CD Diffraction

Purpose:

            The primary purpose of this experiment is to use a simple apparatus to determine the spacing of the lines within a compact disk. This experiment will explore the properties of diffraction gradients using everyday items and a laser of known wavelength. The laser will be used to measure the spacing of the lines by using the relationship learned of light diffraction. Once the spacing have been determined, the obtained results will be compared to the factory requirements of 1600nm and evaluated. In addition to the CD, a DVD will also be evaluated and its spacing will also be compared to the factory specifications of 740nm.

Procedure:

            First, the following supplies were gathered: CD, DVD, piece of paper, meter stick and a laser. The paper was first taken and a hole was placed in the middle of it. Once that was done, the laser was placed on the table so that the beam would strike through the hole created. On the opposite side of the paper, the CD was placed so that the beam would reflect off and bounce diffractively back at the paper. 

Once this was completed, the spacing of the dots were measured and recorded. The length from the CD to the paper was also recorded to be used in later calculations. This entire process was then repeated with the DVD to determine the differences.

Data Analysis:

CD:

            The following data chart displays the raw recorded data for the CD measurements with x representing the distance to the first maxima, l indicating the distance from the paper to the CD, and lambda representing the wavelength of the laser:

Trial	x(cm)	l(cm)	λ(nm)
1	11.5 ± .5	24.3 ± .5	633
2	14.8 ± .5	32.4 ± .5	633
3	16 ± .5	34.8 ± .5	633

The following sample calculation represents the work done to determine the spacing between each line for the CD:

Sinθ = λ/a = x/(x²+l²)^1/2

a = λ(x²+l²)^1/2/x

a = (633nm)(11.5cm²+24.3cm²)^1/2/11.5cm

a = 1480nm

The proceeding table includes the calculated spacing for all three trials:

Trial	Spacing(nm)
1	1480
2	1520
3	1520

DVD:

            Unfortunately, the DVD experiment was only done once due to time restraints. The following table represents the raw data achieved for the DVD, again the same values represent the same quantities as the CD observations:

Trial	x(cm)	l(cm)	λ(nm)
1	9.1  ± .5	5.5  ± .5	633

Using the same calculations as for the CD, the spacing for the DVD is as followed:

Trial	Spacing(nm)
1	739  ± 89

Conclusion:

            After completing all necessary calculations, the spacing for both the CD and DVD were found. The computed spacing of the CD were found to be 1480 nm and 1520 nm. When these values were compared to the factory standard of 1600nm, the range of errors ranged from 5.0% to 7.5%. Considering the small amounts of distances being evaluated, these numbers are rather large. It would be recommended that the factory consider the way their CDs are produced to ensure that the standards are more closely achieved. As for the DVD, the spacing was found to be close to 740nm. When comparing this to the standard of 760nm, the error of 2.6% is not as far off as from the CD. It would not be recommended to the factory to consider the manufacturing process of their DVDs since the error is relatively small.

Measuring a Human Hair

Purpose:

            The primary purpose of this laboratory experiment is to determine the diameter of a human hair using two different methods. The first method that will be used is with the use of a laser with a known wavelength. The second method, is to use a micrometer to determine the diameter of the hair.

Procedure:

            Part 1:

            First, the laser was obtained as well as a note card, a white board, and the hair that will be measured. The note card was punched through with a hole punch to allow for the gap where the hair would be placed. The hair was then placed vertically in the hole created. Once that was completed, the laser was positioned directly behind the hair so as that the hair would split the beam.

 

Once this was complete, the white board was then placed a distance away from the laser and the gap between the hair and the board was measured.

 

The light of the laser was then turned on and the created interference pattern was observed. This pattern was tehn marked using a marker to be measured at a later time.

 

Once this was completed, the values were recorded and logged to be used to calculate the diameter of the hair at a later time.

            Part 2:

            For this part, the micrometer was obtained and placed on the table along with a light source to enable a better viewing of the hair. The hair was then placed under the scope (while still being attached to the note card) and was then looked for through the lens.

 

Once the hair was found, the cross hairs of the microscope where then placed on one side of the hair. The knob on the side of the micrometer was then turned until the cross hairs reached the other side.

 

Once this was completed, the measurement on the side of the micrometer was measured and recorded as the diameter of the hair.

 

Data Analysis:

            Part 1:

The following chart depicts the recorded data for the laser experiment:

Trial	y (cm)	m	λ laser (nm)
1	1.85 ± .05	3	633
2	1.83 ± .05	3	633

 Since the distance from the board to the hair was measured to be 100 ± 1cm, we can use the following equation to determine the diameter of the hair, d.

d = mλL/y

Upon doing this, we get the following values for the diameter of the hair:

Trial	Diameter (mm)
1	.103 ± .038
2	.104 ± .038

          Part 2:

The following table shows the measured values obtained for the diameter of the hair using the micrometer:

Trial	Diameter(mm)
1	.18 ± .01
2	.13 ± .01

 Using these two numbers, the average of the two was found to be .155 ± .02 mm.

