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Chapter 21: Problem 6

Can a material have an index of refraction less than unity? Why or why not?

Short Answer

Expert verified
Provide an explanation for your answer. Answer: No, a material cannot have an index of refraction less than unity (n < 1). This is because the index of refraction (n) is given by the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v), and the speed of light in any medium will always be equal to or less than the speed of light in a vacuum. An index of refraction less than unity would imply that the speed of light in the medium is greater than the speed of light in a vacuum, which contradicts the known properties of the speed of light.

Step by step solution

01

Define index of refraction

Index of refraction (n) is a dimensionless quantity that describes how light (or other electromagnetic waves) propagate in a medium compared to its propagation in a vacuum. It is given by the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v): n = c / v
02

Explain the relationship between the speed of light and index of refraction

Since the speed of light in a vacuum is the maximum possible speed of light (approximately 3 × 10^8 meters per second), it means the speed of light in any medium will always be equal to or less than the speed of light in a vacuum. Mathematically, this is expressed as: v ≤ c
03

Discuss the possibility of an index of refraction less than unity

Now let's analyze the possibility of having an index of refraction less than unity (n < 1). If the index of refraction is less than 1, it means that the speed of light in the medium (v) is greater than the speed of light in a vacuum (c) (from the equation n = c/v). However, this contradicts our previous statement that the speed of light in any medium will always be equal to or less than the speed of light in a vacuum (v ≤ c).
04

Conclude the answer

Based on our analysis, a material cannot have an index of refraction less than unity (n < 1) because it would imply that the speed of light in the medium is greater than the speed of light in a vacuum, which contradicts the known properties of the speed of light.

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