Math Photo: Windowsill Contours

Published by patrick honner on

I have an adjustable screen for my window, the kind you expand horizontally to fill up the windowsill.  It’s somewhat effective at keeping bugs out of the house.

When it’s not opened all the way up, the two layers of screen overlap in the middle.  Depending on the angle you are looking from, you can see some cool images.

At this angle, for example, I see a contour map of a function of several variables.

I wish I understood where the curves come from!

patrick honner

Math teacher in Brooklyn, New York


Jinjer Markley · September 16, 2012 at 9:45 am

The pattern is an optical effect called Newton’s Rings, and now that you know that, you can look it up in Wikipedia.

You can also see Newton’s Rings in bubbles, oil films, two panes of glass pressed together and other close surfaces. Newton’s rings work because of light interference from light bouncing off of two very close surfaces. Basically, the light doesn’t scatter enough in between the the surfaces to get out of alignment, so the wavelengths line up enough to either cancel each other out or amplify each other. The dark bands are where they cancelled, the light bands are where they amplified.

There may be something slightly different going on with screen, which transmits more light than it reflects. Perhaps there’s some kind of diffraction grating effect happening.

I always notice this effect with pieces of organza. I’m a clothing designer, and whenever I play with organza, I want to make a dress with a pattern of Newton’s rings. Moire fabric is permanently marked with Newton’s rings, which looks fascinating because it changes as you look at it from different angles. (hmmm,, that supports the diffraction grating hypothesis..moire is made from faille, a ribbed fabric.) Neat how physics intersects with any path of life, isn’t it?

    MrHonner · September 16, 2012 at 10:28 am


    Thanks for satisfying my curiosity, and for providing such a nice explanation. What a cool effect!

    And thanks, too, for making the connection to fashion and design. Always cool to hear of new ways people are using mathematical ideas to create.

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