A Luneburg lens is a spherical lens with a focal point on its surface. It utilises a gradient refractive index. Luneburg lenses are used for various radio applications but, as far as I can tell, remain a curiosity for visible light.

I propose that the surface of a Luneburg lens be covered with an ultra-fine resolution map. Viewing the Luneburg lens from different angles would zoom into different parts of the map.

Unfortunately it's not quite that simple; the printing on the close side of the lens will obscure the zoomed in image. I have two potential solutions to this problem.

1. The black printing would be over printed with white printing. Thus the black zoomed in image would be partially obscured by the white overprint, but would still be visible.

2. The map could be printed with a circularly polarising filter. The Luneburg lens would be held against a mirror and, because circularly polarising filters do not allow reflected light to pass back through, the zoomed in image would be viewed unimpeded.

Alternatively this could be used as a simple animated toy.
-- xaviergisz, Jul 10 2016

Luneburg lens https://en.m.wikipe.../wiki/Luneburg_lens
[xaviergisz, Jul 10 2016]

Not a mirror http://4.bp.blogspo...rcbk/s1600/Fig1.TIF
A computer generated image of Luneburg Lens in one polarisation plane [wjt, Jul 13 2016]

Cool idea. It's probably easiest to just have the map on one side and leave the other hemisphere as the viewing window.

I wonder if you could embed magnetic particles in the glass without changing its optical properties, so that it could float within another sphere filled with liquid, and always point north.
-- mitxela, Jul 10 2016


Is the magnified image inverted?
-- 2 fries shy of a happy meal, Jul 10 2016


If I understand this correctly, it's cool. Looking at such a sphere would show you the magnified image of whatever is diametrically opposite your viewpoint on the surface of the sphere?
-- MaxwellBuchanan, Jul 10 2016


If the focal point is the surface and your printing on the surface, won't you interfere with the internal reflection?
-- wjt, Jul 11 2016


Actually, hang on a mo.

Thanks for waiting. Is it not possible, therefore, that we are actually living on a vast Luneburg lens, and that all our geography is 180° out?
-- MaxwellBuchanan, Jul 11 2016


A quick read through, and I agree that it seems that the lens magnifies what it is sitting on; the magnification depending on the size of the lens.
-- Ling, Jul 11 2016


Is there a Cliff's Notes guide to the optics here? My mind's eye is all confused by the optical complexity of what's being proposed. Maybe it needs a contact lens or something.
-- RayfordSteele, Jul 11 2016


Any lens alters what is on the otherside of the focal point. I though this lens is special because it alters whats between you and the focal point.

I rationalise this as a fun mirror but in the form of a lens.
-- wjt, Jul 12 2016


This would be very useful if you went to Luneberg.
-- pocmloc, Jul 12 2016


Or if you were trying to hide from Bill Lumbergh.
-- RayfordSteele, Jul 12 2016


I was imagining incorrectly. My fault was misinterpreting the Wikipedia Luneburg Lens ray trace diagram. I don't know what the image would be like if you silvered half of the lens.
-- wjt, Jul 13 2016



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