Designing a planocovex PMMA lens

[Antraxius]

As an electrical engineer, I am an amateur on optics, but I really could use some help.
I am making a lens of PMMA, 2D. To 'convert' a rotary movement into a sweep.

The lens needs to be 120mm long, with its focus at a max distance of 80mm
the light traveling out of the lens needs to be parallel with the main axis of the lens.

To clarify, I’ve uploaded an image.

Could someone help me calculating the curvature of the lens?

 

[Andy Resnick]

As an electrical engineer, I am an amateur on optics, but I really could use some help.
I am making a lens of PMMA, 2D. To 'convert' a rotary movement into a sweep.

The lens needs to be 120mm long, with its focus at a max distance of 80mm
the light traveling out of the lens needs to be parallel with the main axis of the lens.

To clarify, I’ve uploaded an image.

Could someone help me calculating the curvature of the lens?

If I understand you, you simply want to place the center of rotation at the focal point of your lens; any focal length lens will work, the diameter of the lens will set the angular range of scan- not sure why you need to calculate the curvature. So an 80mm focal length lens of diameter 120mm will work, although that's a fast lens and you will have significant aberrations. Making the lens faster (focal length shorter than 80mm, maintaining a 120mm diameter) will increase the aberrations.

 

[Antraxius]

That is correct, the measurements are set as a maximum. Since we have limited space available. I need to know the curvature because I am making the lens myself. Using a CNC laser cutter, and the material isn't glass but PMMA which has a different n-index.

 

[Andy Resnick]

That is correct, the measurements are set as a maximum. Since we have limited space available. I need to know the curvature because I am making the lens myself. Using a CNC laser cutter, and the material isn't glass but PMMA which has a different n-index.

The lensmaker formula (lensmaker equation) is what you are looking for.