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I've been thinking lately about bubble helmets used by many cosmonauts and astronauts. Almost every space suit I've seen features a curved helmet, even the Gemini astronauts.

But a curved piece of glass/plastic should focus sunlight somewhere beyond the convex side, maybe with a little spherical aberration, but potentially still dangerous. We all know what a magnifying glass does when held at the right distance in open sunlight.

Now obviously, no space traveler has suffered this terrible fate, so I will phrase the question these ways: Why doesn't focused heat happen through the curved visors of spacesuit? Why aren't bubble helmets dangerous in direct sunlight?

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    $\begingroup$ I imagine the focus of the sunlight passing through the curvature is substantially behind the person's face. $\endgroup$
    – Jerard Puckett
    Commented May 5, 2016 at 19:49
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    $\begingroup$ There is no focussing for light passing through a curved piece of glass, unless the front and back surfaces have different radii of curvature. $\endgroup$
    – DJohnM
    Commented May 5, 2016 at 21:00

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A curved piece of glass/plastic should focus sunlight somewhere beyond the convex side

This is true; however it requires that the curvature of the two sides of the piece of glass be different

When the Lens Maker's Formula http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/lenmak.html is applied to acurved piece of glass with the two identical radii of curvature, the focal length is infinite...

This image

enter image description here

shows the various categories of converging or diverging lenses, based on the radius of curvature of the two surfaces. Note that a lens with the two surfaces curved and parallel is notable missing...

Curved surface mirrors are of course a different matter. This hotel http://www.dailymail.co.uk/news/article-1315978/Las-Vegas-hotel-death-ray-leaves-guests-severe-burns.html found out the danger of a south facing curved glass wall...

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    $\begingroup$ I see, but keep in mind that a spherical helmet will have different radii, if the thickness is kept constant. The inside radius will be slightly shorter than the outside radius. I plugged in 20 and 21 cm into that formula you linked to and got a focal length of 8.4 m, so it seems the astronaut's head is safe. $\endgroup$
    – DrZ214
    Commented May 5, 2016 at 22:45

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