Previously featured was an article that derived a matrix formation of an equation for a thick lens. This matrix equation, it was said can be used to build a variety of optical systems. This will be undertaken using MATLAB. One of the great parts of using a matrix formula in MATLAB is that essentially any known parameter in the optical system can not only be altered directly, but a parameter sweep can be used to see how the parameter will effect the system. Parameters that can be altered include radius of curvature in the lens, thickness of the lens or distance between two lenses, wavelength, incidence angle, refractive indexes and more. You could also have MATLAB solve for a parameter such as the radius of curvature, given a desired angle. All of these parameters can be varied and the results can be plotted.

**Matrix Formation for Thick Lens Equation**

The matrix equation for the thick lens is modeled below:

Where:

- nt2 is the refractive index beyond surface 2
- αt2 is the angle of the exiting or transmitted ray
- Yt2 is the height of the transmitted ray
- D2 is the power of curvature of surface 2
- D1 is the power of curvature of surface 1
- R1 is the radius of curvature of surface 1
- R2 is the radius of curvature of surface 2
- d1 is the thickness of the lens or distance between surface 1 and 2
- ni is the refractive index before surface 1
- αi is the angle of the incident ray
- Yi1 is the height of the incident ray

The following plots show a parameter sweep on an number of these variables. The following attachment includes the code that was used for these calculations and plots: optics1hw

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