Your work on cylindrical lens has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
Your optional message or comment:
Distance from the back of the cylinder at which the band becomes thinnest, and diameter or circumference of the cylinder.
51.5 cm
8.2 cm diameter, 4.1 cm radius
Distances at which the band focused most clearly and distances at which the focus lessened slightly, in order from closest to furthest; widths of the bands at these distances; distance of source from 'front' of cylinder; description of the bands.
14.9, 19.8, 32.2
1.2, 0.8, 1.8
11.6 cm away, 4.6 cm below water surface
At 14.9 cm the band becomes clearly wider and brighter. At 32.2 cm the band is not as distinct as before.
The candle was supposed to be placed as far from the cylinder as possible.
The measurements you took are meaningful and actually quite interesting, and we'll try to interpret them. So you don't need to go back and reintrepret your data. However set this thing up again with the candle all the way on the other side of the room, and be sure you are seeing the things you were supposed to observe.
You give the distance of the candle from the cylinder, but you give the vertical position with respect to the water surface. The important position here would be with respect to the horizontal piece of paper. Again you don't need to redo your measurements, but when you look at the triangle, note how the vertical position of the candle influences the shape and size of the triangle.
The candle is the image, the most focused band would be the object. I believe that what you reported here indicates that image distance was 19.8 cm, object distance 11.6 cm. Is this correct? If so, what then is the focal distance (1/f = 1/i + 1/o)?
Width of the band; does the width of the band change linearly with position?
7.8 cm. Little shifts in wind affect the flame and hence the band. This makes measuring difficult.
That wouldn't be a problem with a distant candle; the close candle creates a large image, so flickers and movement would be magnified, while a distant candle would focus these distortions on a small region.
Past the point of narrowest focus, what happens to the width of the beam? How would you describe the region of space occupied by the beam?
The width begins to become bigger. THe region itself decreases in brightness.
The region is never a constant brightness. With every inhale and exhale regardless of how small or when the central heating unit kicks on the luminating power is affected. Any small movement disturbs the water which also affect how steady the light is.
Index of refraction of water according to your measurements; details of your analysis and your analysis of uncertainties:
I am so confused about this part. Snell's Law says the sines of the incident (theta I) and refracted angles (theta R) are in the same ratio of the velocities of the light beam. This is also equal to N2 / N1, where N is the index of refraction. Now am I supposed to use the triangle measurements for this? How do I then determine the angles, I am not familiar with the geometry that is needed. I did all the lab work for this assignment last Monday. I have all the measurements but I do not know how to calculate the angles.
The analysis in Class Notes #17 is relevant here, but the formula obtained there requires a distant source. The analysis for a nearby source would be more difficult; that analysis is difficult enough and we won't attempt the more difficult analysis.
However it should only take you a couple of minutes to determine the distance behind the cylinder at which a distant source focuses, and you can then use that distance to calculate index of refraction.
Index of refraction of second liquid.
I will calculate the index of refraction as soon as I can. I will go ahead and give the results of this part.
The candle was 10.1 cm away. The most distinct band was at 16.1 cm away and it had a width of 0.8 cm. The furthest point measured was 19.4 cm away and the width of the band was 1.6 cm. The closest point was 11.5 cm away and 1.6 cm band width.
The measurements of the observed triangle are 6.4, 6.7, and 3.4 cm.
Index of refraction of a stack of CDs.
Again the information I have (just to show you I have done all the raw work for the lab) is the candle is 10.0 cm away. At 35.1 cm the band is most distinct and the band width is 2.1 cm. The furthest point was 53.0 cm away and has a bandwidth of 3.0 cm. The closest observed point is at 31.1 cm and has a band width of 3.2 cm.
How could you use the information in the first part of the experiment, where you measured the triangle, to determine the index of refraction of the light?
The triangle was 8.9, 8.9, and 4.1 cm. The triangle was very distinct but when trying to trace the outline on to paper (so I could have it after the experiment was over) was difficult because I would block the light with my arm. Also the flame was dancing during certain parts of the measurement. My rough estimate is that the triangle has a measurement of 22.5 deg. This is from a protractor of sorts and not through geometric calculation.
Index of refraction using halfway-screened cylinder, comparison between halfway-screened and unscreened cylinder.
How long did it take you to complete this experiment?
The experiment itself took about 2 hours and 45 minutes.
Optional additional comments and/or questions:
This experiment was so neat. Initially when I read through the first couple steps I thought it would be very difficult to observe the beams and such. It was to my surprise that my jar worked extremely well for this experiment. I noticed that the vegetable oil made the edges of the bands to seem fuzzier. This is expected since it is not as clear as water. Thank you in advance for the help, I hate that it has taken me so long to get this up here. I wish it was complete. I am sorry!
I've had to ask you for a little more information and analysis, and to take another look at the 'triangle' and the focusing distance using a distant candle. If you can copy those parts of this document, with my notes and your responses, I think we can get this fixed up pretty easily.