Roots in water is fine, its kind of like DWC. You have a few improvements to make. first off you should cover the top of your perlite media so that light does not get in and cause algae. Algae will not grow in the dark. You also want to cover your tank so light isn't getting to the roots either.
Remove your bowl looking reflector and get a wide angle hood or a flatter piece of polished metal to "unfocus" the MH light. once its unfocused it won't present nearly as much radiant heat into such a narrow area, you will be able to get the light much closer. Put a fan blowing across the bulb and you can get even closer. Your plants are a bit stretched due to lack of light, and you can clearly see that the plants are searching for the light as they turn the top toward the highest intensity. Get light closer and remove that "Bowl" reflector. Even the bare bulb would be preferable to the bowl.