6.4. Transfer of Scintillation Photons 363
For the generally used light guides havingn≈ 1 .5 for visible light, this gives
θi≥ 41. 80. (6.4.3)This shows that the photons striking the wall of the light guide at an angle less than
41. 80 will suffer some loss. The light guide should then be constructed such that all
probable incident angles are greater than this value. This implies that the geometry
of a light guide plays a crucial role and should therefore be carefully designed.
To demonstrate the use of condition 6.4.2 in constructing a practical light guide,
let us have a look at one of the commonly used light guide geometries, the so called
fish tail. Fig.6.4.2 shows how a scintillator can be connected with a photodetector
through such a light guide. The most widely used photodetectors are photomultiplier
tubes, which usually have rounded entrance windows. Therefore one end of the fish-
tail light guide is made round shaped. The other end that is connected to the
scintillator is usually flat and thin to fit on the flat edge of the scintillator. The
photons from the scintillator enter the light guide and travel outwards in straight
lines. Obviously the ones that are in theline of sightof the photodetector, are
captured by the detector most efficiently. However since the scintillation photons
are emitted in all directions therefore some of them also hit the outer surface of the
light guide. If the condition of total internal reflection is fulfilled, these photons get
reflected from the surface. After one or more such reflections the photons eventually
reach the photodetector.
Equation 6.4.3 implies that the light guide must be tapered at an angle such that
the angle of incidence is always greater than 41. 80. However the choice tapering
angleθtdoes not depend only on this criterion. To minimize the loss of light due to
reflections from the surface it is always desirable that the photons make minimum
number of total internal reflections before reaching the photodetector. Also the
angle at which the light enters the photodetector might be of significance for good
photon collection efficiency. As shown in Fig.6.4.2, this angle can be determined
by simple geometric considerations. Here we have used the fact that the angles of
incidence and reflection are equal. Adding the angles of the triangle we get
π
2−θp+π
2+θt+π
2−θi=π.Rearrangement of this equation gives us the required dependence ofθpon the angle
of incidence and the tapering angle.
θp=π
2−θi+θt (6.4.4)Let us now apply the condition of total internal reflection, that is equation 6.4.2,
to the above relation. This gives
sin(π
2
+θt−θp)
≥
1
n. (6.4.5)
This simple relation can be used to determine the lower bound on the tapering angle
required for a certainθp(see Example below).