Monday, August 9th, 2004

Today, Matt, Jon, Yaagnik, Danielle, and I revisited the topic of converging lenses. The impromptu venture into lens optics was inspired by Dr. Noé's description of the thin lens formula. We really got into discussing the image-distance relationship based on focal points. We talked about various scenarios such as comparing the distance from the lens of an object at 2f to the distance from the lens to an object at f. We discovered that an object at the focal point of the lens would be focused at infinity. We proved this by using the thin lens formula and setting the object distance equal to the focal length. The thin lens formula is shown here:




Since the object distance o equaled the focal length f, the image distance i equaled infinity.

Following this procedure, we derived the image distance, shown here:

This formula illustrates many things about the relationship of image and object distance. First of all, image and object distance are interchangeable in the formula. We can also make some statements about the object distance if the determinant is set equal to zero. If d is equal to 4f, then there is one focus. If d is less than 4f, then there are no focal points because the discriminant is negative, so the image distance is imaginary. If d is greater than 4f, there are two focal points. Once again, all of these statements can be made for either d or i.

After the derivation, Dr. Noé suggested that we use Danielle's carriage to illustrate the relationship between image size and distance from the lens. As the lens was moved so that the light source was between f and 2f and then outside 2f, we watched the image size dilating and then contracting as it approached the focus. Then, Dr. Noé suggested that we all take data points so that we could compare our values for the focal length of the lens. Here is our data:




So as you can see, our data varied slightly but was mostly correct.