 2 value = 107.077 + 103.494

2= 105.285

Below are tables 2 and 3 for the 300 line/mm and 600 line/mm plates:

7

Table 2:

300 line/mm

h (m) s #lines(1/d)

First Order


First Order


1

0.27

6 0.057 0.12 308.7841103 304.3710774

2

0.25

2 0.052 0.109 308.5366851 303.0489145

3

0.23

4 0.047 0.1 300.6439765 299.9775109

4

0.21

4 0.043 0.092 300.7589015 301.4925861

5

0.18

4 0.037 0.079 300.9781186 301.16178

Average: 303.9403584 302.0103738


8

Table 3:

600 line/mm

h (m) s #lines(1/d)

First Order


First Order


1

0.06

7 0.029 0.086 606.4473371 602.1817127

2

0.06

5 0.028 0.083 604.0059482 600.9960263

3

0.06

2 0.027 0.078 609.5675836 597.5750036

4

0.05

8 0.025 0.074 604.3196146 600.8060421

5

0.10

1 0.045 0.132 621.3395779 606.2496379

Average: 609.1360123 601.5616845


This is the end of the calculations for Part 1.

9

Part 2:

Below is the table of the measurements and colors of the spectral lines for the unknown source:

Table 4:

Spectral Lines (unknown source)

Color First Order

(m=1)

Second Order

(m=2)

Third Order

(m=3)

Orange

Right 183.5 + 9' Right 186.5 + 29' Right 190 + 20'

Left 176.5 + 15' Left 173.5 Left 170 + 6'

Green

Right 183 + 20' Right 186.5 + 10' Right 189.5 + 15'

Left 177 + 5' Left 173.5 + 20' Left 170.5 + 4'

Purple

Right 182.5 + 15' Right 185 + 22' Right 187.5 + 19'

Left 177.5 + 11' Left 175 + 6' Left 172.5 + 5'

Using the information in this table, the wavelengths were calculated using the following

equation:

=dsin()

m (Equation 3)

Sample calculation for where = 183.5 + 9' and m = 1:

d =1mm

100

1m

1000mm1.0 109nm

1m= 3333.33nm

10

= 183.5 + 9 1

60= 183.65

=(3333.33nm)sin (183.65)

1= 607.7711nm

All of the wavelengths were calculated and then the right and left wavelength values were

averaged for each order to find the average wavelength.

Table 6 Wavelengths (nm)

1st Order 2nd Order 3rd Order

Orange 601.77113 586.95958 585.50614

Green 545.14141 558.7847 555.41567

Purple 442.00287 447.36507 441.81303

Here is some select data from Logger Pro. The selected data shows the spikes in intensity which

correspond closely to the wavelengths in Table 6. The first and last value in each "set" is used to

compare before and after the spike in intensity. The spikes will also be bolded.

11

Table 7:

Wavelength

(nm) Intensity

434 0.024419

435 0.340712

436 0.863028

437 0.364691

438 0.008236

544 0.005379

545 0.339473

546 0.751611

547 0.53279

548 0.249145

549 0.035406

602 0.001

603 0.001406

604 0.001102

605 0.001095

606 0.001047

607 0.001042

608 0.001

12

Below is the screen shot of the data captured in Logger Pro.

As you can see from the screenshot above, these are the most likely candidates for the colors we

saw through the spectrometer. The first color is purple which has a wavelength of approximately

450 nm. The next two are green and orange with respective wavelengths of about 550 and 580

nm.

Purple Green Orange

13

Discussion and Analysis

Part 1

In this part of the experiment light diffraction was used in order to count the number of lights in

each section of the lens. We observed this by counting the distances between the diffractions

along the white sheet of paper. Errors in this experiment can occur do to not measuring from the

exact midpoint of the circle, the distance from the lens to the board, and the error in the

wavelength physically emitted by the laser used in the experiment.

