Can Your Eyes Make Sense Of These Images?
Your new mirror and poster are technically a work of catoptric anamorphosis; anamorphosis is any optical trick involving viewing something that’s presented in a distorted perspective, and catoptrics describes the science of reflections and images that are seen when viewed with a mirror. It’s also the subject of the very earliest book on the science of optics, Euclid's Catoptrics, written in 280 BCE. Setups like yours, where a circular mirror is used to view the real image, are first known in Chinese illustrations of adult content from the 16th century. In Europe, mirror landscapes and portraits became super popular for home viewing in the 18th and early 19th centuries.
That’s the history, what about the science? Optically, what’s happening here? The key to how the setup works is in the concepts of angle of incidence (the angle at which the light hits the mirror) and angle of reflection (the angle at which it bounces off). The law of reflection tells us that these will be the exact same angle – light rays bounce off a mirror at the same angle that they hit it. This is true for your circular mirror just as it is for a flat one, but due to the convex nature of the circular mirror, there’s a greater divergence of the light beams when they’re reflected, which causes the image to be distorted; it’s the same principle as the skewed reflections in a fun house mirror. With your setup, the anamorphosic images are presented in an already stretched form, so the distortion actually returns them to the “normal” perspective and you see a regular image again!
And if you have a really, really solid grasp of how diagram out the intersecting rays, you can move beyond 2D drawing and make 3D objects as well! Artist Jonty Hurwitz makes 3-dimensional sculptures that are meant to be viewed with catoptric anamorphosis. He specializes in wildly distorted children chasing butterflies, frogs on lily pads, and giant grasping hands, which look like stretchy blobs until viewed in the circular mirror. And if you’d like to understand the process of making those 3D anamorphic sculptures, with diagrams of the full optics involved, take a look here.
So how the heck did these images save people from accusations of treason? Well, back in the Renaissance, when Europeans first became aware of the effect, it was considered a code: the Italian artist and mathematician Pietro Accolti actually used anamorphic drawings to encrypt diagrams of fortresses he visited in foreign countries, and anamorphic messages were used by spies to send messages.
That brings us to this artifact in the West Highland Museum of Scotland: a fancy serving tray with a weird streaky design on it. In 1746, Bonnie Prince Charlie led a revolt against English King George II. He was defeated at the Battle of Culloden and went into exile, but still had a ton of fans, who had to keep their allegiance secret - supporting him was treason, and could be punished by death! So how do you and your Bonnie Prince-loving pals keep up the appearance of being loyal to the king you hate? With this mirror anamorphosis serving platter. When you’ve got a bunch of random nobles over for a party, it’s just a plate to hold drinks. But the minute they leave and you’re with people you know will keep your secret – you plunk a mirror in the middle of the tray, and the Bonnie Prince’s image appears as if by magic! You can toast to his health, and curse King George.
While we can’t claim it will be useful when you engage in royal warfare, we’re very excited to have been able to provide you with special radiant graph paper, to make your own anamorphic images. And we’d love to see what you come up with. Tag #curiositybox on Twitter and Instagram, show us what you’ve made!