Creative Solutions to Impossible Engineering Problems

This whole lecture series is by Dan Gelbart who is a Fantastic Educator and generally a very smart dude. He has several extremely high value videos on YouTube that teach more in a few hours than most people get out of their entire college career.

Pursue the Impossible

Pursing Ideas that are thought to be impossible is often how new industries are born

Being Clever is learning how to investigate, and gain insights from "flukes"

Examples

Chromatic Aberration

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A Lens that is made from a clear material uses the geometry of the lens element to concentrate the light that is passing through it. Since light is made of different wave lengths, the light of each color concentrates to a different plane. The amount of dispersion that is observed is dependent on the material properties of the optics.
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High Quality Glass can improve how "tight" of an image you can get by limiting how much chromatic dispersion occurs. But all materials bend light in the same way.

It's difficult to correct this with Reflective Optics like a mirror though because the mirror needs to be 4x more accurate than the equivalent lens.

If instead you make the inverse lens(at a weaker magnification, but change the speed at which light disperses through it, you can correct for the chromatic aberration without reducing magnification.
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Sources

Creative Solutions to Impossible Engineering Problems
A Magnet that attracts aluminum and copper