In this experiment we used the following equation to solve 1/d by using trials and calculations in

order to find the distance d. The equation used was Equation 2:

=1

=

2+2

In this equation s is the refracted light distance, lamda is the wavelength from the laser pointer,

m is the order of diffraction, and h is the distance the diffraction grade was from the screen. This

calculation is based heavily on the accuracy of the numbers entered into this equation therefore if

there are any errors in the variables for this problem then this error must be taken into account

when forming the final value for the unknown variable. It is because the error is so important in

this equation that the errors must be propagated through all of the values in order to find the true

possible values for the data collected.

To properly propagate the errors in this equation each of the know variables (s,h,lamda) partial

derivatives must be taken with respect to the equation above. The partial derivatives for this

equation are shown below.

14

=

22+ 2 ( 2)

This is the partial for the lamda variable.

=

(2+ 2)3/2 ( 2)

This is the partial for the h variable.

=

2

(2+ 2)3/2 ( 2)

This is the partial for the s variable.

From these equations the complete propagated error equation can be created using Deltas as the

uncertainty in the value itself and the partial derivatives given above. This complete equation is

shown below with N being the uncertainty in the 1/d value.

= (

)

2

+ (

)

2

+ (

)

2

( 4)

Then using the partial derivative equations derived earlier we can use these in the equation for

N.

= ((

22+ 2) )

2

+((

(2+ 2)3/2) )

2

+((2

(2+ 2)3/2) )

2

The only missing elements from the above equation that was not physically measured for the

experiment is the uncertainties in the variables, thus we needed to calculate or measure the affect

each would have and the errors associated with s h.

15

The h value is determined by calculated our smallest unit of measurement and dividing by two.

The measurement tool for this experiment was a ruler and its smallest increment was a

millimeter. Therefore the error for the h value is half of 1mm or .5mm.

The is given on the laser itself. It gave us a range of uncertainty. The laser said the value

was between 630 and 680 m. Therefore the uncertainty in this value is 25m.

The error for the s value was not given in the experiment and therefore had to be calculated.

There is an error much like the error for h as it can only be as accurate as the smallest unit of

measurement. Therefore there is an error of at least .5mm, however there is more error involved

in this value. When measuring from the center of the lasers light to the center of the next light

you have no way of knowing exactly where you are on the circle. There is a chance that the

measurement was not taken at the middle, therefore there is an error in this as well. This error is

evaluated by finding the minimum distance between the two circles from just the edge of the

circle to the edge of the other, and then finding the maximum distance between the two circles by

measuring from the outer points. By subtracting the maximum and the minimum and dividing

by 2 you get the error for not being able to measure the exact center of the circle. After doing

this 10 times we found the average for this value to be 2.8mm. Then the total error for the s value

is given below.

= (. 0005 +

2) ( 5)

Giving us an s value of 3.3mm.

After finding the uncertainties in the quantities above we can now rewrite the propagated error

equation and fill in the proper values for the uncertainties. This new rewritten Equation 4 is as

follows:

16

= ((

22 + 2) (2.5 105))

2

+((

(2 + 2)3/2) .5)

2

+ ((2

(2 + 2)3/2) 3.3)

2

We can know use this equation for each measurement taken in the first part of the lab. We can

use this for both the second and first order calculations of the propagated error. Below is a

sample calculation using the 300 lines/mm grating, and h value of 276m. For this trial the

s=57mm, m=1, and lambda = 6.55*10^-4. Using the equation above you can calculate this

sample equation.

=

((57

1(6.55 104)22762 +572) (2.5 105))

2

+ (((57)(276)

(1)6.55 104(2762+572 )3

2

) .5)

2

+((2762

(1)6.55 10^4(2762+572)3/2) 3.3)

2

=(11.78)2+ (.54)2+ (17.14)2

=19.304mm

Which would give us for that value a N=308.78419.304 lines per millimeter.

Now using the same method showcased in the sample equation above you can fill out the rest of

the error table for the 300 lines per millimeter as well as the 100 and 600.

17

The table below shows the uncertainty values for the 100 lines/mm Grating trials.

Table 8:

Distance

(mm)

First Order

(m=1)

(lines/mm)

Second Order

(m=2) (lines/mm)

313 107.04516.372 103.8958.186

288 105.76716.362 102.4378.181

266 108.77416.387 102.3788.194

243 106.54716.369 105.7788.185

213 107.07716.375 103.4948.1876

This table below has the uncertainty values for the 300 lines/mm Grating.

