So I installed my Regent scoop light (100w MV) and it works fine except when the a/c kicks on the voltage drops just enough to extinguish the arc tube, then it restrikes. The fixture just has an H38 ballast with no capacitor and not really any room that I saw. If I add a capacitor will it stop this and if so, which capacitor should I use?

I think not because what happens is the voltage peak dropping down

On normal AC it is dropping down too and then going back up to a peak value of about 170V, average 120V, and the lamp is restriking immediately 120 times/sec

When the A/C starts it is pulling high current (for way more than 1 cycle). During this time there is voltage lost on the overloaded wiring of the home and the supply. This overload is very fast (about 1 sec) so it is not posing a danger for the wiring like "normal" overloads do. But the lost voltage does cause a drop of voltage on the line - for this 1 sec you get say 100V peak instead of 170V, and 70V average instead of 120V. at those voltages the lamp canot restrike, and if this happens for a few cycles, as it does, the ionization in the lamp is lost

What you should do is separate the A/C and the light as far as possible from each other electrically, to reduce the extent to which the voltage drops. Ensure that the circuits to the A/C and the light are separated right from the panel, they are on different breakers, and preferrably on different phases of the supply (unless the A/C is 240V then it does not matter)

If there is noticable dimming of incandescent lights when the A/C starts then there may be a problem of bad connection - usually around the panel, meter, or service inputs, and should be checked. If some of the lights in the home are _brightening_ when the load kicks in, then you have a failing neutral connection and this issue is to be treated immediately because it can damage a lot of your appliances or cause a fire

Based on your description, you are using a HX autotransformer ballast, what does not provide much margin for line dips.
If you find a CWA, it should perform better, but I guess CWA would be very hard to find and maybe even fit there.

A question: The AC run on 120 or 240V?
If on 120V, try to rewire the light to the other 120V "leg", so the Neutral wire voltage drop would compensate out the overall voltage drop a bit.

If the AC is fed from across the whole 240V, only another ballast (with higher OCV) could help.

What would help for sure is connecting the lamp to the different phase, but I don't know if it is available for you (and I would rather guess no)...

It's 120V here and unfortunately we rent this house so I cannot mess around with rewiring circuits and there is no where else to plug in the A/C so I guess I will have to live with it if I want to use a mercury vapor fixture.

Not really. You can allways use extension cable, or tap into the panel in a way that is easy to remove later

It's 120V here and unfortunately we rent this house so I cannot mess around with rewiring circuits and there is no where else to plug in the A/C so I guess I will have to live with it if I want to use a mercury vapor fixture.

If the A/C have a plug and this plug is larger than usual 120V one, it run on 240V.

If you consult the rewiring with the owner and he agree (he would likely ask for a certified electrician to do the job and an inspection to certify the safety of the result for the insurance, well of course all on your expenses)
It depend, what loan you have. If it is some short term one, it would not work (paying such expenses for few months or years does not make as much sense).
If it is a long term rental, the owner have a motivation to keep you there happier (he get money from you), mainly if it does not cost him anything extra...

Well I ended up changing to a fixture with a 50 mg ballast with a capacitor and this is not an issue anymore. Mayne because its now only 50 watts or different ballast but the a/c has no effect so im happy now. Thanks for the replies.

Is your light on the same circuit as the AC?

Yes.

Well I ended up changing to a fixture with a 50 mg ballast with a capacitor and this is not an issue anymore. Mayne because its now only 50 watts or different ballast but the a/c has no effect so im happy now. Thanks for the replies.

 
I forgot to mention that my scoop light did the same thing whenever I would go to start mowing my lawn with my electric lawnmower.  The light would kick off because of that initial 12a draw that only lasts a milisecond but then it would cool down and re strike.  Iam glad that adding a fixture with a capacitor did the trick. That's typically what they do. After all their primary intention is to smooth out AC ripple currents by temporarily storing energy and discharging it.

Not exact

Big motors have start currents in the 10's and 100's of A. For example a 240V air conditioner that normally draws 10A, is drawing a surge of 100A and more at the moment it is powered up

As such currents are many times more than the normal draw in the system, the voltage drop on the wires resistance is many times more than normal respectively. As such, it can drop to well below what is needed to keep the lamp up

In DC, a smoothing capacitor stays charged at all times and discharges if there is a voltage drop, to reduce the drop seen at the load. In AC circuits however this is not possible - each 1/2 cycle of the AC, the capacitor is fully discharged and then charged in the opposite direction - in the US its 120 time a second

A discharge lamp which is working on AC is extinguishing and restriking at the same frequency. The ballast makes a kick on zero crossing which helps restrike the arc. If a voltage drop would be very quick (on the same order of length as the "normal" interruptions of the AC), and unless especially unluckily timed, probably won't affect the lamp since the ballast can deal with those dropouts, it deals with them 120 times in a second

What does pose a problem, is if the voltage on the upcoming 1/2 cycle never reaches the value needed to restrike the lamp, since the voltage is too low. The lamp does not restrike in this 1/2 cycle, ionization is lost, ballast has no current so it cannot react to the condition, and the lamp has to cool down (an ignitor can often restrike it immediately, esp. with HPS, but a merc and some MH dont have ignitor, and other MH are too hard to restrike and the ignitor does not help