Hi Bani,
My seven week old has been doing the same thing since about 2 weeks. I don't know if it's normal - I read that young babies should be awake for 15 minutes per hour that they're awake, so if the baby sleeps for 2 hours, he should be awake for half an hour, etc.
My baby does not do that! If I'm lucky he'll have one two-hour nap during the day and otherwise be awake from 4am to 9pm!
What I find works to make him sleep is wearing him in a sling or wrap- he can sleep 4 hours at a time like that.
HTH - see you on the playgroup board!