Students will learn why light refracts when entering different substances like water, glass, etc. and how to calculate the angle of refraction using Snell's Law.

### Key Equations

\begin{align*}c = 300,000,000 \;\mathrm{m/s}\end{align*} ; the speed of light

\begin{align*} n = \frac{c}{u}\end{align*}

The index of refraction, \begin{align*}n\end{align*}, is the ratio of its speed \begin{align*}(c)\end{align*} in a vacuum to the slower speed \begin{align*}(u)\end{align*} it travels in a material. \begin{align*}n\end{align*} can depend slightly on wavelength.

\begin{align*}n_i \sin{\theta_i} = n_f \sin{\theta_f} \end{align*} ; Snell's Law

Fermat's principle states that light will always take the path that takes the least amount of time (not distance). Refraction follows from this. When light travels from air into another material (like glass), its speed through the material is reduced due to interactions between photons that make up the light ray and the densely packed atoms of the material. Because light is effectively moving slower in the glass, for example, as compared to air, the light ray bends in order to get out quicker and satisfy Fermat's Principle of least time. This is called refraction. The figure below demonstrates the refraction a light ray experiences as it passes from air into a rectangular piece of glass and out again.

#### Example 1

### Watch this Explanation

### Simulation

Bending Light (PhET Simulation)

### Explore More

- Using the
**Table**(below), which states the indices of refraction for a number of materials, answer the following questions:- For which of these materials is the speed of light
*slowest*? - Which two materials have the most similar indices of refraction?
- What is the speed of light in cooking oil?

*Material*\begin{align*}n\end{align*} vacuum \begin{align*}1.00000\end{align*} air \begin{align*}1.00029\end{align*} water \begin{align*}1.33\end{align*} typical glass \begin{align*}1.52\end{align*} cooking oil \begin{align*}1.53\end{align*} heavy flint glass \begin{align*}1.65\end{align*} sapphire \begin{align*}1.77\end{align*} diamond \begin{align*}2.42\end{align*} - For which of these materials is the speed of light
- A certain light wave has a frequency of \begin{align*}4.29 \times 10^{14} \;\mathrm{Hz}\end{align*}. What is the wavelength of this wave in empty space? In water?
- A light ray bounces off a fish in your aquarium. It travels through the water, into the glass side of the aquarium, and then into air. Draw a sketch of the situation, being careful to indicate how the light will change directions when it refracts at each interface. Include a brief discussion of why this occurs.
- A light ray goes from the air into the water. If the angle of incidence is \begin{align*}34^\circ\end{align*}, what is the angle of refraction?

- Nisha stands at the edge of an aquarium \begin{align*}3.0 \;\mathrm{m}\end{align*} deep. She shines a laser at a height of \begin{align*}1.7 \;\mathrm{m}\end{align*} that hits the water of the pool \begin{align*}8.1 \;\mathrm{m}\end{align*}from the edge.
- Draw a diagram of this situation. Label all known lengths.
- How far from the edge of the pool will the light hit bottom?
- If her friend, James, were at the bottom and shined a light back, hitting the same spot as Nisha’s, how far from the edge would he have to be so that the light never leaves the water?

- You are to design an experiment to determine the index of refraction of an unknown liquid. You have a small square container of the liquid, the sides of which are made of transparent thin plastic. In addition you have a screen, laser, ruler and protractors. Design the experiment. Give a detailed procedure; include a diagram of the experiment. Tell which equations you would use and give some sample calculations. Finally, tell in detail what level of accuracy you can expect and explain the causes of lab error in order of importance.

#### Answers to Selected Problems

- b. vacuum & air c. \begin{align*}1.96 \times 10^8 \;\mathrm{m/s}\end{align*}
- \begin{align*}6.99 \times 10^{-7}\;\mathrm{m}; 5.26 \times 10^-7\;\mathrm{m}\end{align*}
- .
- \begin{align*}25^\circ\end{align*}
- b. \begin{align*}11.4\;\mathrm{m}\end{align*} c. \begin{align*}11.5\;\mathrm{m}\end{align*}
- .