# Chapter 20 - Traveling Waves - Exercises and Problems - Page 587: 25

(a) $t = 1.5\times 10^{-11}~s$ (b) In the same amount of time, light could travel through water with a thickness of 3.5 mm

#### Work Step by Step

(a) We can find the speed of light as it travels through glass. The index of refraction of glass is $n = 1.5$ $v = \frac{c}{n}$ $v = \frac{3.0\times 10^8~m/s}{1.5}$ $v = 2.0\times 10^8~m/s$ We can find the time to travel through 3.0 mm of glass. $t = \frac{d}{v}$ $t = \frac{3.0\times 10^{-3}~m}{2.0\times 10^8~m/s}$ $t = 1.5\times 10^{-11}~s$ (b) We can find the speed of light as it travels through water. The index of refraction of water is $n = 1.3$ $v = \frac{c}{n}$ $v = \frac{3.0\times 10^8~m/s}{1.3}$ $v = 2.3\times 10^8~m/s$ We can find the distance that light could travel through water in a time of $1.5\times 10^{-11}~s$: $d = v~t$ $d = (2.3\times 10^8~m/s)(1.5\times 10^{-11}~s)$ $d = 3.5\times 10^{-3}~m$ $d = 3.5~mm$ In the same amount of time, light could travel through water with a thickness of 3.5 mm.

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