[Little Demos] 01 – Wine Glass Einstein Rings

Originally written for a friend in late 2016. Updated in 2020 to remove some inaccuracies and humble brags.

Catpic used under (cat’s) permission.

Do you know that thanks to some convenient optics, we can demonstrate a “gravitational lens” could be demonstrated in my living room (without myself eating 1024 kg of food)?

We will be using a light sources and a wine glass. That’s all.

Demonstration Setup
Close-Up at the “lens”. Ideally, you get a piece of glass with only this part…

It’s then easy – and somehow intuitive, unlike most of General Relativity – to observe an Einstein Ring for yourselves.

Place your light receptacle (eyes, for example) right above the opening of the cup, and shine light upwards, from the bottom.

I managed to get one like this.

More GIF! A blackhole passing in front of a star cluster. Rendered in Space Engine 0.97.1

We can make some baby mathematical steps to justify this “ring”, though. For simplicity, we treat the cross-section of a wine glass as the shape below: flat edge on the bottom, and circular on top. Further, we assume the refraction coefficient stays uniform throughout the lens.

Rotational symmetry transforms the disk into a ring.

An earlier FWNotebook article discussed the “effective optics” of a Schwarzschild BH, as done in most introductory GR cources. Of course, the resemblance stops somewhere, as geometric optics in no way provide fully analogous models of general relativity.

On the astrophysical scales, we have well-established evidence of the GR Einstein rings, like this picture, where the lens and background objects are two massive galaxies, respectively.

Source: Wikipedia

FW, 2016