Table 9:

Distance

(mm)

First Order

(m=1)

(lines/mm)

Second Order

(m=2) (lines/mm)

276 308.78419.305 304.3719.652

252 308.53619.301 303.0499.651

234 300.64419.146 299.9789.573

214 300.75919.15 301.4929.573

184 303.9419.159 301.1629.576

18

The table below shows the uncertainties for the 600 lines/mm Grating.

Table 10:

Distance

(mm)

First Order

(m=1)

(lines/mm)

Second Order

(m=2) (lines/mm)

67 606.44727.025 602.18213.5123

65 604.00626.97 600.99613.4854

62 609.56827.161 597.57513.581

58 604.31927.053 600.80613.526

101 621.33927.308 606.24913.654

We can use the values above to find the errors in each order of the problem. To do this all we

need to do is take the average of all the errors from the 5 trials in each order. The equation for

the average error is the following.

=

( 6)

Sample calculation for the error in the first order of the600 grating.

=27.025 + 26.97+ 27.161+ 27.053+ 27.308

5= 27.103

This value being the average error for the first order of the 600 grating.

The chart below shows the average errors for both the first and second orders of all of the

gratings.

19

Table 11:

Grating

First Order

(m=1)

(lines/mm)

Second Order

(m=2) (lines/mm)

100 107.2516.376 103.4948.188

300 303.9419.214 302.019.607

600 609.13627.103 601.56213.552

Once again we can look at the errors on an even closer level by average the errors across the two

orders. We can take the average values as well as the average errors and find the values for the

range of the values we found experimentally. We can use the same average equation as above,

but instead of going down each order for the different gratings, we are going across the two

orders for each grating. The table below shows the final values for the uncertainties in the

grating reading.

Table 12:

Grating Average Value and

Uncertainty (lines/mm)

100 105.28512.282

300 302.97514.41

600 605.34920.3275

There is also a manufacturing error for the grating sheet itself. The number listed below each

grating are not exact values and carry an inherent uncertainty with them. The uncertainty within

20

each grating is 5% of the grating value. Therefore the error in the manufactured grating is as

follows, using 100 as the sample calculation.

= .05 ( 7)

= 100 .05 = 5 /

Using this same equation you find the uncertainties in the manufactured product to in the table

below.

Table 13:

Grating Value

(lines/mm)

Uncertainty

Value (lines/mm)

100 5

300 15

600 30

Part 2:

The second part of this lab involved using a spectrometer in order to find the wavelengths of an

unknown light source by reading the diffractions of its light and measuring the colors that

appeared in the first three orders. We needed to know the angle between the light source and its

diffracted orders as well as a few distances. Equation 3 for the lambda value is shown below.

= sin

106

First look at the error in the angle. There are two possible errors that could come about when

measuring the angle. One is that the spectrometer can only measure to certain degrees. Since it

can measure minutes we can conclude that you can get within half a minute because a minute is

21

the smallest value possible. The other possible error was when the reading was made the

crosshairs were not exactly on the middle of the beam of light. Therefore this brings an error

found my taking the smallest value possible and the largest value possible, finding the difference

and dividing by two. If you did that you would find the error to be 1 minute. Therefore the total

error in the angle is the .5 from the device and the 1 from not being able to measure to the

center, giving a total of .025 degrees as the uncertainty.

1

60+. 5

60= .025 = ( 8)

Next we can look at the error in the diffraction grating which is a given value of 5% uncertainty.

In this case we used the 300 lines/mm diffraction grating meaning our uncertainty in the d value

is .000167mm since we are looking for 5% of 1/300

=1

300 .5 = .000167 ( 9)

Now we can begin to calculate the uncertainty in the wavelength. Since the wavelength has

errors all throughout its calculation the error will need to be propagated for both the error in d as

well as the error in the angle. Before we start propagating the error we need to find the partial

derivatives for the angle and the d values. The partial derivative with respect to d is below.

=sin

( 3)

The partial derivative with respect to the angle is:

= cos

( 3)

22

Then we can plug these equations into the magnitude equation in order to find the error in the

lambda value.

