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I was watching a video where Physics Girl describes tricky spoons and how they shift reflections from the convex to the concave – in other words – how they flip the image. In the convex view one’s image is upside down, in the other the concave, one can be viewed upright (though remember its a mirror and one is still the wrong way round despite the distortion.) Its a good video and one that poses a few questions as to the reality of nature.

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The Physics Girl with her tricky spoon!

What intrigued me was the explanation of what would happen if one were to observe one’s image as it shifted from the convex through to a flat plane view (eg a normal mirror perspective) before shifting further to the convex.

The general consensus was that an image would rotate in order to right itself the right way up.

Very luckily I had been eating while watching the video and had a spoon at hand, so I cleaned this and proceeded to test the scenario as per the video – and what in fact happened in my expereince is the image – when one gets much closer to the concave side of the spoon (as the Physics Girl was saying bring your eye right up to the spoon itself and observe that your eye is upright) the image becomes doubled, before becoming a resultant clearer upright view of the finger itself. I will explain a bit more in depth on this. Here’s Physics Girl’s video on the matter first…

Having the spoon at hand enabled me to think on this and I devolved a further discovery. If one stays a distance from the spoon one’s image is indeed upside down, but instead of getting closer to it and observing one’s eye (or nose whatever) becoming upright, use one’s finger instead.

At this stage I must add I was using a mere desert spoon – not a soup spoon, I’m not that exquisite a culinary artist as others are – thus it was a desert spoon I used and the effects were slightly different to a true soup spoon. How do I know that? Well as it turns out I do have just one soup spoon, I dug it out – its a tool rather thus very scratched as I use it for decorating – and its also extremely tough because I use it as a lever for prising open paint tins!

Holding up the spoon, I moved slowly my finger towards the concave surface and watched this image of the finger (at the same time keeping a close observation on my own upside down image.) What I saw as a result was my image upside down BUT my finger the right way up!

That happens once it is very close to the concave side of the spoon. That as as well as blurred images of both upside down and right side up images of the finger – in fact three images of flipped or inverted as well as the normal version!

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The shapes of the concave and convex spoon surfaces. Source: Science Source

What I found was the placement of the finger does in fact illustrate (without special graphics, maths, whatever) what actually happens to an image when it shifts from the concave to the convex.

The image itself is not clear though, its blurred, but one can discern what it is meant to be. The doubled views (the concave and convex views of the finger) in fact slowly disappeared and one’s finger became as if it was being observed on a convex surface instead.

This shows in terms of progressing towards a flat image (eg a mirror) the image should then become more defined (the blurry bits should go away – rather they should disappear into the now clearly defined image of the finger.)

There was some discussion in the video whether the image actually rotated as it transferred from a concave to a flat then to a convex surface – and there seemed to be some consensus that the image must rotate in order to fully render as upright.

From my tests as the short video above shows, I don’t think it rotates at all. Its rather convoluted because of the various angles the image can be seen. At one point (almost the end of my video) a quite perfectly formed fingertip can be seen – as shown below.

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The brief second or so when a well formed image of my fingertip can be seen on the spoon, rather looking as if it is on the convex plane and not the concave.

What actually happens is nature becomes very confused (because this isn’t a normal representation of reality) and it tries to pull the image together according to how these are seen in the concave mirror.

In my view it ultimately it pulls the image fully into shape and one gains a perfect flat mirror representation of it.

Something else I found too was the fact it proved difficult to watch the monitor on the back of the camera (because I wanted to keep the spoon in range and in focus) and also visually watch it too – because the image I saw and the image I was seeing on the monitor were two very different ones!

It means if there’s two people present they wont be seeing the image the other person sees! Its a bit like the well known fact a rainbow is totally unique to each observer and its just one of those quirks of nature which makes doing these kind of experiments considerably more difficult than one thought.

Another thing I found is the convex position is less exciting than the concave view. Its interesting yes in how it distorts but it just doesn’t have the same morphing as the concave one. In other words one cannot do much with the convex image or learn very much from what is happening.

Its not to say convex mirrors are rubbish. They are indeed useful and there are quite a few applications of these such as mirrors placed at strategic locations at road junctions to give people a better view of what is about, and they are also used in car wing mirrors to give a good view of what is happening behind and to the sides of one’s car.

