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

Published by Pearson

Chapter 34 - Ray Optics - Exercises and Problems - Page 990: 4

Answer

$t = 0.40~ns$

Work Step by Step

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 time required for light to travel a distance $d$ in a medium: $t = \frac{d}{v}$ $t = \frac{d~n}{c}$ We can find the time required for light to travel through the glass layer: $t_g = \frac{d~n}{c}$ $t_g = \frac{(1.0\times 10^{-2}~m)(1.50)}{3.0\times 10^8~m/s}$ $t_g = 5.0\times 10^{-11}~s$ We can find the time required for light to travel through the oil layer: $t_o = \frac{d~n}{c}$ $t_o = \frac{(5.0\times 10^{-2}~m)(1.46)}{3.0\times 10^8~m/s}$ $t_o = 2.43\times 10^{-10}~s$ We can find the time required for light to travel through the polystyrene layer: $t_p = \frac{d~n}{c}$ $t_p = \frac{(2.0\times 10^{-2}~m)(1.59)}{3.0\times 10^8~m/s}$ $t_p = 1.06\times 10^{-10}~s$ We can find the total time: $t = t_g+t_0+t_p$ $t = (5.0\times 10^{-11}~s)+(2.43\times 10^{-10}~s)+(1.06\times 10^{-10}~s)$ $t = 4.0\times 10^{-10}~s$ $t = 0.40~ns$

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