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I know that plant grow faster depending on the hours of sunlight it has, but what happens if i put a giant mirror focusing light to the plant?.
Will the growth rate be limited by the damage the sunlight produces, or will it be limited by the speed of the photosythesis?
In nature, there is often ample sunlight available to plants. From this NIH page:
However, even at the maximum light intensity encountered by photosynthetic organisms (tropical noontime sun, ≈1.2 × 1020 photons/m2/s), each reaction-center chlorophyll a absorbs about one photon per second, which is not enough to support photosynthesis sufficient for the needs of the plant. To increase the efficiency of photosynthesis, especially at more typical light intensities, organisms utilize additional light-absorbing pigments.
In other words, plants are not entirely photosynthetically efficient and do not typically use all of the light available to them. From Wikipedia:
Photosynthesis increases linearly with light intensity at low intensity, but at higher intensity this is no longer the case (see Photosynthesis-irradiance curve). Above about 10,000 lux or ~100 watts/square meter the rate no longer increases. Thus, most plants can only utilize ~10% of full mid-day sunlight intensity.
Up until a point more light will accelerate plant growth. Beyond that it will stop helping and then become damaging. The optimal level of light to give commercially valuable plants has been studied extensively, and varies substantially between plants.
This concept is formalized in the daily light integral, the number of moles of photons per square meter per day a plant optimally needs, and the photoperiod which is the number of hours per day that light should be distributed over. You can look up values for different plants.