You Do Need power plug adapter while traveling from Libya to Faroe Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Faroe Islands are C, E, F and K and in Libya are C and L. This is how they look like.

Libya

In Libya, outlets of type C and L are in use.

Type C

Type L

Faroe Islands

In Faroe Islands, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K