Focal length of a distorted window

[AaronBurr]

Homework Statement

1. What is the focal length of a dewar window distorted by a pressure difference? As a result of the pressure difference, the radius of the first surface of the window is R1 = 100 meters. The window is 3 mm thick, with an index n = 4 at l = 4 um.

Homework Equations

I think I can just use the thin lens equation? 1/f=(n-1)/R

The Attempt at a Solution

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My concern with using the thin lens equation is I'm not sure if a distorted window creates a lens? I know the focal length of a window is naturally infinite. If its bent does it then act as a lens? If not what formula do I use to prove it still acts as a window?Thanks for any help!

 

[CalcNerd]

This is an excellent problem in that it teaches you practical applications. Basically, you still have a window if you are about 1/2 way, inside of the focal length. And that is, from a practical aspect, a window. However, crank out the numbers and you find that if you are far enough away (and with a good magnifying device, not sure what is applicable, Cause I didn't crunch the numbers either, maybe binoculars, maybe a large telescope), you will see an image, because it will behave like a lens past its focal point (at that distance, you may have trouble finding the focal point, hence the calculation).