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.
-- xaviergisz, Apr 30 2021

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]

I don't understand. Can you both magnify and change the spectrum viewed at the same time?

(+) if so.
-- 2 fries shy of a happy meal, Apr 30 2021


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).
-- xaviergisz, Apr 30 2021


I think my grandfather had a paperweight a bit like this - but only a bit. I remember boggling at it as a small child.
-- pertinax, Apr 30 2021


thanks for the nifty title, I tried to guess what it was about before reading it:

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.

X ray optics based on the dielectric effect could be used for better CT scanning

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).

[xaviergisz] idea might function even better as a GRIN (Gradient refractive index) lens, with an imitation air gap between (((o))) layers
-- beanangel, Apr 30 2021


If the spherical shell was left empty it would have the interesting property of inverting images at any distance without distortion.

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.
-- xaviergisz, Sep 20 2021


^ That black box, copper pipe solar sink is going to look lovely with some glass snails randomly tracking across the collector surface.
-- wjt, Sep 21 2021


[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.

As [beanangel] noted, this invention could be done with GRIN (gradient refractive index) layers. Doing this might make the shell thinner and more practical.
-- xaviergisz, Sep 22 2021


// 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.

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.
-- scad mientist, Sep 23 2021


Argh, you're right [scad mientist]!

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.

Looks like a gradient refractive index is the only way to salvage this idea!
-- xaviergisz, Sep 23 2021


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.

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.
-- scad mientist, Sep 23 2021


//...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.//

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.

However, my idea doesn't require a focal point in the exact centre, and only requires a focal region.
-- xaviergisz, Sep 23 2021


Still only the manipulation of two variables, material and shape.
-- wjt, Sep 26 2021



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