It will not, I specifically included the F-stops for that reason.
The depth of field is determined by the focus distance and the aperture of the lens. Both remain unchanged.
Note that 35mm F/2.0 is the same aperture as 70mm F/4.0. Both lenses have an aperture of 17.5mm. (35/2.0 == 70/4.0)
You can easily verify this with your favorite zoom lens. If you have an 24-70 F/2.8 available to you, you can verify by taking 2 pictures; one at 35mm F/2.8 and one at 70mm F/5.6. Crop the 35mm one to 25% area (half the width, half the height). Render both images to the same size (print, fill screen, whatever) and see for yourself.
The depth of field is determined by the focus distance and the aperture of the lens. Both remain unchanged.
Note that 35mm F/2.0 is the same aperture as 70mm F/4.0. Both lenses have an aperture of 17.5mm. (35/2.0 == 70/4.0)
You can easily verify this with your favorite zoom lens. If you have an 24-70 F/2.8 available to you, you can verify by taking 2 pictures; one at 35mm F/2.8 and one at 70mm F/5.6. Crop the 35mm one to 25% area (half the width, half the height). Render both images to the same size (print, fill screen, whatever) and see for yourself.