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In this series of papers we develop a formalism for constraining massprofiles in strong gravitational lenses with extended images, using fluxes inaddition to positional information. We start in this paper with a circularpower-law profile and show that the slope $\gamma$ is uniquely determined byonly two observables: the flux ratio $f_1/f_2$ and the image position ratio$\theta_1/\theta_2$ of the two images. We derive an analytic expressionrelating these two observables to the slope, a result which does not depend onthe Einstein angle or the structure or brightness of the source. We then findan expression for the uncertainty on the slope $\sigma_\gamma$ that dependsonly on the position ratio $\theta_1/\theta_2$ and the total S/N in the images.For example, in a system with position ratio $\theta_1/\theta_2=0.5$, S/N$=100$ and $\gamma=2$ we find that $\gamma$ is constrained to a precision of$\pm0.03$. We then test these results against a series of mock observations. Weinvert the images and fit an 11 parameter model, including ellipticity andposition angle for both lens and source and measure the uncertainty on$\gamma$. We find agreement with the theoretical estimate for all mockobservations. In future papers we will examine the radial range of the galaxyover which the constraint on the slope applies, and extend the analysis toelliptical lenses.

Galaxy mass profiles from strong lensing I: The circular power-law model