Lighting for plants in a custom vivarium with frogs

[jakeyost89]

Im looking to build a terrarium with a living area of 36"x36"x36"-40" for a Gray Tree Frog, FBT, and RETF. I'm going to add living plants to this, and my question is, how many lumens of light would be necessary to get adequate lighting to the bottom of a tank of this size? I plan on planting parts of the bottom, as well as the background. I'm planning on making a custom led lighting system with the light wavelengths necessary for good plant growth, but I am unsure of how many lumens would be necessary. Any input about this would be great, as well as about anything else that I need to consider with the lighting of this terrarium. Thanks!