Light entering a fiber is not always trapped, even when the cladding index of refraction is less than the core index.  Consider the situations shown in the pictures below, which show the path of laser light through a plastic fiber immersed in water.  Coffee creamer was added to the water to increase the visibility of the laser light through the water.  The path of the light through the fiber is visible due to impurities in the fiber scattering some of the light toward the camera.
 

(a)		(b)
(a) For this plastic (n @ 1.5)  fiber core surrounded by a water (n @ 1.33) cladding, light can be trapped in the fiber, as shown above.  The close-up shows the light being totally internally reflected, while the view of the entire fiber shows the light being emitted at the end of the fiber.		(b) Light is not always trapped by this fiber.  As these pictures show, light entering the fiber at a slightly larger entrance angle escapes the fiber.  The view of the entire fiber shows no light being emitted at the end of the fiber, while the close-up shows how most of the light escapes right after entering the fiber.

As the photos above show, whether or not light is trapped in the fiber will depend upon the angle at which it enters the fiber.  Acceptable angles form a cone of acceptance.  But whether light is trapped also depends upon the materials which comprise the fiber. The  photos below show how changing the cladding from water to air changes the cone of acceptance to include all physically possible angles of entry.  Chalk dust has been used to make the laser beam in air visible to the camera.
 

(c)		(d)
(c) Just as when water provided the cladding layer, light entering the plastic fiber core at small entrance angles is trapped in the air-clad fiber.		(d) Unlike the fiber with water cladding, the air-clad fiber continues to trap light at large entrance angles approaching 90°.

What determines the cone of acceptance for a given fiber? Continue to the next page to find out!