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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
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
[xaviergisz, Jul 10 2016]
Not a mirror
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.
||Is the magnified image inverted?
||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?
||If the focal point is the surface and your printing on the surface, won't you interfere with the internal reflection?
||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?
||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.
||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.
||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.
||This would be very useful if you went to Luneberg.
||Or if you were trying to hide from Bill Lumbergh.
||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.