= (

)

2

+ (

)

( 10)

As calculated above the delta d value is .000167 and the delta theta value is .025. Using these

values and the partial derivatives found above the following equation emerges.

= (sin

.000167)

2

+ ( cos

106 .025)

A sample calculation is shown below using the first order of the orange light to the right. m=1,

d=.00333, and theta=3.65

= (sin3.65

1 000167)

2

+ (cos3.65

1 300 .025)

1000000

= 83.84

The following table has the propagated error calculations for the first three orders of the colors

blue, green and yellow, measured both to the left and the right.

Table 14:

Color 1st order 2nd order 3rd order

orange 601.77183.52 586.95967.085 585.50664.5155

Green 545.14183.208 558.78566.8345 555.41663.51

Purple 442.00383.2485 447.36567.1295 441.81363.899

23

Now knowing the errors and values for the three colors for the three orders from both the left and

the right side we can combine the errors and form an average. We can do this by looking at the

colors separately but by finding the average for all three orders and both sides. We can do this by

using Equation 6.

=1 +2 +3+ 4+5+ 6

6

Therefore the average for the sample calculation below is using the delta lambda values from the

green color.

=83.19+ 83.225 + 67.089+ 64.21+ 62.811+ 66.58

6= 71.184

Following this same procedure for the delta lambda and lambda values can give us the following

chart.

Table 15:

Color

Orange 591.412 71.59

Green 553.114 71.184

Purple 443.727 71.42

The digital spectrometers digital measures the wave lengths of colors emitted by the unknown

light source and plots them on a graph of colors with the intensity shown on the graph. This

graph as an inherent uncertainty that can be calculated by using the maximum subtracted by the

minimum then divide that by two.

24

=

2 ( 11)

The minimum is the point at the very beginning of the spike and the maximum is at the very end

of the spike. The values and the graph of the intensity is given below.

min

min

min

max

max

max

25

Using the figure above we can find the values of the minimum and maximum lambda explained

above. Once you find those values you can take the difference to find the uncertainty. The

equation below is the uncertainty in the digital spectrometer with the intervals given in the first

part of the lab. The sample calculation below is for the green wavelength.

=570 565

2= 2.5 ( 12)

Using the above equation for all of the colored wavelengths we can calculate the uncertainty in

all of them.

Table 16:

Color Min

(nm)

Max

(nm)

Wavelength

(nm)

Orange 576 582 5793

Green 565 570 567.52.5

Purple 434 438 4362

Throughout this experiment there are many systematic and random errors. Random errors are

hard to account for and can happen without you even knowing they affected your experiment.

The table being moved, a flashlight messing with you color spectrum, the light having a power

surge and so on. The list is endless but these do not have a large enough value to be significant.

Then there is also systematic errors that come from the devices you are using. The following is a

list of those different errors and uncertainties in the order in which they cause the most

uncertainty.

26

1. The uncertainly in measuring the center of the circle from the laser point. This is a

random error. There is no true way for us to calculate the center of the laser point.

Therefore there is a random that anywhere we calculate from inside the circle could be

the considered the middle.

2. The uncertainty in in the measuring device itself. The ruler can only measure to a certain

value, therefore it is a systematic error because you know the uncertainty from the

measuring device is half the smallest value.

3. The uncertainty in the manufactured gratings. This is a systematic error because the

values come directly from the manufacturer. It is a known value.

4. The error in the d value. This is a systematic error because once again we are using the

ruler to make the measurements which has an error of half the smallest measurement.

5. The error in the spectrometer in find the angle. This is a systematic error from the vernier

caliper readings which is half the smallest measurement.

6. The error in the wavelength from part 1. This is a systematic error from the laser pointer

itself.

7. The error in the wavelength form the digital spectrometer. This is a systematic error

because it is given on the digital spectrometer itself as a systematic error.

27

Results and Conclusion:

The objectives of this experiment were to study the interference properties of light, to study the

diffraction pattern of laser light on different diffraction gratings, and to determine the unknown

element in the light box by the analysis of its emission spectrum. This experiment was broken

down into two main parts.

