The converter will reduce your fstop and slow down the camera's ability to focus on the subject.
I got the impression he was talking about film-era OM, so there will be no autofocus at all.
In general 35mm film 2x telextenders were of poor optical quality. I never found one that produced results I enjoyed showing to people, though if one needed magnification of something for a particular reason they could sometimes do the job - e.g. bird ID, documenting something on a broadcast tower, figuring out whether a distant object was a sasquatch or a bear, etc.
Yes quite right - I will use it on a digital camera (Olympus OMD-EM-1) - through an adapter. So for both of the legacy lenses that I have (film day OM fit) - it will have to be manual focus. Tamron/Vivitar x2 teleconverters (used) retail for about 10-15 UK pounds - so I figured it might be worth getting one as one of my legacy lenses is 75-300mm f4.5 with which I get acceptable (for me) pictures of garden birds, planes etc. A x2 teleconverter will give me more reach - but, as you say, it will depend on the optical quality - and how well I am able to stablise the camera+adapter+teleconverter+lens combo!
I'm using the same combo. Olympus E-M1.1, with Various Takumars, and Olympus lenses. I too looked for the best solution to this issue, and whilst some put their stead in the older Vivitars, I found that the solution for me was a slightly newer variant, the Olympus C-210, which is a frontal TC designed for the very early Olympus DSLR's.
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The C210, has a compatriot the C-180, both these TC's are front mounted TC's and extremely light. 125grams. The C-210 is a 1.9x TC, with 4 lenses in 2 groups. It comes with its own lens hood built in, and I have step down rings for the Takumars and a step up ring for the Olympus Plastic Fantastic 40-150mm. It has a filter size of 52mm, so the step up and down rings cause no issues at all. I can imagine the 58mm thread for the 70-300mm, which is the same as the plastic fantastic will offer no issue, and you will gain a 2000mm lens, for the addition of an infinitesimal weight, cost, and optical compromise. These TC's were designed for Olympus Lenses and electronics in mind.
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It was an elegant and perfect solution for me... and cost me the princely sum of $12.50 on Ebay!
This is an image taken last year with it on the plastic fantastic during the autumnal full moon.
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It works superbly on the Takumars 55mm f1.8 and 105mm f2.8, no vignetting on either, and gives me superb lightweight carry for my needs, with all the extra reach that M43 affords.
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I just realized I already replied to this thread LOL... getting lazy and not reading through the entire thread

... hope it all worked out!
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P.S. by the way you are factoring in the onboard E-M1.1 ETC? because if you use that, the 300mm becomes a 2400mm lens, not a 1200mm! just a thought.The 70-300, like the 75-300II is a bit soft on the long end, so dial it back a bit to 250mm, then use the onboard ETC and adapted TC and you should still hit the magical 2000mm zoom factor.
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P.S.S. The E-M1.1 has onboard manual focus assistance, I use it continually with the Takumars, and it makes life so easy... just assign Magnify and Peeking to the front two buttons and toggle on/off as required.
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Photography is poetry made visible; it is the art of painting with light!