Experiment 12: CD Diffraction

In this experiment we used a laser with a known wavelength to measure the width of the grooves in a compact disk. To do this we first set up the experiment with a laser at an angle of about 45 degrees to the normal of the surface of the disk. As the laser became hit the surface of the CD the laser beam would diffract and split into multiple beams of light. The reason why we decided to place the CD at a 45 degree angle was so the the diffracted beams could be shown a white board that was facing parallel to the laser beam before hitting the CD. The picture below better illustrates the apperatus.

Using this setup we measured the distance from the CD to the white board to be 0.070 meters +/- 0.0005. We also know that the wavelength of the laser to be 670 nm +/- 0.10 and that the distance from the central maximum to the first maximum is 0.028 m +/- 0.0005. Using the equation y=[m*(lambda)*x]/a where x = 0.7 meters, lambda = 670*10^-9 meters, m = 1, and y = 0.028 meters we can solve for (a) (the slit spacing in the CD). As a result we found that the CD was 1.675*10^-6 meters. The accepted value for the slit spacing is 1.6*10^-6 meters which gives us a percent difference of 4.6%. This falls well within our percent uncertainty of 31%.

This experiment allowed us to find a real world application for laser diffraction and how it can be used to measure defects in CD spacing. With more precise instrumentation would could significantly decrease our percent uncertainty and difference to more accurately the CD's spacing. Also, in this experiment we made a small angle approximation in order to use our equation y=[m*(lambda)*x]/a. Uncertainty due to this approximation was unaccounted for but because of the small angles between the central and first maximums this uncertainty could be safely ignored.

Experiment 11: Measuring a Human Hair

In this experiment we used the a micrometer and a laser to measure and compare the thickness of a human hair. We began by using the laser and pointing it directly at the hair. We then measured the diffraction of light, the distance our image was from the object, and knew that the wavelength of our laser to be about 670 nm +/- 20 nm.

We then took three trials and on each trial we measured the distance from the hair to the image on a board, the node number, y_m, and lamda which we took to be 670 nm +/- 20nm. We then used the equation d=L*m*(lamda)/y to find the thickness of the hair d.

Trial	Length (L, m)	Node Number (m)	y (m)	Lamda (m, +/- 20 nm)	d (m)
1	1.68	4	0.063	6.7E-07	7.15E-05
2	2	4	0.076	6.7E-07	7.05E-05
3	3.62	3	0.11	6.7E-07	6.61E-05

We found after three trails the thickness of the hair to be about  6.9*10^(-5) meters thick. This fits within our estimation that the thickness of the hair would be between 1.7*10^(-5) to 1.8*10^(-4) meters thick. Using the micrometer we found the thickness of the hair to be about 7*10^(-5) meters which falls well within our trials for the thickness of the hair.

Experiment 10: Lenses

We began this experiment by measuring the focal distance of the lens that were were using. To do this we used the sun as our source and moved the lens until the light was focused at a single point. We then measured the distance from this point to the lens. We determined that the focal distance for our particular lens to be about 19.5 centimeters. We then shined an image through our lens and measured the object distance, image distance, object height, image height, and we calculated the magnification. We also stated whether or not the image was inverted.

Object distance (d_o, cm)	Image distance (d_i, cm)	Object height (h_o, cm)	Image height (h_i, cm)	Magnification	Type of Image
100	26.5	3	0.8	0.266	Inverted
80	28.5	3	1	0.333	Inverted
60	32	3	1.5	0.5	Inverted
40	43.5	3	3.5	1.16	Inverted
30	71	3	6.7	2.23	Inverted

We found that in every case the image was inverted, but when be placed the object within the focal distance no image could be seen. Only when you looked though the lens could you see an image in the lens. To describe the relationship between image distance and object distance we took the inverse of d_i and plotted it against the negative inverse of d_o. We then obtain the following graph.



This graph illustrates that the equation 1/d_o + 1/d_i = 1/f. However this graph shows that the focal length of our lens to actually be 20.9 cm long. This is a percent difference of 6.6% which is in a reasonable percent error when considering the error that went into this experiment. If we wished to decrease the percent error we could have used more accurate measuring equipment and have used a different method when it came to measuring the focal length of our lens.

Experiment 9: Concave and Convex Mirrors

In this experiment we gained an understanding of how concave and convex mirrors create an image. We began by looking into these two types of mirrors and analyzed the differences between them. After that we used simple geometry to draw diagrams that would help illustrate how each of the mirrors formed their images. The first diagram shows the image from a convex mirror.

The second diagram shows how we found the image in a concave mirror.

To create each of these diagram we began by drawing a line from the object to the center. Then we drew a line from the object parallel to the optic axis and then when the line hit the mirror we drew the line though the focus. Next we drew a line to the focus but when the line hit the mirror we then drew it parallel to the optic axis. Where all these lines intersected was our image. From these diagrams we could easily see where our image was relative to our object and out mirror and whether the image was erect or inverted. We were also able to tell that the image would have some magnification.