Problem — Microwave oven

Problem

A microwave oven operates at frequency $f\approx 2{,}45$ GHz, corresponding to a wavelength $\lambda\approx 12$ cm. (a) Why must the food turn on the plate? (b) Why doesn’t a dry slice of bread heat up like a soup? (c) Why does the door have a metal grille, yet you can still see inside?

Solution

(a) The rotating plate. Inside the metal cavity the microwaves reflect off the walls and interfere, forming standing waves with nodes (minimum field) and antinodes (maximum field) at fixed positions. If the food stayed still, it would heat up a lot at the antinodes and little at the nodes. Rotation makes each portion pass through different zones, evening out the heating.

(b) Dry bread versus soup. Microwaves give up energy mainly to water molecules, dipoles that rotate following the oscillating field and heat up through molecular friction. Soup is almost entirely water and absorbs a lot; dry bread contains little, so it heats up much less.

(c) The grille on the door. The behaviour of a metal mesh depends on the comparison between its size $d$ and the wavelength:

$d\ll\lambda_\text{micro}\approx 12\;\text{cm}\qquad d\gg\lambda_\text{visibile}\approx 5\cdot 10^{-7}\;\text{m}$

For microwaves the holes are tiny: the grille behaves like a continuous wall and reflects them (shielding). For visible light the holes are enormous: the light passes through and you can see inside.

In summary $d\ll\lambda$) but is transparent to light ($d\gg\lambda$).

Same object, opposite effects at different wavelengths: the grille blocks microwaves (

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Topics: Onde elettromagnetiche Concepts: Onda elettromagnetica