Focal Length Question

[bvy]

What would be the focal length of a hemispherical (half ball) lens of radius r? I'm only finding details related to ball lenses and plano-convex lenses. Thanks.

 

[Leigh B]

A hemispherical lens is just a plano-convex lens of appropriate dimensions (disregarding distortion & aberrations).

- Leigh

 

[bvy]

I see. The lensmaker's equation with radius of curvature of zero (?) for the flat side and, and r for the hemispherical side. I just need to find the refractive index of clear acrylic.

 

[Leigh B]

I just need to find the refractive index of clear acrylic.

Google it.

- Leigh

 

[Helen B]

I see. The lensmaker's equation with radius of curvature of zero (?) for the flat side and, and r for the hemispherical side.

The radius of a flat surface is infinite, not zero (so the reciprocal of the radius is zero). You may be better off using Gullstrand's equation for a thick lens rather than the lensmaker's equation, which is only intended for thin lenses.

Best,
Helen

 

[bvy]

Thanks Helen. I knew there were a few equations, and I think that's the one I need. (And, yes, I was actually referring to the reciprocal term in the lensmaker's equation. I misstated that.)