Difference between revisions of "Problem Set 1"
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For this question, you will need to stop by the lab and make a few measurements of lenses. The whole thing should take about twenty minutes. | For this question, you will need to stop by the lab and make a few measurements of lenses. The whole thing should take about twenty minutes. | ||
| − | #Measure the focal lengths of the lenses marked A, B, | + | ===Part a — measuring lens focal length=== |
| − | + | #Measure the focal lengths of the lenses marked A, B, C and D | |
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| − | + | * What is your estimate of the focal lengths each lens? | |
| − | * What is your estimate of the focal lengths | + | |
===Part b=== | ===Part b=== | ||
| − | * What is the relationship between d<sub>1</sub>, d<sub>2</sub>, and H? Make a plot of your measurements that shows this relationship. | + | * What is the relationship between d<sub>1</sub> (the distance from the object to the lens), d<sub>2</sub> (the distance from the lens to the image plane), and H (the height of the image formed)? |
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| + | Measure this relationship using the 50mm lens, illuminator, and object provided in the lab. Make a plot of your measurements that shows this relationship. | ||
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| + | To make the measurements: | ||
| + | #Turn on the LED illuminator — make sure the current is below 0.5 A at all times. Ask a TA if you are unfamiliar with the power supply settings. | ||
| + | #Log on to the computer and run IC Capture. This will bring up a window of the live image from the CCD camera. | ||
| + | #Move the lens and imaging target to produce a focused image (the target has <b>50 line pairs per inch</b>). | ||
| + | #Measure the distance d<sub>1</sub> from the imaging target to the 50mm lens, the distance d<sub>2</sub> from the lens to the screen, and the height H of a feature on the image. | ||
| + | #Repeat this measurement for several values of d<sub>1</sub>. Make enough measurements to get a smooth plot. | ||
==Question 2== | ==Question 2== | ||
Revision as of 02:13, 9 September 2009
Contents
Question 1
For this question, you will need to stop by the lab and make a few measurements of lenses. The whole thing should take about twenty minutes.
Part a — measuring lens focal length
- Measure the focal lengths of the lenses marked A, B, C and D
- What is your estimate of the focal lengths each lens?
Part b
- What is the relationship between d1 (the distance from the object to the lens), d2 (the distance from the lens to the image plane), and H (the height of the image formed)?
Measure this relationship using the 50mm lens, illuminator, and object provided in the lab. Make a plot of your measurements that shows this relationship.
To make the measurements:
- Turn on the LED illuminator — make sure the current is below 0.5 A at all times. Ask a TA if you are unfamiliar with the power supply settings.
- Log on to the computer and run IC Capture. This will bring up a window of the live image from the CCD camera.
- Move the lens and imaging target to produce a focused image (the target has 50 line pairs per inch).
- Measure the distance d1 from the imaging target to the 50mm lens, the distance d2 from the lens to the screen, and the height H of a feature on the image.
- Repeat this measurement for several values of d1. Make enough measurements to get a smooth plot.
Question 2
In lab, you are going to build a microscope. As discussed in lecture, a single lens can act as a magnifier. (You have certainly used a magnifying glass to look at something small.) But all modern microscopes that achieve very high magnifications use multiple lenses in series to make an image. This is clearly a much more expensive design. Why not use a single lens as a high-magnification microscope?
- List three potential problems with a single-lens, high-magnification microscope design. Explain the problems in few sentences and a simple sketch.
HINT: Use the information about the behavior of light in that was presented in lecture. Think about the underlying assumptions of geometric optics. Under what circumstances in a real microscope design would each assumption be violated? How do these violations impact the final image? (If you are stuck, go back to the lecture slides and take a close, logical look at each assumption. Where does each assumption break down? What is the effect of this breakdown in the assumption?)
Extra credit
For each problem you identify with a single-lens, high-magnification microscope design, explain in a sentence or two and a brief sketch how multiple lenses might ameliorate the problem.
Question 3
Consider the two-lens system shown in the figure below, where the rectangle on the left represents an unspecified lens of focal length f1 separated by 0.5 cm from another lens with focal length of 1cm. Find the value of f such that all the rays incident parallel on this system will be focused at the observation plane.
