sqlite: avoid full table scan while querying one to many databse

Lets say I have two tables in a database:

user:
---------------
|  name | id  |
|-------|-----|
|  foo  |  1  |
|  bar  |  2  |
---------------

comments:
 ------------------
|  comment  |  id |
|-----------------|
| comment 1 |  1  |
| comment 2 |  1  |
| comment 3 |  1  |
| comment 4 |  1  |
| comment 5 |  1  |
| comment 1 |  2  |
 ------------------

Lets says I want to pull up all comments made by foo so my query will be

SELECT c.comment from comments c, user u WHERE u.name='foo' and c.id = u.id

will the above query do a FULL table scan on comments table to get comments made by user foo or is there a better query to optimize this and avoid a full table lookup ? Should I create index for these tables ?