I have done this, so here is some advice ... use LED strip lighting. Good light, easy to install, no heat, low electricity usage.
Ultrabright flexible strips are perfect for under cabinets, in offices and in other areas requiring a great amount of light. Superbright is the middle range of brightness and works great in spaces that need some light but not too much. Normal bright is perfect for accent lighting, such as for above cabinets, inside cabinets, in coves and around toe kicks, and for lighting art and more ...
For kitchen and bathroom applications, it's a good idea to go with coated tape ... more durable where chips are exposed to heat, moisture and food spills. Noncoated tape works best in areas such as inside cabinets where the chips aren’t exposed to damaging elements.
The cost of a decent-quality LED tape is about $8 to $10 per foot plus the cost of a driver to power it, which starts at $150.
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