External cell phone antennas - How?

My work vehicle is equipped with an older, bag-type cell phone. The phone utilizes an external antenna cable, which terminates in a metal box which is affixed to the windshield. On the other side of the windshield sits the antenna proper, also held on by some sort of adhesive. I assume this to be a fairly commonplace setup, as I’ve seen it on several other vehicles. My question is: How does the antenna mechanism transmit the signal through the windshield? Does the safety glass really provide so little resistance that the [radio waves?] can pass through unimpeded? It seems to me that if I placed a piece of Plexiglass between my home stereo and it’s antenna the reception would be degraded.

Most cell phones operate in the 800-900 Mhz band. At that frequency, the glass poses little, if any, impedance to the RF.

Actually, the small impedance is from the capacitor formed by the antenna base and metal box on either side of the glass, with the glass itself acting as the dielectric. The impedance of a capacitor decreases with frequency, so (broadly speaking) the higher in frequency you go, the easier it is to get the signal through. As Catenary said, cell phones are in the 800-900 MHz, band, while your stereo is down around 100 MHz. You could do the same thing with your stereo antenna, but you’d need much bigger metal surface area on either side of the glass (or much thinner glass, since the capacitance goes up as the distance decreases).