Can I get this kind of DOF out of the 35mm 1.8 DX???

You can't get the same narrow DoF on DX as you could on FX but I do think the kind of shot you posted is achievable with the 35mm f1.8. The BG looks like it is far enough away to be blurred with a 35mm f1.8. The FOV from the 35 on DX will be very similar to the FOV of the 50 on FX so the amount of blur will be similar with a slight advantage going to the FX set up.

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