Problem Set 1

20.309 Spring Semester 2008 Problem Set 1 Due Thursday, February 12, 2009

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.

1. Measure the focal lengths of the lenses marked A, B, and C
2. Turn on the halogen lamp.
3. Move the screen to produce a focused image.
4. Measure the distance d₁ from the imaging target to the 75mm lens, the distance d₂ from the lens to the screen, and the height H of a feature on the image.
5. Repeat this measurement for several values of d₁

Part a

• What is your estimate of the focal lengths of lenses A, B, and C?

Part b

• What is the relationship between d₁, d₂, and H? Make a plot of your measurements that shows this relationship.

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 microscopes that achieve very high magnifications use multiple lenses in series to make an image. This is clearly a much more expansive design. Why not use a single lens as a high-magnification microscope?

• List three potential problems with this idea. Explain how the problems arise, using the information you learned about the behavior of light from lecture.

HINT: Think about the underlying assumptions used in geometric optics. Under what circumstances in a real microscope design is each assumption 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?

Extra credit

For each problem you identify with using a single lens microscope, explain in a sentence or two and a brief sketch how multiple lenses might ameliorate the problem.