Part 1: Experimentation

The objectives for part one of the experiment were to study the interference properties of light

and to study the diffraction patter of laser light on different diffraction gratings. The first part of

the experiment mainly focused on determining the number of lines per unit length for each of the

diffraction gratings. The research team aimed a red beamed laser at a white paper screen that was

at least 1.2 meters away. The researcher marked the initial position and then placed the 100

lines/mm diffraction grating directly in the laser beam. The first and second orders were

measured from five different distances. This process was completed for the 300 lines/mm

diffraction grating as well as the 600 lines/mm diffraction grating. These experimental values can

be compared to the manufacturer values.

Comparison Line #1: 100 Lines/mm Comparison

Manufacture Rating: 100 lines/mm 5 lines/mm

Experimental Rating: 105.285 lines/mm 12.282 lines/mm

91 93 95 97 99 101 103 105 107 109 111 113 115 117 119 121

28

This number line compares the manufacture grating values to the values the research team found

experimentally. Because the two comparison lines overlap, several conclusions can be made. The

main conclusion is that the number of lines per millimeter can be found by the procedure

completed in the experiment. If the horizontal distance between the screen and the grating is

known as well as the vertical distance from the laser to the screen, the number of lines per

millimeter can be accurately calculated. Using Equation 13 below, we can calculate the percent

difference between these two values:

% =|1 2 |

(1 + 22 )

100% ( 13)

Using our values:

% =|100 105.285|

(100 + 105.285

2 ) 100% = 5.1489%

This also shows that our values are not significantly different.


Manufacture Rating: 300 lines/mm15 lines/mm


284 286 288 300 302 304 306 308 310 312 314 316 318 320

29

The comparison line above compares the manufacture ratings for the 300 lines/mm diffraction

grating versus the experiment value found for the number of lines per millimeter. Because these

two lines overlap, the results from the experiment are accurate. Another conclusion that can be

made is that if you know the horizontal distance between the screen and the grating is known as

well as the vertical distance from the laser to the screen, the number of lines per millimeter can

be accurately calculated.

Using Equation 13, the percent difference is 0.9868%. This also shows that our data and

calculations are not significantly different.


Manufacture Rating: 600 lines/mm 30 lines/mm


The number line above compares the manufacture rating for the 600 lines/mm diffraction grating

plate to the experimental values for the diffraction grating plate. Because these two numbers

lines overlap, several conclusions can be made. The main conclusion, however, is that using the

experimental procedures described in this report is an equivalent way to find the diffraction

grating. So, for this setup and equipment, if the horizontal distance between the screen and the

570 575 580 585 590 595 600 605 610 615 620 625 630

30

grating is known as well as the vertical distance from the laser to the screen, the number of lines

per millimeter can be accurately calculated.

Using Equation 13, the percent difference between these two values is 0.8875%. Again, this

shows that our data and calculations are not significantly different.

Overall, the first part of this experiment was a success. The two main lab objectives where to

study the interference properties of light and to study the diffraction patter of laser light on

different diffraction gratings. Both of these objectives were met and understood in depth by the

research team. Because there was overlap present on all three of the number lines, the procedure

used in the experiment was an accurate method in obtaining the ratings for each of the three

diffraction grating ratings. The overlap also signifies that the equipment used in the experiment

was accurate to a certain degree.

Part 2: Determination of the Unknown Spectral Source

The objective for the second part of the experiment was to determine the unknown element in the

light box by the analysis of its emission spectrum. The second part of the experiment focused

primarily on using the spectrometer and the diffraction gratings to measure angles for the first,

second, and third orders for three different colors seen through the telescope. This data was then

used to calculate the different wavelengths for each of the three colors. The digital spectrometer

was then used to measure the wavelengths of the colors omitted from the unknown light source.

The values of the experimental wavelengths and the wavelength obtained from the digital

spectrometer can be compared.

