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A transparent slab of thickness d has a refractive index n(z) that increases with z. Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n1 and n2 (>n1), as shown in the figure. A ray of the light incident with angle θi from medium 1 and emerges in medium 2 with refraction angle θf with lateral displacement l.Which of the following statement(s) is (are) true?

a) l is independent of n2 b) n1 sinθi = n2sinθf c) l is dependent on n(z) d) n1 sin θi... View Article

A crew of scientists has built a new space station.The space station is shaped like a wheel of radius R with essentially all its mass M at the rim.When the crew arrives the station will be set rotating at a rate that causes an object at the rim to have radial acceleration g thereby simulating Earth’s surface gravity.This is accomplished by two small rockets each with thrust T newtons mounted on the station’s rim. How long a time t does one need to fire the rockets to achieve the desired condition?

Answer:  t = √gR (M/2T) Solution: In order to simulate a gravity of g, we need the centripetal acceleration to be equal... View Article