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I wonder, how does a car rear-view mirror work?

When there is a car behind me with high-beam, all I do is flip a tong at the bottom of the mirror to relax the lights!

Are there two mirrors in it, one darker than the other?

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    $\begingroup$ I think you should make your title more specific. It sounds like you're asking how mirrors work in general, not specifically about the anti-glare feature. $\endgroup$ – Barmar May 11 '19 at 9:53
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For manual anti-glare mirrors, the glass is actually a prism with the silvered rear surface not parallel to the front surface

In day-time position, drivers are seeing reflections from the rear surface with large amounts of reflected light reaching their eyes

In night-time anti-glare position, drivers are seeing reflections from the front surface of the glass, with much less light going into their eyes; the brighter rear reflection goes elsewhere. This is still enough to distinguish headlights behind, but not much else, and substantially less than if the day-time position was used at night, so reducing the contrast which could be blinding if the following vehicles were foolish enough to use full-beam headlights

See https://en.wikipedia.org/wiki/Rear-view_mirror#Anti-glare for more (and the automated alternative) which has these two diagrams

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