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Air
90 Water

i r
Reflected ray
Critical
angle
Light source

FIGURE 7.16 When the angle of incidence results in an angle
of refraction of 90°, the refracted light ray is refracted along the
water surface. The angle of incidence for a material that results in
an angle of refraction of 90° is called the critical angle. When the
incident ray is at this critical angle or greater, the ray is reflected in-
FIGURE 7.14 A ray diagram shows refraction at the boundary ternally. The critical angle for water is about 49°, and for a diamond
as a ray moves from air through water. Note that θ i does not equal it is about 25°.
θ r in refraction.

Thus, light traveling from water into the air is refracted away
from the normal as it enters the air (Figure 7.15B).
The magnitude of refraction depends on (1) the angle at

which light strikes the surface and (2) the ratio of the speed
of light in the two transparent materials. An incident ray that
is perpendicular (90°) to the surface is not refracted at all. As
the angle of incidence is increased, the angle of refraction is

also increased. There is a limit, however, that occurs when
the angle of refraction reaches 90°, or along the water surface.
Figure 7.16 shows rays of light traveling from water to air at
various angles. When the incident ray is about 49°, the angle
of refraction that results is 90° along the water surface. Th is
limit to the angle of incidence that results in an angle of refrac-
tion of 90° is called the critical angle for a water-to-air surface
(Figure 7.16). At any incident angle greater than the critical
angle, the light ray does not move from the water to the air
but is refl ected back from the surface as if it were a mirror. Th is
is called total internal refl ection and implies that the light is
A
trapped inside if it arrived at the critical angle or beyond. Fac-
eted transparent gemstones such as the diamond are brilliant
because they have a small critical angle and thus refl ect much

light internally. Total internal reflection is also important in
fi ber optics.

CONCEPTS Applied

Internal Reflection

Seal a flashlight in a clear plastic bag to waterproof it, then
investi gate the critical angle and total internal reflection
in a swimming pool, play pool, or large tub of water. In
B
a darkened room or at night, shine the flashlight straight
up from beneath the water, then at diffe rent angles until
FIGURE 7.15 (A) A light ray moving to a new material with a it shines almost horizontally beneath the surface. Report
slower speed of light is refracted toward the normal (θ i > θ r ). (B) A
your observation of the critical angle for the water used.
light ray moving to a new material with a faster speed is refracted
away from the normal (θ i < θ r ).

184 CHAPTER 7 Light 7-8