We presented a detailed observational study of the capabilities of the Palomar Adaptive Optics System and the PHARO near infrared camera in coronagraphic mode. The camera provides two different focal plane occulting masks consisting of completely opaque circular disks of diameter 0.433 arcsec and 0.965 arcsec, both within the cryogenic dewar. In addition, three different pupil plane apodizing masks (a.k.a. Lyot masks) are provided which downsize the beam. The six different combinations of Lyot mask and focal plane mask provide for different levels of suppression of the point spread function of a bright star centered on the focal plane mask. We obtained images of the bright nearby star Gliese 614 with all six different configurations in the K-band filter. Herein, we provide an analysis of the dynamic range achievable with these configurations. The dynamic range (the ratio of the primary star intensity to the intensity of the faintest point source detectable in the images) is a complicated function of not only the angular separation of the primary star and companion, but also of the azimuthal angle because of the complex point spread function of the primary star, which is also wavelength dependent. However, beyond 2.5 arcseconds from the star, regardless of the wavelength of the observation, the detection limit of a companion is simply the limiting magnitude of the image, as determined by the sensitivity of the PHARO camera. Within that radius, the dynamic range is at least 8 magnitudes at the 5(sigma) level and as high as 12 in a one second exposure. This represents a substantial gain over similar techniques without adaptive optics, which are generally limited to radii beyond two arcsec. We provide a quantitative discussion and recommendation for the optimal configuration along with a detailed comparison with recent theoretical predictions of AO coronagraphic performance.