You designed an optical fiber scope for directing light into a confined area. You want to keep light within the fiber. You made the fiber of a material of an index of refraction of n = 1.74. From the design you want to allow angles of up to 40⁰ measured with respect to the direction of the fiber is no greater than . Assuming you will be using the scope in something other than air, what is the maximum index of refraction of the external surrounding material in which this opitcal fiber will be functional? (Please be sure you are aware of what is the question asking, what is your goal.)

In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. the cylinder begins to rotate about a vertical axis. then the floor on which the passengers are standing suddenly drops away! if all goes well, the passengers will “stick” to the wall and not slide. clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. part a what is the minimum rotational frequency, in rpm, for which the ride is safe? express your answer using two significant figures. f f = rpm