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Convex mirror placed at a road junction to expand a motorist’s field of view. Source: Pittman Traffic (Note: The site no longer hosts this image thus it is now the Internet Archive.)

I tested the reflection with the soup spoon and also a ladle. The way it very clearly worked on the desert spoons did not work so well on these. The soup spoon and the ladle are more perfectly circular in shape and especially the concave/convex sides are more profound than the desert spoon – thus the effect works somewhat different. In fact it was almost impossible to get the images that could be got with the desert or table spoons.

The desert/table spoons were the only ones to show clearly what happens in terms of the stages of the image as it progresses from a perfectly concave reflection towards a flat mirror view and this is because the desert/table spoons are obviously not perfectly concave.

In terms of naturalness there isn’t anything too reasonably perfect convex or concave in nature. Googling the web it seems there’s practically nothing. Apparently the internet doesn’t think concave and convex is anything other than an artificial adjunct!

Perhaps the most perfect example of a concave/convex image in nature would be the bubble (or half bubble if its on a surface of some sort, like rain that has landed on the surface of a pond.)

Here are some other somewhat sort of examples I also thought of…

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The Brocken spectre. The image can be seen from most mountains in the right circumstances. Source: Germany is Wunderbar

The Brocken spectre is a sort of distorted convex view, curiously with the concave bit of the image ironically the right way up. This is because the image is projected from behind and sort of low down in elevation onto a cloud or mist. The resulting halo is one of the few examples of an almost perfect circle in nature (besides bubbles and whatever else) and the spectre is a fascinating phenomenon if one is lucky enough to be able to see it.

The phenomenon of gravitational lensing or places where space illustrates its curvature – as per Einstein’s relativity (for example the way light bends around the edges of planets) are perhaps some of the other examples nearest to concave/convex perfection in nature.

The lowdown of distortions upon camera lenses

When one looks at the various issues behind these concave/convex lensing effects, one must wonder about camera lenses. In fact its not just spoons that can present difficulties therefore those are not too much of a unique situation.

In fact the specialist industries such as camera and lens manufacturers without a doubt know images can become blurred or grossly distorted therefore its not just physics people that have the notion of this!

Its actually a wonder anyone can capture fantastic images with their cameras given these huge distortions!

A camera of course records the final produced image upside down and it is the software (in a dslr) that turns it the right way up (or alternatively it is etched upside down on a film strip but printed the right way up when processed.)

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Zoom lenses use both concave and convex lens thus manufacturers have to employ clever mathematical ingenuity to ensure the image stays constant and doesn’t suffer any distortions.

In designing for cameras (and a good reason why smartphones have barely anything than a basic camera lens) there’s a whole gamut of distortions and permutations that have to be considered.

The fact is no matter how well a lens is designed, there is nearly always going to be some barrel distortion and images will often be slightly distorted or more blurry towards the edges of the picture. There’s also chromatic aberration and other deficiencies usually seen in older lenses – however with technology and the use of special lenses and filters those sort of artifacts have been reduced.

The fact there is distortion in lenses is also why it has been technologically difficult to produce efficient superzooms until recently. The Tamron 18 – 270 was one of the first to break new ground in terms of the sheer optical difficulties rendering images across a vast spectrum of distances from the wide angle to the zoom end.

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My Tamron 18-270 zoom lens. This is the second generation (2010) of Tamron’s earlier ground breaking model.

Optical distortions can be corrected almost entirely but only with the most expensive professional grade lenses (such as Canon’s ‘L’ white lens) series or those used in astronomy. This is exactly what Physics Girl was saying in her video when she pointed out how astronomers and observatories (such as Hubble) have to compensate for natural distortions in space.

When I said smartphones (or even the most basic point and shoot cameras) do not have any complex lens systems, they can at least produce depth of fields or other permutations artificially – it is the software that is doing this not the lens. Alternatively it could be the smartphone has a special lens attached to it to achieve these creative optics.

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Samsung smartphones with three cameras (usually these are normal, depth of field, and a telephoto lens.) Some have four.

In terms of old fashioned point and shoot cameras it would be the processing side of things where any special effects or distortions were made, unless one happened to have a bottle, or other lens, magnifying glass or whatever that could put in front of the camera to achieve certain desired effects. Of course one can do this with digital cameras too and bring the processes in at the start rather than do it later in Photoshop or Gimp.

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