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Diving masks often have lenses built into the glass for divers who do not have perfect vision. The lenses in a diving mask faceplate often only have a curved surfaces on the inside glass. Why is this design desirable?

I know that curving of inner surface of the lenses in the diving mask faceplate is so that diver can see clearly straight ahead while in underwater and in air. I want to know how the light travels when falling on the mask if it approaches the mask along the normal to the plane of faceplate, or at any angle $\theta$. Do we see a blurred image when the light falls at angle greater than some specific $\theta$?

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The answer is purely a matter of engineering and cost, I think. I've bought prescription masks in the past, and they are as you say: basically a stock faceplate with a correcting lens attached to the inside face. This allows the manufacturer to stock a standard (flat) faceplate and pull units from stock to build specialized prescription items.

Now, if you were actually asking why or how the curvature is selected, then you need to read any introduction to simple lens design. Blur, for example, can be caused by a number of factors, one of which is extreme off-axis object position.

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