135
edits
Changes
Jump to navigation
Jump to search
Line 37:
Line 37: + + + + + + + + + + + + + + + + + + + + +
Lens Assembly Structural Analysis (view source)
Revision as of 17:20, 17 December 2009
, 17:20, 17 December 2009no edit summary
where <math> M _1 </math> is the size of the object and <math> M _2 </math> is the size of the image.
where <math> M _1 </math> is the size of the object and <math> M _2 </math> is the size of the image.
By repeating these calculations for all lenses in the lens assembly, a final image magnification could be calculated.
Unfortunately, there were problems with this approximation, namely that it uses the wrong type of light. This approximation assumes that the object is a physical thing, which would allow light rays to leave it from any angle, allowing the required light rays shown in the illustration to pass through the lens. However, the light used is collimnated laser light, meaning that all the light rays are parallel when they enter the lens assembly. Therefore, this approximation is invalid.
== Second Iteration ==
(Illustration pending)
If the light entering the lens assembly is colimnated and enters the , then the top and bottom beams (the only two beams needed to locate the image) will travel through the first lens parallel, and both will cross through the focal point. The size of the image will then be
<math> \frac{M _1}{f} = \frac{M _2}{L-F}</math>
which can be expressed as
<math> M _2 = \frac{L-F}{F} M _1</math>
Using the same logic as the first iteration, this magnified image can be treated as the object for the next lens. This approximation has the advantage of being very simple, mathematically, while also being more accurate for collimnated light.
Unfortunately, that approximation cannot be used. Because the light is collimnated, we must instead follow the paths of the beams as they are deflected through the lenses rather than simply treat the image as a new object. Worse yet, the light paths will almost certainly not pass through the focal point; rather, they will pass through some point aligned with the focal point. The rays will all pass through one certain specific point on the focal plane. This mst be approximated, and the math must be rectified to correct for this.
== Third Iteration ==
== Fourth Iteration? ==