The first photograph of a fourth order rainbow
 A third-order and fourth-order rainbow can be seen at the center of this photograph. The tertiary and quaternary rainbows appear on the sunward side of the sky, rather than the opposite side of the sky,
as is the case for primary and secondary rainbows. This is the first picture of a quaternary rainbow in nature, and the second picture ever of a tertiary rainbow.

"A fourth order creation.

It's like fourth derivatives.

Actually... the equations of general relativity are second order in terms of derivatives.

But the second order of derivatives in terms of something called the metric tensor on the space–time continuum.

The idea of the fourth order, equatian, is not new.

But nobody's found anything that really looks good."

John Nash

A Fourth Order Fresnel Lens at The St Augustine Lighthouse museum.