How are microwaves a spin off of military technology?

Answer:

When RADAR was first invented, in the 1930s, it didn't work very well because high directional accuracy required either a gigantic antenna or very short wave-lengths. Vacuum tubes had great difficulty in producing wavelengths below about 1.5 meters. In 1940 two men named Randall and Boot, working at Birmingham University in England, invented a device called a Resonant Anode Cavity Magnetron which could generate wavelengths about a thousand times shorter. Now called just a magnetron, this transformed RADAR; it has also transformed cooking, because there is at least one in almost every kitchen, inside the microwave oven.

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