When you cook food in a microwave oven, why does't the plate get cooked? When you cook food in a microwave oven, why doesn't the plate get cooked?
 A: Microwave ovens primarily operate at 2450 MHz, which corresponds to a photon energy level about $10^{-5}$ eV. This energy level is within the range that separates molecular rotation and torsion quantum states. The photon energy associated with molecular vibration is in the range of 0.001 to 1.7 eV (ref: Hyperphysics Interaction of radiation with matter), well above the microwave energy level.
The wavelength of the microwaves is about 12 cm. The peak absorption of water (due to dielectric loss) occurs at a lower wavelength, but the range is broad and encompasses 12 cm. The design of a microwave oven’s frequency is more about the need for the FCC to assign values taking into account the needs of other equipment, than it has to do with ideal water absorption.  However, water absorption is the primary mode of increasing the temperature of food items. 
Finally, the dielectric loss of water is greater than the dielectric loss of glass (a primary component of a plate). Thus the increase in temperature of water is significantly greater than that of the plate exposed to microwaves.
Hope this helps.
A: Water is a polar molecule (it has positive and negative charged parts) and interacts with microwaves (exciting vibrational and rotational modes) very much better than the non-polar molecules of which the containers are made.  In effect the containers are transparent to microwaves whereas the food which contains water molecules is not.  
The container etc will get hot by the conduction of heat from the food which is a relatively inefficient process.
