The kinetics of the growth of depletion zones around a static trap in an effective one-dimensional geometry were studied with a new fluorescence-based setup. The experiment consists of a photobleaching reaction of fluorescein dye by a strong laser beam, which served as a phototrap in the experiment, inside a 150-mum gap between two parallel microscope slides. The kinetics of the growth of the depletion zone were monitored by the previously defined theta distance, which can be directly measured experimentally. The effect of trap strengths on the kinetics was tested experimentally by changing the photobleaching laser power. The strong laser power acted as a perfect trap, which gives a t(1/2) scaling behavior for the theta distance over most of the time range. However, the experiment with a weak laser power produced an anomalous early-time behavior for the theta distance, which is faster than the t(1/2) time scaling. A crossover behavior was observed with an intermediate laser power. The experimental results are consistent with an exact one-dimensional analytical solution and were also reproduced in Monte Carlo simulations as well as by exact enumeration calculations. The latter two methods show that the asymptotic results for an exact one-dimensional lattice are still valid in a quasi-one-dimensional system, for both perfect and imperfect trapping reactions.