[50-150mm/f2.8 + 2X converter] What's the effect?

Will it become:

1. 100-300mm with f5.6 DOF and f5.6 brightness?

or

2. 100-300mm with f2.8 DOF and f5.6 brightness?

I'm looking at the discontinued Sigma 50-150mm/f2.8 + 2X converter as my collection but I'm not sure if I would still get the f2.8 DOF if I put 2X converter on it.

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http://www.exp1orer.com

Remember the 50-150mm is a HSM lens and therefore the Sigma TC won't work.

If you do have a 2x that works, the DOF will not magically reduce, the effective opening (aperture diameter) will be the same and the focal length will be longer.

That's not incorrect but maybe too easy. You must consider that the same image at the CCD is spread out over twice its original size. That means each pixel looses 4x light, so two stops less. The DOF depends on your criterion. The (un)sharpness remains the same but it is 2x enlarged at the pixel level so it will appear less sharp. Also this will correspond to twice the focal length and two stops less aperture.

As the previous poster indicated: the absolute aperture remains the same so the lens performance in terms of arcseconds it can resolve remains the same or is slightly deteriorated because of the extra optics.
Simply said: you'l have a 100-300mm/f5.6 lens.