After switching to synthetic oil there is smoke coming from under the hood and the oil light is on

Hello,

Typically, when oil leaks and gets on the exhaust manifold it will create smoke.
First you will need to verify the oil level.
In order to do this correctly you first want to make sure that the vehicle is parked on a level surface.
Be sure that the engine is off.
Then pull out the dip stick, wipe it clean of any oil and re-insert into the tube all the way. Then pull out and check the level.

The oil level should not rear full / empty / full.

Let me know what the oil level is. If it is low, then there is a leak somewhere.
Make sure that the oil cap is on securely and check for any leak around the engine.

Let me know what you find if you have any questions.
Thank you.