Teaching Modern Physics - QuarkNet - Fermilab

Student Worksheet
Index of Refraction Problems
1. Assume that you have a long optical fiber with core index of refraction ncore = 1.59 and
cladding nclad = 1.49. The fiber is 2 m long with an inner-core diameter of 1 mm. Light is
generated on the axis of the fiber at one end and bounces along it to the other end. Due to
small imperfections in manufacturing, the light is not quite perfectly reflected at each
bounce. Calculate what fraction of light is reflected at each bounce so that 50 percent of
the light makes it out of the far end of the fiber. Assume that the reflection fraction is
identical for each bounce and consider only light transmitted at the critical angle.
2. Standard materials used in scintillating fiber in particle physics experiments are
polystyrene (n = 1.59), acrylic (PMMA, n = 1.49) and fluorinated acrylic (fPMMA, n =
1.42).
Calculate the critical angle (i.e., the angle at the core-cladding interface) for light trapped:
a. In a fiber with a polystyrene core and a PMMA cladding.
b. In a fiber with a polystyrene core and an fPMMA cladding.
c. In a fiber with a polystyrene core and two claddings, an inner one of PMMA,
followed by an outer one of fPMMA.
3. A large particle detector uses optical fiber technology. The fiber consists of a core with
index of refraction = 1.59, surrounded by a cladding with index of refraction 1.49. The
fiber is 14 m long. If light is injected so that it bounces at the critical angle in the fiber,
how long does it take to travel the length of the fiber and exit?
4. A common particle detector technique involves optical scintillating fiber, which emits
light when crossed by a charged particle. If the fiber consists of a core with index of
refraction 1.59 and a cladding of index of refraction 1.49, what fraction of the light is
trapped in the fiber and transported to an end? Assume all light is emitted at the center of
the fiber (i.e., on the fiber axis) and that the light emission is isotropic.
5. Cerenkov light is a form of light emitted when a charged particle travels in a transparent
medium faster than light travels in the same medium. Calculate the minimum velocity an
electron must have to emit Cerenkov light in water.
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