Question 11

  On most cameras one can select the f-number setting, or f-stop. The f-number gives the ratio of the focal length of the camera lens to the diameter of the aperture through which light enters the camera. If one wishes to resolve two closely spaced objects in a picture, should a small or a large f-number setting be used? Account for your answer.

SOLUTION:
Lord Rayleigh hath said that two point objects are just resolved when the first dark fringe in the diffraction pattern of one falls directly on the central bright fringe in the diffraction pattern of the other. If you believe equation 27.6,

$$\theta_{min} \approx 1.22 \frac{\lambda}{D},$$

then you'll agree that optical instruments with the highest resolution should have the largest possible diameter D.
The f-number setting on the camera gives the ratio of lens focal length to diameter of aperature. Hence, smaller f-number means larger aperature. Then, by equation 27.6, we want the smallest f-number since we want the largest aperature diameter D.