Conclusion:
            According to online sources, the actual diameter of a human hair is about 180 micrometers, or .180 millimeters. It is clear that the use of the micrometer is the best and most accurate way to measure the hair but the laser, did in fact come close, at least certainly within the orders of magnitude. To conclude, the seemingly difficult task of measuring such small distances can be made simpler with the use of a laser, or better yet, a micrometer, fairly easily.

Lenses

Purpose:

            The purpose of this lab experiment is to observe a few characteristics of a converging lens then an object is placed on one side of the lens and the real, inverted image is placed on the other side of the lens.

Procedure:

1.      A lens was picked out as well as a light source, meter stick, and a V-shaped holding stand for to place the stick in as well as a lens holder.

2.      The converging lens was taken outside to have its focal length measured.

3.      The lens was brought back inside and the apparatus for which it will be held on was set up. 

4.      Once this was set up, the lens was then moved further and closer from the light source and the image was measured and compared to the original object, the light source. The light source was measured and determined to be used as the object height. First, we stared by moving the image a distance of 4 times the foal length found from the object, the object distance. This image was then shown by holding a notebook on the back side of the lens and determining when the object was at most focus. This was then measured with a ruler and the distance from the lens was recorded from the meter stick. These values would become the image height and image distance. 

5.      Once all of these values were recorded, the magnification (M) of the lens was then determined by using the formula, M = h_i/h_o. That is, the height of the image over the height of the original object.

6.      Next, the lens was taken out of the holding fixture and flipped to determine if the image properties differed. For this specific lens, the image remained unchanged since it was a converging lens with equal radius curvatures. It should be noted that the image was inverted, as some of the pictures will point out.

7.      The steps of 4 and 5 were repeated with the following object distances: 5f, 3f, 2f, 1.5f.

8.      For the next part, we covered half of the lens with a ruler to determine how that would affect the image projected. 

9.      Lastly, we took the lens and moved it a distance of half its focal length to see what would happen.

Data Analysis:

             Listed below is a table of all of the recorded values for the various object distances used as described in step 7. 

Object distance do­ cm	Image distance di cm	Object height ho cm	Image height hi cm	M	Type of image
5f = 91	23.6	8.6	1.8	.21	Real
4f = 73	25.7	8.6	3.1	.36	Real
3f = 54.6	29	8.6	4.6	.53	Real
2f = 36.5	39	8.6	9.5	1.1	Real
1.5f = 27	63	8.6	20.3	2.4	Real

The data  suggest that as the lens is moved closer to the focal point, the height of the image increases, along with the magnification. This is confirmed with our experiment as we saw the image getting gradually bigger as we moved towards the focal point. 

As step 8 indicates, we used a ruler to cover up half of the lens. Our initial guess was that only half of the image would be projected onto the page. This conclusion was wrong however. As the image from step 8 shows, the entire image is still present at the same height as it would be without the ruler. The only thing affected by the ruler is the intensity of the light that was viewed. As the ruler covered more of the lens, the image got dimmer. This is because the ruler only blocked some of the light from entering. Less light going through meant that the brightness of the picture will be less as well.

For the next step, step 9, we moved the lens inside of its focal point. When this was done, no matter how close we got to the lens or further away, we could not see the image. Once the lens was viewed directly, as the image shows, we were able to see the image. This image changed from the original image in that it is now erect and no longer real but virtual. 

After all the data was collected, the relationship of image distance versus object distance was then graphed and compared. 

As the picture shows, this relationship is an inverse one. This suggests that when an object is placed a certain distance from the lens, the image distance goes to infinity (much like how telescopes work!).

Next, a graph of inverse image distance vs. negative inverse object distance was plotted. This graph is shown below. 

This line suggests a linear relationship. The slop of this line was found to be .9965 and the y intercept was -.05283. This graphs shows a linear relationship of their reciprocals. This leads us to the conclusion that this is the basis for the 1/p + 1/q = 1/f equation.

Summary:

            Through this experiment, a number of results and characteristics of lenses were able to be observed. It was found that a when the image of a converging lens is real, the image is always inverted and goes through either magnification or demagnification. Once the image is placed within the focal point however, the image changed to become erect and virtual. It is also shown that the distance of the object and the distance of the image share an inverse relationship to one another and at some point the image distance will go to infinity.