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Older flashes could have higher voltage than newer flash for DSLR. In that case one risks that there is an higher than expected voltage difference with all the subsequents possible consequences for the camera (but not for the flash, I guess).

My question is: is it always safe to use a newer flash on an old film camera? If I put a speedlite on a mechanical camera from 40 years ago, am I going to risk something? Or am I always safe, since the voltage difference is much lower ?

I think that at worst I will risk that the flash doesn't trigger/sync correctly (but older cameras had very slow sync speed, like 1/60...). Is that true?

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The trigger voltage you are worrying about doesn't come from the camera; it's all in the flash. All the camera does, in effect, is "flip a switch"; it shorts out the centre pin of the flash and the contacts at the side of the flash's foot.

The voltage problem comes from the kind of "switch" used to short out those contacts. In (most) modern cameras, that "switch" is actually a transistor (part of a chip). That transistor can't handle a lot of voltage or current without overheating and burning out. If the voltage is high enough, it can go right through the "off" state of the transistor almost as if it were a straight wire (which it definitely isn't), so the transistor, the chip it's on, and the components around it can be destroyed simply by turning the flash on while it's mounted to the camera — there's no need to actually use the flash to cause the damage.

Older flashes were a lot simpler. There is a capacitor used to store a lot of electrical charge at a voltage that's high enough to arc across the flash tube once the arc is "lit". That's usually something around 300 volts or so (give or take 150 volts). That's a lot, but it's not enough to get the arc started. For that, you need a much higher voltage (usually about 4000 volts). That 4kv trigger voltage was usually gotten by sending the 300v through a small transformer. Your camera contained the switch for that circuit; the moment that 4000 volts was present, the arc would be "lit" and the 300 volt charge would keep it going. (For the technically inclined, there was almost no current in the 4kv circuit; it just went to the equivalent of a teeny-tiny capacitor that would reach full charge almost instantly. It was just the presence of the potential that was required to light the arc. Similarly, the 300v side of the circuit only had to create the leading edge of a potential change on its side of the transformer, so it could be fed from a small capacitor that dumped all of its charge quickly through the primary. There wasn't enough charge to cause any damage to people, and the potential was below the "I think I felt a shock" threshold of about 600v.) The switch in your camera back then was a real, physical mechanical switch hooked up to the shutter.

Modern flashes contain all of the high-voltage stuff too, but they keep it to themselves. The camera is only required to short out a low-voltage circuit (usually under 6 volts), which the transistors can handle no sweat, and that's used to trigger the high voltage circuit inside the flash. Your old camera will be able to trigger a modern flash reliably and safely; it's only the old-flash-on-a-modern-camera scenario that's dangerous.

As long as your camera has X sync, the flash will sync properly. Very old cameras may not have an X sync, which is meant for electronic flash; they may have an M sync instead (which is meant for flashbulbs, and fires earlier to give the bulb a chance to heat up a bit before the shutter is fully open), or they may have both X and M sync terminals and you have to make sure you're connected to the right terminal. The sync speed only determines the fastest shutter speed you can use with the flash, it (almost always) has no effect otherwise. (There are a few cameras that won't sync at all except at the sync speed, and others that won't do TTL/OTF except at sync.)

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