Changes

== Data Recording ==

== Data Recording ==

In our lab experiments, we must measure and record a collimnated light beam. This is done by shining the beam into a camera (the Casio Exilim EX-F1) and photographing the results. In order to properly interpret the information, it is necessary to understand the effects of the lenses on the image. This is incredibly difficult because of a number of factors. Most importantly, we have no way to directly measure the camera and acquire most of the information that we need. The lens assembly on the Exilim EX-F1 cannot be removed, so we cannot replace it with a custom- built lens assembly of known dimensions. All we can measure are a limited number of lengths, and we know the ranges of F-numbers and focal lengths. In order to solve this problem, a number of significant approximations and generalizations must be made. While the actual lens assembly contains twelve disparate lenses, our approximation has only four, and unlike the actual assembly, our approximation contains only perfect, idealized spherical lenses. These approximations would certainly affect our final results, but most likely not enough to severely skew our results.

In our lab experiments, we must measure and record a collimated light beam. This is done by shining the beam into a camera (the Casio Exilim EX-F1) and photographing the results. In order to properly interpret the information, it is necessary to understand the effects of the lenses on the image. This is incredibly difficult because of a number of factors. Most importantly, we have no way to directly measure the camera and acquire most of the information that we need. The lens assembly on the Exilim EX-F1 cannot be removed, so we cannot replace it with a custom- built lens assembly of known dimensions. All we can measure are a limited number of lengths, and we know the ranges of F-numbers and focal lengths. In order to solve this problem, a number of significant approximations and generalizations must be made. While the actual lens assembly contains twelve disparate lenses, our approximation has only four, and unlike the actual assembly, our approximation contains only perfect, idealized spherical lenses. These approximations would certainly affect our final results, but most likely not enough to severely skew our results.

== Inside the Lens Assembly ==

== Inside the Lens Assembly ==

We know logically that the image will not be compressed or stretched by passing through the lenses, as this cannot be seen in photography. First, therefore, we will track the center of the image as it passes through the lenses. This is done using the equation

We know logically that the image will not be compressed or stretched by passing through the lenses, as this cannot be seen in photography. First, therefore, we will track the center of the image as it passes through the lenses. This is done using the equation

<math> \arctan{\tan{\theta_p}-{{X_p}/{F}}}</math>

<math> \arctan{\tan{\theta_p}-\frac{{X_p}{F}}}</math>

== Aperture ==

== Aperture ==