Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 33 - Electromagnetic Waves - Problems - Page 1006: 66g

Answer

none

Work Step by Step

Let $\theta_2$ be the refracted angle inside the block. We can use Snell's law to find $\theta_2$: $n_2~sin~\theta_2 = n_1~sin~\theta_1$ $sin~\theta_2 = \frac{n_1~sin~\theta_1}{n_2}$ $\theta_2 = sin^{-1}~(\frac{n_1~sin~\theta_1}{n_2})$ $\theta_2 = sin^{-1}~(\frac{1.00~sin~70^{\circ}}{1.56})$ $\theta_2 = sin^{-1}~(0.60237)$ $\theta_2 = 37.0^{\circ}$ If the ray travels a vertical distance of $H = 2.00~cm$, we can find the horizontal distance $x$ that the ray travels: $\frac{H}{x} = tan~\theta_2$ $x = \frac{H}{tan~\theta_2}$ $x = \frac{2.00~cm}{tan~37.0^{\circ}}$ $x = 2.65~cm$ Since $x \lt W$, then the point of first reflection is on side 2. Let $\theta_3$ be the refracted angle in air. Note that the incident angle at the point of first reflection is $90^{\circ}-37.0^{\circ}$ which is $\theta_i = 53.0^{\circ}$ We can use Snell's law to find $\theta_3$: $n_3~sin~\theta_3 = n_2~sin~\theta_i$ $sin~\theta_3 = \frac{n_2~sin~\theta_i}{n_3}$ $sin~\theta_3 = \frac{1.56~sin~53.0^{\circ}}{1.00}$ $sin~\theta_3 = 1.25$ Since there is no angle such that $sin~\theta_3 = 1.25$, there is no refraction at the point of first reflection.
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