Q. 106 Optical methods of measurement o... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 106 (page 475)

Optical methods of measurement often rely on the interference of two light waves. If two light waves, identical except for a phase lag, are mixed together, the resulting intensity, or irradiance, is given by $I_{1} = 4 A^{2} \frac{(c s c 胃 - 1) (s e c 胃 + \tan 胃)}{c s c 胃 s e c 胃}$
Show that this is equivalent to $I_{1} = {(2 A \cos 胃)}^{2}$

Short Answer

Expert verified

The given expressions are equivalent.

Step by step solution

Step 1. Given Information

The given expressions are $I_{1} = 4 A^{2} \frac{(c s c 胃 - 1) (s e c 胃 + \tan 胃)}{c s c 胃 s e c 胃} a n d$ $I_{1} = {(2 A \cos 胃)}^{2}$

Step 2. Calculation

Consider one expression and prove it is equivalent to the other given expression.

$4 A^{2} \frac{(c s c 胃 - 1) (s e c 胃 + \tan 胃)}{c s c 胃 s e c 胃} = 4 A^{2} \frac{(\frac{1}{\sin 胃} - 1) (\frac{1}{\cos 胃} + \frac{\sin 胃}{\cos 胃})}{\frac{1}{\sin 胃} 脳 \frac{1}{\cos 胃}} = 4 A^{2} \frac{(\frac{1 - \sin 胃}{\sin 胃}) (\frac{1 + \sin 胃}{\cos 胃})}{\frac{1}{\sin 胃 \cos 胃}} = 4 A^{2} \frac{\frac{(1 - \sin 胃) (1 + \sin 胃)}{\sin 胃 \cos 胃}}{\frac{1}{\sin 胃 \cos 胃}} = 4 A^{2} \frac{(1 - \sin 胃) (1 + \sin 胃)}{1} = 4 A^{2} (1 - \sin^{2} 胃) = 4 A^{2} (\cos^{2} 胃) = {(2 A \cos 胃)}^{2}$

Thus, we can conclude that the given expressions are equivalent.

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91影视

Optical methods of measurement often rely on the interference of two light waves. If two light waves, identical except for a phase lag, are mixed together, the resulting intensity, or irradiance, is given by I1=4A2(csc胃-1)(sec胃+tan胃)csc胃sec胃Show that this is equivalent toI1=(2Acos胃)2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Decision Maths

Mechanics Maths

Logic and Functions

Probability and Statistics

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