The correct sentence is ‘Please turn on the light as I am afraid of the dark’ instead of ‘Please turn on the light as I am afraid for the dark’. Unfortunately, in the English grammar, there is no definite rule or principle that can be applied to ascertain which preposition should be used with which adjective. They simply need to be memorised.

 The adjective ‘afraid’ is generally always followed by the preposition ‘of’.  You have to just remember it in the beginning, but with time and usage it will start coming naturally to you. Some examples of prepositions after adjectives are: contributed to, ashamed of, embarrassed about, etc.