31

Comparison Line #4: Orange Digital vs. Mechanical Wavelength

Mechanical Wavelength: 591.412nm 71.59nm

Digital Wavelength: 579nm 3nm

There are several conclusions that can be made because the two comparison lines overlap. The

main conclusion is you can use the spectrometer and the diffraction gratings to measure angles

for the first, second, and third orders for three different colors seen through the telescope. This

data was then used to calculate the different wavelengths for each of the three colors. This

procedure is that same as measuring the wavelengths with the digital spectrometer. The other

conclusion that can be made is that all the equipment used was accurate to a certain degree.

Using Equation 13, the percent difference is 2.121%. This shows that our data and calculations

are not significantly different.

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Comparison Line #5: Green Digital vs. Mechanical Wavelength


Digital Wavelength: 567.5nm 2.5nm









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Comparison Line #6: Purple Digital vs. Mechanical Wavelength


Digital Wavelength: 436nm 2nm









The Unknown Spectral Source: Mercury

To begin the narrowing down process, we looked up the emission spectrum from possible

sources provided by TA Justin Woods on the day of Part 2 of the lab. From these, we looked at

the ones that only contained a bluish light. These possible elements were Argon, Iodine and

Mercury. Argons visible light is a lot closer to purple, which could be confused with a darker

blue. However, Argons emission spectrum contains red light, our unknown light source did not

have any red in it. Argon was eliminated because it also had a lot of red light. Iodines visible

light was close to a kind of pale purple/white light. This too might be confused with a bluish

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light. Looking at Iodines emission spectrum, we noticed that Iodine contained red, our light

source did not. For this reason, Iodine was eliminated. This left us with Mercury which appeared

to be the most likely candidate because its visible light was blue and its emission spectrum

contained purple, green and orange light. This led us to conclude that our unknown light source

was Mercury. The wavelengths from mercury for purple, green, and orange from the online

source (see references) were 443.727, 553.114, and 591.4. After analyzing the website we used

for our reference we found the uncertainty in these values to be the differences between the max

and min of the peak values. We found this uncertainty to be approximately 2nm per color and

wavelength value.

Comparison Line #7: Oranges Mechanical Wavelength vs. Mercury Wavelength

Orange Mechanical Wavelength: 591.412nm 71.59nm

Mercurys Wavelength: 579.065nm 2nm

There are several conclusions that can be made because these two comparison lines overlap. The

main conclusion is that the experiment procedure described above is equivalent to accurately

finding an elements wavelength. Another conclusion that can be made from the overlap, is that

the equipment used was accurate and the procedure was done correctly. We can now take a

percent difference of the orange mechanical wavelength and the comparable wavelength of

Mercury. The percent difference, using Equation 13, is 2.1097%. This is not significantly

different and helps confirm one color of the spectrum.

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Comparison Line #8: Greens Mechanical Wavelength vs. Mercury Wavelength

Green Mechanical Wavelength: 553.114nm 71.184nm

Mercurys Wavelength: 546.074nm 2nm





percent difference of the green mechanical wavelength and the comparable wavelength of



Comparison Line #9: Purples Mechanical Wavelength vs Mercury Wavelength

Purple Mechanical Wavelength: 443.727nm 71.42nm

Mercury Wavelength: 435.835nm 2nm

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percent difference of the purple mechanical wavelength and the comparable wavelength of



Overall, the experiment was successfully completed without any significant sources of error. The

objectives for part one of the experiment were to study the interference properties of light and to

study the diffraction patter of laser light on different diffraction gratings. The first part of the

experiment mainly focused on determining the number of lines per unit length for each of the

diffraction gratings. These objectives were successfully met. For the second part, the objectives

were to determine the unknown element in the light box by the analysis of its emission spectrum.

The second part of the experiment focused primarily on using the spectrometer and the

diffraction gratings to measure angles for the first, second, and third orders for three different

colors seen through the telescope. This data was then used to calculate the different wavelengths

for each of the three colors. The digital spectrometer was then used to measure the wavelengths

of the colors omitted from the unknown light source. Another objective for this experiment was

to determine the unknown spectral source. After careful analysis and comparison, the research

team determined that bulb #6 was Mercury.

final draft

Documents

data table

laser light

linesmm diffraction

lab manual

diffraction grating

diffraction pattern

linesmm diffraction

understanding of light