h a l f b a k e r yYou could have thought of that.
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Imagine a ball that changed the colour of the entire surface
facing you depending on the direction that you look at it. So
from
one angle it would look entirely blue, from another angle
entirely
red.
The ball is a thick shell of high refractive index material (e.g.
cubic zirconia). Supported
in middle of the shell (e.g. by thin
threads extending from the inner shell surface) would be a
small
polyhedron with each face a different colour. The shell would
act
as a meniscus lens focusing onto the face of the polyhedron.
For example, a cubic zirconia shell with outer radius of 8cm
and
inner radius of 2cm, would have a focal length at the middle of
the shell (if I have used the lensmaker's equation correctly).
Instead of different coloured polyhedron, the centre piece
could
be a globe of the world, thus providing zoomed-in globe. The
centre piece could be any interesting small approximately
spherical object.
Lensmaker's equation
https://en.wikipedi...ensmaker's_equation
[xaviergisz, Apr 30 2021]
Lensmakers Equation interactive visualization
https://demonstrati...LensmakersEquation/
Click the + icon by controls to enter numbers. Don't for get to invert R1 and R2. [scad mientist, Sep 23 2021]
Luneburg Lens
https://en.wikipedi.../wiki/Luneburg_lens
Example of GRIN that is somewhat similar to this idea [scad mientist, Sep 23 2021]
Spherical GRIN lens
https://iopscience....978/14/7/075705/pdf
PDF [xaviergisz, Sep 23 2021]
[link]
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I don't understand. Can you both magnify and change the spectrum viewed at the same time? |
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Not sure where you got 'spectrum' from. The colour you see is
just a magnified view of the surface of the centre piece (e.g.
a polyhedron with different colour faces). |
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I think my grandfather had a paperweight a bit like this - but
only a bit. I remember boggling at it as a small child. |
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thanks for the nifty title, I tried to guess what it was
about before reading it: |
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those little acrylic containers that coin vending machine
toys come in could, if cupped together )) have an air gap
and two separate rotateable lenses making such things as
a magnifier or a kaleidoscope. That would make the toy
even more fun. |
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X ray optics based on the dielectric effect could be used
for better CT scanning |
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That effect where you can see underwater if your goggles
have an air gap between the eyes and the water, but all
on land. Sort of: a layered stack of lenses with one layer
acting as an air gap equivalent (a GRIN lens). |
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[xaviergisz] idea might function even better as a GRIN
(Gradient refractive index) lens, with an imitation air gap
between (((o))) layers |
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If the spherical shell was left empty it would have
the interesting property of inverting images at any
distance without distortion. |
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This would make a cool outdoor sculpture without
the risk of focusing sunlight onto a point and
burning, blinding etc. The sunlight is focused safely
into the direct centre of the spherical shell. |
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^ That black box, copper pipe solar sink is going to look lovely with some glass snails randomly tracking across the collector surface. |
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[wjt], yep, this would work as an omni-directional solar
concentrator. The only problem being the enormous amount of
high refractive index material that would be needed to make
it in a decent size. |
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As [beanangel] noted, this invention could be done with GRIN
(gradient refractive index) layers. Doing this might make the
shell thinner and more practical. |
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// if I have used the lensmaker's equation correctly // No
one else said anything, but I'm going to go out on a limb
and say I don't think you are. As I apply the equation for
your example:
n = 2.15
R1 = 8
R2 = 2
d = 6
focal distance is -4.98. |
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To make sure I was getting the signs right, I put these into
the Wolfram Alpha lens equation [link], and it makes a nice
drawing of the lens. It only shows a slice of your sphere,
but this make it clear that this is a negative meniscus lens,
which will spread parallel rays, not focus them. |
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Argh, you're right [scad mientist]! |
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The focal length is measured from the middle of the lens (is at
3cm), so a focal length of f=5 would put the focal length in
the centre of the sphere. But the focal distance is indeed
f=-5. |
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Looks like a gradient refractive index is the only way to
salvage this idea! |
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I'm not sure about the details of a gradient refractive index
lens, but I'm pretty sure that it's impossible to create a
rotationally symmetric sphere that focuses parallel beams
of light at the exact center of the sphere. It's easier to
realize if you think of a point light source at the focal
point. The light is going in all directions from the center of
the sphere. If the sphere is rotationally symmetric, there
is no reason the beams of light would bend at all to go
more one direction than any other. |
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The above thought experiment does not preclude creating
a spherical lens that focuses parallel beams on the surface
of some smaller sphere so that light from any one direction
focuses on a the point of that inner sphere closest to the
direction of incoming light. If such a thing were possible,
it might have similar applications to this, but I don't
actually have any confidence that such a device is
physically possible either. A Luneburg lens is an interesting
example of a GRIN that is approaching what we're talking
about here. See cross section diagram in [link]: to focus
on a point less that half way through the sphere would
require the rays to bend much more tightly than in that
diagram, and it is clear that parallel rays hitting the right
and left edges (almost tangent to the sphere) cannot
possibly bend back to a point closer the light source than
the center of the sphere. If they did, the would cross
through the inner focal sphere. |
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//...I'm pretty sure that it's impossible to create a
rotationally symmetric sphere that focuses parallel beams of
light at the exact center of the sphere.// |
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Yep, for a perfect lens with a focal point at the centre, I
agree it wold be impossible. The paper I have linked to has
an equation to describe a Gutman lens which shows that the
refractive index of such a lens would need to be infinite. |
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However, my idea doesn't require a focal point in the exact
centre, and only requires a focal region. |
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Still only the manipulation of two variables, material and shape. |
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