PhysicsLAB Amusing Problems
Santa's Helper

 
Christmas is coming and Dr. J has applied for a seasonal job as Santa's helper. One Santa just can't handle all the requests for electronic toys and gadgets this year. As a result, he has advertised for an assistant to help make and deliver the beeping little goodies. (The elves are mad at Santa for bringing in an outsider. To show Dr. J that they know a little something about computerized games, and as a form of protest as well, they all vow to carry chips on their shoulders.) Time is running out as Santa anxiously awaits Dr. J's arrival. Finally, at the last minute, he sees Dr. J's sleigh on the horizon. (Dare we say, "in the nick of time"?) At first, Santa pictures Dr. J to be some valiant warrior out of medieval times, because instead of reindeer, he uses two sleigh dragons. However, upon closer inspection, Santa finds Dr. J's sleigh to be equipped with a futuristic guidance and lighting system. For example, he uses a 6328 A He-Ne laser with a 2600 line/cm diffraction grating to help him spot the right house.
 
Theoretically, what is the maximum number of houses that Dr. J could spot at once?

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