Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 34 - Ray Optics - Exercises and Problems - Page 990: 2

Answer

(a) $t = 3.3~nm$ (b) In water, the light travels $~~0.75~m$ In glass, the light travels $~~0.67~m$ In cubic zirconia, the light travels $~~0.46~m$

Work Step by Step

(a) We can find the time it takes light to travel $1.0~m$: $t = \frac{d}{c}$ $t = \frac{1.0~m}{3.0\times 10^8~m/s}$ $t = 3.3\times 10^{-9}~m$ $t = 3.3~nm$ (b) We can write an expression for the speed of light in a medium: $v = \frac{c}{n}$ where $n$ is the index of refraction of the medium. We can write an expression for the distance traveled by light in a medium in a given time $t$: $d = v~t$ $d = \frac{c~t}{n}$ We can find the distance that light travels in water in a time of $3.3~nm$: $d = \frac{c~t}{n}$ $d = \frac{(3.0\times 10^8~m/s)((3.3\times 10^{-9}~m))}{1.33}$ $d = 0.75~m$ In water, the light travels $~~0.75~m$ We can find the distance that light travels in glass in a time of $3.3~nm$: $d = \frac{c~t}{n}$ $d = \frac{(3.0\times 10^8~m/s)((3.3\times 10^{-9}~m))}{1.50}$ $d = 0.67~m$ In glass, the light travels $~~0.67~m$ We can find the distance that light travels in cubic zirconia in a time of $3.3~nm$: $d = \frac{c~t}{n}$ $d = \frac{(3.0\times 10^8~m/s)((3.3\times 10^{-9}~m))}{2.16}$ $d = 0.46~m$ In cubic zirconia, the light travels $~~0.46~m$
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