Could be burns. How close to the light are those top leaves? Have you sprayed anything on the leaves? Liquid on foliage under the sun or even lights can act the same way as a magnifying glass in the sunlight...

FWIW spider mites are often hard to see. You can vigorously tap the plants and brush the leaves off onto a piece of paper (try it on both dark and light colored papes) and the mites are more visible against the paper. Mites and aphids are very common problems on indoor plants because they can grow their populations quickly in that kind of sheltered environment.

Could be a nutrient supply issue, either too much or not enough. Other common problem could be problems absorbing nutrients because the soil is always wet, or simply problems getting oxygen to the roots because the soil is too wet. Watering from bottom is fine, but you have to be sure to let the soil dry out in between watering, especially with hot climate herbs like basil. Be aware that some kinds of potting soil can hold onto more water than others, so stick a finger in it or get a feel for the weight of a pot that has not been recently watered so that you have some idea of how much water is still in the soil before you add more. Overwatering a more frequent cause of plant death than underwatering.

You burnt them with the extra light, and/or heat produced by the bulbs depending on how close you've got them. There isn't anything you can do for the leaves that are damaged but the plants will soon outgrow this and the new leaves will be fine.

Rodney

It looks like some combination of:

• sunburn (fluorescents put out a lot of UV light)
  and/or
• overwatering
  and/or
• lack of nutrients

How long since the seeds sprouted? Most "seed starting mix" has only enough nutrients for a few weeks of growth. If you're past 3 to 4 weeks, either transplant into bigger containers (yogurt cups) with good potting mix or very sparingly apply some (nearly) balanced fertilizer.

For the UV, there are clear plastic (polycarbonate) "fluorescent tube protectors" which slide over the tubes. Some of those protective covers are UV blocking, and the ones that don't say that can be painted with a UV blocking clear coat paint.

Overwatering is preventable, but common.

ADDED with Edit: When you transplant, cut off the lower burnt leaves (have a pesto dinner) and bury the plant so only a few leaves are above the soil. Basil grows from cuttings, and it will develop additional roots from buried leaf nodes.

I agree with the others when they say light burns. Instead of using Kelvin to measure light, you should your Nanometers(nm). Most lights, especialy LED lights will have the (nm) specification on the box. Do not use anything below 410nm and nothing higher then 780nm. Everything from 500nm - 580nm is usually bounced off and not absorbed by the pigment. Learn more on what spectrum a grow light should produce so you can save money on useless Watts doing nothing for your plant.