There are various different devices over at Amazon that can help with this. There are clip on lights like those little book reading light clips that you can buy for a couple of dollars. However, because they have the name 'Kindle reading light' in the name, they shoot up to around $20.

There are also cases which permit the addition of a light. These cases are fairly cheap to begin with, but once you add that extra light (which is usually sold separately) it can add up. Also, batteries in a light are something that you will also need to deal with, replacing them when they die etc. Most reading lights will probably last around 20 hours of illumination, so depending on how often you read in the dark, this could range from one week, to a couple of months.

Once case that solves this is the official Kindle Lighted cover which includes a light in the case that hooks into the battery. It solves the issue of replacing batteries, as only the Kindle itself needs to be charged. more information about kindle cover review you can visit : Kindle Cover