# What happens in a microwave oven with hole in the shielding?

We have a question on cooking asking about the safety of a microwave with a hole in it. The question isn't totally clear whether the hole has actually penetrated shielding or just the plastic wall of the microwave, but for the sake of argument, let's say you have a microwave with a hole clean through it.

How big does that hole have to be, compared to the wavelength of the microwaves, to leak enough energy to worry about? (Surely not the full wavelength as claimed by the existing answer?)

However you wish to visualize the principals that govern how a Faraday cage works, it is well established that to block a transmission of a particular frequency, size of the largest hole in the Faraday cage must be AT MOST 1/2 the wavelength of the frequency of the undesired transmission.

Which is a bit less clear than I was hoping for - does that mean that at half the wavelength, nothing gets out? Does that apply even to the thin type of shielding typically used in microwaves, at least on the door? And if it does apply, how does the effectiveness decrease once you pass that cutoff?

When the hole is smaller than the wavelength of the signal, the transmission of the signal through the hole is proportional to $$(r/\lambda)^4$$ where $$r$$ is the radius of the hole and $$\lambda$$ is the wavelength of the signal.