9.6.2: Refraction
- Page ID
- 472632
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- Determine the index of refraction, given the speed of light in a medium.
It is easy to notice some odd things when looking into a fish tank. For example, you may see the same fish appearing to be in two different places. (See Figure \(\PageIndex{1}\).) This is because light coming from the fish to us changes direction when it leaves the tank, and in this case, it can travel two different paths to get to our eyes. The changing of a light ray’s direction (loosely called bending) when it passes through variations in matter is called refraction. Refraction is responsible for a tremendous range of optical phenomena, from the action of lenses to voice transmission through optical fibers.
Definition: REFRACTION
The changing of a light ray’s direction (loosely called bending) when it passes through variations in matter is called refraction.
Why does light change direction when passing from one material (medium) to another? It is because light changes speed when going from one material to another. As stated earlier in this chapter, the speed of light is now known to great precision. In fact, the speed of light in a vacuum \(c\) is so important that it is accepted as one of the basic physical quantities and has the fixed value. The speed of light depends strongly on the type of material, since its interaction with different atoms, crystal lattices, and other substructures varies. We define the index of refraction \(n\) of a material to be
\[n=\frac{c}{v}, \nonumber \]
where \(v\) is the observed speed of light in the material. Since the speed of light is always less than \(c\) in matter and equals \(c\) only in a vacuum, the index of refraction is always greater than or equal to one.
Definition: INDEX OF REFRACTION
\[n=\frac{c}{v} \nonumber\]
That is, \(n \geq 1\). Table \(\PageIndex{1}\) gives the indices of refraction for some representative substances. The values are listed for a particular wavelength of light, because they vary slightly with wavelength. (This can have important effects, such as colors produced by a prism.) Note that for gases, \(n\) is close to 1.0. This seems reasonable, since atoms in gases are widely separated and light travels at \(c\) in the vacuum between atoms. It is common to take \(n=1\) for gases unless great precision is needed. Although the speed of light \(v\) in a medium varies considerably from its value \(c\) in a vacuum, it is still a large speed.
Example \(\PageIndex{1}\): Speed of Light in Matter
Calculate the speed of light in zircon, a material used in jewelry to imitate diamond.
Strategy
The speed of light in a material, \(v\), can be calculated from the index of refraction \(n\) of the material using the equation \(n=c / v\).
Solution
The equation for index of refraction states that \(n=c / v\). Rearranging this to determine \(v\) gives
\[v=\frac{c}{n}. \nonumber\]
The index of refraction for zircon is given as 1.923 in Table \(\PageIndex{1}\), and \(c\) is given in the equation for speed of light. Entering these values in the last expression gives
\[\begin{aligned}
v &=\frac{3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}}{1.923} \\
&=1.56 \times 10^{8} \mathrm{~m} / \mathrm{s}.
\end{aligned} \nonumber\]
Discussion
This speed is slightly larger than half the speed of light in a vacuum and is still high compared with speeds we normally experience. The only substance listed in Table \(\PageIndex{1}\) that has a greater index of refraction than zircon is diamond. We shall see later that the large index of refraction for zircon makes it sparkle more than glass, but less than diamond.
Law of Refraction
Figure
The amount that a light ray changes its direction depends both on the incident angle and the amount that the speed changes. For a ray at a given incident angle, a large change in speed causes a large change in direction, and thus a large change in angle.
TAKE-HOME EXPERIMENT: A BROKEN PENCIL
A classic observation of refraction occurs when a pencil is placed in a glass half filled with water. Do this and observe the shape of the pencil when you look at the pencil sideways, that is, through air, glass, water. Explain your observations. Draw ray diagrams for the situation.
Section Summary
- The changing of a light ray’s direction when it passes through variations in matter is called refraction.
- The speed of light in vacuum \(c=2.9972458 \times 10^{8} \mathrm{~m} / \mathrm{s} \approx 3.00 \times 10^{8} \mathrm{~m} / \mathrm{s} \).
- Index of refraction \(n=\frac{c}{v}\), where \(v\) is the speed of light in the material, \(c\) is the speed of light in vacuum, and \(n\) is the index of refraction.
Glossary
- refraction
- changing of a light ray’s direction when it passes through variations in matter
- index of refraction
- for a material, the ratio of the speed of light in vacuum to that in the material