CK-12-Physics - Intermediate

20.3. Index of Refraction http://www.ck12.org

FIGURE 20.14

Refraction of light makes the straw appear

“broken.”

The index of refraction

We define the ratio of the speed of light through vacuumcto the speed of the light through a particular mediumvas
theindex of refractionof the medium(n):

n=cv

Sincec>v, the index of refraction is always greater than 1 when traveling through any medium other than vacuum.

Table20.1 gives the indices of refraction for several common media.

TABLE20.1:

Medium Index of Refraction(n)

Vacuum 1.0000

Air 1.0003

Water 1.33

Ethyl Alcohol 1.36

Plexiglas(Lucite) 1.51

Crown glass 1.52

Diamond 2.42

Check Your Understanding

What is the speed of light through water?

Answer:nw=vcw→vw=ncw=
3. 00 × 108 ms

1. 33 =^2.^255 →^2.^26 ×^10
   8 m
   s

Snell’s Law

The mathematical relation between changing wave speed and the angle of refraction was discovered in 1621 by the
Dutch mathematician Willebrord Snell (1591-1626). This relationship is known asSnell’s Law, or the Law of
Refraction.

We can demonstrated that when light passes from a medium with a smaller index of refraction (higher speed of light)
into one with a larger index of refraction (lower speed of light), it refracts toward the normal as shown inFigure
20.15. If the light originates in the water, we need only reverse the direction of the rays in order to see the path of
the light rays.

Many of the apparently “strange effects” observed when objects are partly or fully submerged in water are due to
refraction. For example, the depth of a submerged object appears less deep than it actually is.

Snell’s Law

Snell’s Law is defined in terms of the index of refractionn. It expresses the relationship between the angle of
incidenceθ 1 and the angle of refractionθ 2 at the interface of two media.

The index of refractionn 1 is the medium from which light originates andn 2 is the index of refraction of the medium
to which light passes. Angleθ 1 is measured with respect to the normal at the interface of medium 1 and angleθ 2 is
measured with respect to the (same) normal at the interface of medium 2, as shown inFigure20.15.

n 1 sinθ 1 =n 2 sinθ 2

Snell’s Law can also be expressed in terms of the velocities of light in the respective media, as in
c
v 1 sinθ^1 =

c

v 2 sinθ^2 →v^2 sinθ^1 =v^1 sinθ^2

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