The following matrix product is used in discussing two thin lenses in air: (1 -1/f2 M where fi and f2 are the focal lengths of the lenses and d is the distance between them. As in Problem 9, element M12 is –1/f where f is the focal length of the combination. Find M, det M, and 1/f.
The following matrix product is used in discussing two thin lenses in air: (1 -1/f2 M where fi and f2 are the focal lengths of the lenses and d is the distance between them. As in Problem 9, element M12 is –1/f where f is the focal length of the combination. Find M, det M, and 1/f.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The following matrix product is used in discussing two thin lenses in air:
\[
M = \begin{pmatrix} 1 & -1/f_2 \\ 0 & 1 \end{pmatrix}
\begin{pmatrix} 1 & 0 \\ d & 1 \end{pmatrix}
\begin{pmatrix} 1 & -1/f_1 \\ 0 & 1 \end{pmatrix},
\]
where \( f_1 \) and \( f_2 \) are the focal lengths of the lenses and \( d \) is the distance between them. As in Problem 9, element \( M_{12} \) is \(-1/f\) where \( f \) is the focal length of the combination. Find \( M \), \(\det M\), and \( 1/f \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b6d687b-9b3f-47af-8b4d-c251df44093c%2F6841fdd8-5279-4f9c-8c2a-356f90ef92bc%2Fjc7ljz_processed.png&w=3840&q=75)
Transcribed Image Text:The following matrix product is used in discussing two thin lenses in air:
\[
M = \begin{pmatrix} 1 & -1/f_2 \\ 0 & 1 \end{pmatrix}
\begin{pmatrix} 1 & 0 \\ d & 1 \end{pmatrix}
\begin{pmatrix} 1 & -1/f_1 \\ 0 & 1 \end{pmatrix},
\]
where \( f_1 \) and \( f_2 \) are the focal lengths of the lenses and \( d \) is the distance between them. As in Problem 9, element \( M_{12} \) is \(-1/f\) where \( f \) is the focal length of the combination. Find \( M \), \(\det M\), and \( 1/f \).
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