How do you create a rewrite rule to foward requests from /path1 to /path2/path1?

Question

This rule is too greedy, "my-dir" should only redirect when it is the root directory e.g. /my-dir

RewriteRule ^my-dir/(.*)$ new-dir/my-dir$1 [R=301,L]

But this rule does not work at all!

RewriteRule ^/my-dir/(.*)$ new-dir/my-dir$1 [R=301,L]