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Chapter 1: Problem 2

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

Short Answer

Expert verified
The index of refraction (n) is always greater than or equal to \(1\) because it is a ratio between the speed of light in a vacuum and the speed of light in a medium (\(n = \frac{c}{v}\)). According to the theory of special relativity, light cannot travel faster than it does in a vacuum, so the speed of light in a medium (v) is either equal to or smaller than the speed of light in a vacuum (c). Therefore, the ratio between c and v will always be greater than or equal to \(1\).

Step by step solution

01

Understand the Index of Refraction Formula

The index of refraction (n) of a medium is given by the formula: \[n = \frac{c}{v}\] where c is the speed of light in a vacuum, and v is the speed of light in the medium.
02

Analyze the Speed of Light in a Vacuum and a Medium

According to the theory of special relativity, the speed of light in a vacuum (c) is the maximum possible speed any object or information can travel. In a medium, light generally travels slower due to the interaction between photons and the particles in the medium. In this case, the speed of light in the medium (v) is either equal to or smaller than the speed of light in a vacuum (c).
03

Apply the Analyzed Information to the Index of Refraction Formula

As mentioned above, the speed of light in the medium (v) is either equal to or smaller than the speed of light in a vacuum (c). Therefore, when we apply these values to the index of refraction formula, we get: \[n = \frac{c}{v}\] Since \(v \leq c\), we can deduce that the value inside the fraction will always be greater than or equal to \(1\). This implies that: \[n \geq 1\]
04

Conclusion

The index of refraction is always greater than or equal to \(1\) because light cannot travel faster than it does in a vacuum, and the material can only slow it down or maintain the same speed. Consequently, the ratio between the speed of light in a vacuum and the speed of light in the material will always be greater than or equal to \(1\).

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Most popular questions from this chapter

In order to rotate the polarization axis of a beam of linearly polarized light by \(90.0^{\circ},\) a student places sheets \(P_{1}\) and \(P_{2}\) with their transmission axes at \(45.0^{\circ}\) and \(90.0^{\circ},\) respectively, to the beam's axis of polarization. (a) What fraction of the incident light passes through \(P_{1}\) and (b) through the combination? (c) Repeat your calculations for part (b) for transmission-axis angles of \(30.0^{\circ}\) and \(90.0^{\circ},\) respectively.

A narrow beam of light containing red (660 nm) and blue \((470 \mathrm{nm})\) wavelengths travels from air through a \(1.00-\mathrm{cm}\) -thick flat piece of crown glass and back to air again. The beam strikes at a \(30.0^{\circ}\) incident angle. (a) \(\mathrm{At}\) what angles do the two colors emerge? (b) By what distance are the red and blue separated when they emerge?

If \(\theta_{b}\) is Brewster's angle for light reflected from the top of an interface between two substances, and \(\theta_{\mathrm{b}}^{\prime}\) is Brewster's angle for light reflected from below, prove that \(\theta_{\mathrm{b}}+\theta_{\mathrm{b}}^{\prime}=90.0^{\circ}\).

Under what conditions can light be modeled like a ray? Like a wave?

At what minimum angle will you get total internal reflection of light traveling in water and reflected from ice?
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