As a general rule, one may not derive benefit from light that was turned on by a non-Jew on Shabbat specifically for a Jew. For example, if a Jew was sitting in a dark room, and a non-Jew – such as a housekeeper – saw that the room was dark and turned on the light, the Jew may not perform any activity in that room which he could not perform in the dark (such as reading). This Halacha is codified by the Shulhan Aruch (Orah Haim 276).
An interesting exception to this rule is noted by the Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933), who writes that if one specifically told the non-Jew not to turn on the light, but the non-Jew insisted on turning it on, then one may make use of the light. Since the Jew told the non-Jew not to turn on the light, the non-Jew is considered as having turned on the light for his own purposes, and not for the Jew. Therefore, the light is permissible for use. Of course, one may not try to "trick" the system and plan with the non-Jew ahead of time that he will refuse and the non-Jew will then turn on the light. As long as the Jew sincerely expressed his wish that the light not be turned on, one may use the light if the non-Jew turned it on against the Jew’s wishes.
If a Jew asks a non-Jew to come with him to a certain place to help him get something, and at that place – which is dark – the non-Jew turns on the light so they can see what they are doing, the Jew may not then benefit from the light. Even though the non-Jew turned on the light for both himself and the Jew, the light is nevertheless forbidden for use, because the non-Jew is there only because the Jew requested that he join him. However, Hacham Ovadia Yosef rules that this Halacha does not apply if a Jew asked a non-Jew to go alone to bring him something from a certain room, knowing that the non-Jew will have to turn on the light in that room. In this case, since the non-Jew turned the light on solely for his own purposes, the Jew may then benefit from the light. Despite the fact that the non-Jew needed the light to fulfill the Jew’s request, nevertheless, since he went there alone and turned the light on only for himself, the light is permissible for use once it is turned on.
Summary: Although one may not benefit from a light turned on by a non-Jew for a Jew on Shabbat, one may benefit from the light if he had specifically told the non-Jew not to turn on the light, but the non-Jew insisted on turning it on. If a Jew asked a non-Jew to bring him something from a certain room, knowing that it is dark and the non-Jew will have to turn on the light, he may then make use of the light once the non-Jew turns it on. However, if a Jew asks a non-Jew to come help him bring something from a certain dark room, and the non-Jew turns on the light when they arrive in the room, the Jew may then not make use of the light.
