By changing the angle of the (internal) silvered surface without changing the angle of the (exterior) glass.
In most mirrors the majority of reflected light is bouncing off a material (silver, in early mirrors) that’s bonded directly to the back of the glass. But, glass is reflective too – you can see reflections in windows – just not as reflective as a silvered surface. In a common (flat) mirror, the front surface and silvered rear surface of the glass are parallel (same angle) so you get the combined reflection of the glass + silver at all times. However, if the silver were applied to a *different* surface immediately behind the glass, you’d be able to separate these two reflections by changing the angle of either the glass or the silver.
That’s where the switch comes in: when you flip it, you’re just tipping the silvered surface so it’s no longer parallel with the glass. The dim reflection you’re left with is the reflection off the glass only, and the brighter reflection off the silvered surface is pointed elsewhere (usually over the driver’s head – if you sit up really high you might be able to see it). Thus, you can change how much light is being reflected into your eyes with the flip of a switch.
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