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If I look through the microwave window I can see through, which means visible radiation can get out. We know also that there is a mesh on the microwave window which prevents microwave from coming out.

My question is how does this work? how come making stripes or mesh of metals can attenuate microwave radiation yet allow visible radiation?

Looks like an electrodynamics problem to me with periodic boundary conditions (because of the partitions on the microwave oven window). Is it discussed in any textbook?

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Try calculating the wavelength of the microwaves vs. that of visible light. –  user2963 Jun 2 '12 at 1:04
    
I won't make this an answer since zephyr has basically answered your question and he deserves any upvotes! Anyhow the wavelength of the EM waves used in your oven is 122 millimetres (according to Wikipedia) and as long as the holes in the grid are much less than this the grid behaves as a solid screen. –  John Rennie Jun 2 '12 at 14:48
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As John and others have said, the wavelength of the microwaves is very large compared to the size of the holes in the screen which allows the screen to act as a solid. Visible light has much smaller wavelengths and can pass through the holes unobstructed. It isn't possible to see (resolve) objects and features smaller than the wavelength of light (electromagnetic radiation) used so this is why the mesh works. See http://hyperphysics.phy-astr.gsu.edu/hbase/waves/mwoven.html for more details.

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