Is there a sentence fragment?
Even though rainbows often appear to contain a band of purple. It's just an optical illusion.

 - no
 - yes
There is a sentence fragment that does not express a complete thought.
Even though rainbows often appear to contain a band of purple. It's just an optical illusion.
Here is one way to fix the sentence fragment:
Even though rainbows often appear to contain a band of purple, it's just an optical illusion.