# 25.3 The law of refraction  (Page 6/9)

 Page 6 / 9

Students in a lab group are given a plastic cube with a hollow cube-shaped space in the middle that fills about half the volume of the cube. The index of refraction of the plastic is known. The hollow space is filled with a gas, and the students are asked to collect the data needed to find the index of refraction of the gas. What information would you need to collect, and how would you use this information in order to deduce the index of refraction of the gas in the cube?

First, measure the angle of incidence and the angle of refraction for light entering the plastic from air. Since the two angles can be measured and the index of refraction of air is known, the student can solve for the index of refraction of the plastic.

Next, measure the angle of incidence and the angle of refraction for light entering the gas from the plastic. Since the two angles can be measured and the index of refraction of the plastic is known, the student can solve for the index of refraction of the gas.

Light travels through water and crosses a boundary at a non-normal angle into a different fluid with an unknown index of refraction. Which of the following is true about the path of the light after crossing the boundary?

1. If the index of refraction of the fluid is higher than that of water, the light will speed up and turn toward the normal.
2. If the index of refraction of the fluid is higher than that of water, the light will slow down and turn away from the normal.
3. If the index of refraction of the fluid is lower than that of water, the light will speed up and turn away from the normal.
4. If the index of refraction of the fluid is lower than that of water, the light will slow down and turn toward the normal.

A laser is fired from a submarine beneath the surface of a lake ( n = 1.33). The laser emerges from the lake into air with an angle of refraction of 67°. How fast is the light moving through the water? What is the angle of incidence of the laser light when it crosses the boundary between the lake and the air?

The speed of light in a medium is simply c / n , so the speed of light in water is 2.25 × 10 8 m/s. From Snell’s law, the angle of incidence is 44°.

## 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 $c=2\text{.}\text{9972458}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s}\approx 3\text{.}\text{00}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s}.$
• 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.
• Snell’s law, the law of refraction, is stated in equation form as ${n}_{1}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}{\theta }_{1}={n}_{2}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}{\theta }_{2}$ .

## Conceptual questions

Diffusion by reflection from a rough surface is described in this chapter. Light can also be diffused by refraction. Describe how this occurs in a specific situation, such as light interacting with crushed ice.

Why is the index of refraction always greater than or equal to 1?

Does the fact that the light flash from lightning reaches you before its sound prove that the speed of light is extremely large or simply that it is greater than the speed of sound? Discuss how you could use this effect to get an estimate of the speed of light.

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