What is this kind of ceiling light called?

And where could I find one? It’s about 3.5 inches in diameter and about 12 inches in length. I need to replace it because when I tried to change the bulb in the matching light, this happened.

I doubt you will be able to find an exact match (except at a flea market), but how about this:
http://www.bellacor.com/productdetail/progress-lighting-946145174wb-p6145-174wb-directionals-urban-bronze-one-light-ceiling-light-285800.htm

Google cylinder light and you will find a lot of similar fixtures. It will be difficult to find and exact match, though. Can you have it rewired?

It’s called a “directional light”, or “directional” for short.

Thanks for the tips. I don’t need an exact match since I’m going to replace both of them. I just like the style.

Here in Australia they are called interior spot lights. This is from their use as lights for theatre art gallery or museum where you point it at the subject… and if you move the subject adjust the light.

However you can use it to spotlight the dining table or coffee table or to help you read while sitting or anything like that.

Here’s one example, I’m sure you could find cheaper ones.

In the stores we called them can lights.

I’ve heard of them called mood lights.

To tall people they are those annoying, eye-burning, pieces of junk.

These are on a vaulted ceiling so it’s not so bad.

I have only heard the term “can lights” refer to recessed lighting fixtures.