Is the camera sensor or the lens the limit to resolution?

I have a pretty high res sensor on my camera, but sometimes I have the feeling my lens doesn't even get to this resolution. How can I tell if my camera sensor has not enough resolution or if the lens is the limit?

For example I have a 5DMarkII with 22 Megapixel Sensor. And a Canon 35mm 1:2 Lens. (For example aperture at 11 shutter at 1/2000)

How can I visually see whether the bottleneck is the lens or the cameras resolution? Is there any place were I can look up the optical resolution of a lens?

Answer

There is no hard limit to resolution - details don't just vanish they fade out gradually as the contrast between light and dark is reduced. This reduction in contrast is expressed by means of the modulation transfer function (MTF). It's just a fancy way of saying details of size X will experience a loss of contrast Y.

The MTF of a camera system is the mathematical product of the lens MTF and sensor MTF. This means that any improvement in either lens resolution or sensor resolution will result in an improvement of the overall MTF.

So the technical answer to your question is, it is both.

However you do experience diminishing returns after a point, that is improvements in sensor resolution yield smaller and smaller improvements to system resolution (you can't take sharp images with a coke-bottle by using a sufficiently high resolution sensor.

Is there any place were I can look up the optical resolution of a lens?

Canon publish the MTF charts for all their current lenses on their website, your 35mm f/2.0 has been superseded by the IS version, however a google search turned up the MTF chart:

For information on how to read the chart, see this answer:

How do I interpret an MTF Chart?

What you can see clearly from the thin black lines is that wide open at f/2.0 that lens delivers pretty low contrast for high frequency details, less than 60% over most of the frame. This probably accounts for the poor results you're seeing.

As your sensor is currently pretty much the highest resolution available from Canon I don't think it's holding you back particularly. Switching to the 36MP Sony A7R would yield a measurable increase in resolution, but much less than upgrading the lens (to something like the Canon or Sigma 35mm f/1.4, or even the newer Canon 35mm f/2.0 IS) would.