(a) Explanation Formula used: The equations in Gaussian optics are, n 1 l 0 + n 2 l i = 1 R ( n 2 s i l i − n 1 s 0 l 0 ) (1) l 0 = R 2 + ( s 0 + R ) 2 − 2 R ( s 0 + R ) cos ϕ l i = R 2 + ( s i − R ) 2 + 2 R ( s i − R ) cos ϕ (2) n 1 s 0 + n 2 s i = n 2 − n 1 R (3) n 1 s 0 + n 2 s i = n 2 − n 1 R + h 2 [ n 1 2 s 0 ( 1 s 0 + 1 R ) 2 + n 2 2 s i ( 1 R − 1 s i ) 2 ] (4) Calculation: Approximate the value of cos ϕ as 1 in equation (2). Then, l 0 = R 2 + ( s 0 + R ) 2 − 2 R ( s 0 + R ) cos ϕ l 0 = R 2 + ( s 0 + R ) 2 − 2 R ( s 0 + R ) = R 2 + s 0 2 + 2 s 0 R + R 2 − 2 R s 0 − 2 R 2 = s 0 Similarly, the value of l i is as follows (b) To determine To show: The Equation 1 becomes Equation 4 for third-order optics, if cos ϕ is replaced by its third-degree Taylor polynomial in Equation 2.

8th Edition

ISBN: 9781305266636

Author: James Stewart

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 11.11, Problem 34E

(a)

To determine

To derive: The Equation 3 for Gaussian optics from Equation 1 by approximating cosϕ in Equation 2 by its first degree Taylor polynomial.

(b)

To determine

To show: The Equation 1 becomes Equation 4 for third-order optics, if cosϕ is replaced by its third-degree Taylor polynomial in Equation 2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.11, Problem 33E

Chapter 11.11, Problem 35E

Students have asked these similar questions

Consider the following system of equations, Ax=b : x+2y+3z - w = 2 2x4z2w = 3 -x+6y+17z7w = 0 -9x-2y+13z7w = -14 a. Find the solution to the system. Write it as a parametric equation. You can use a computer to do the row reduction. b. What is a geometric description of the solution? Explain how you know. c. Write the solution in vector form? d. What is the solution to the homogeneous system, Ax=0?

2. Find a matrix A with the following qualities a. A is 3 x 3. b. The matrix A is not lower triangular and is not upper triangular. c. At least one value in each row is not a 1, 2,-1, -2, or 0 d. A is invertible.

Find the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)

Chapter 11 Solutions

Single Variable Calculus

Ch. 11.1 - (a) What is a sequence? (b) What does it mean to...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To derive: The Equation 3 for Gaussian optics from Equation 1 by approximating cos ϕ in Equation 2 by its first degree Taylor polynomial.

Solution Summary: The author explains how to derive the Equation 3 for Gaussian optics by approximating mathrmcosvarphi by its first degree Taylor polynomial.

Videos

To derive: The Equation 3 for Gaussian optics from Equation 1 by approximating cosϕ in Equation 2 by its first degree Taylor polynomial.

To show: The Equation 1 becomes Equation 4 for third-order optics, if cosϕ is replaced by its third-degree Taylor polynomial in Equation 2.

Want to see the full answer?

Chapter 11 Solutions