Special Relativity Math Thing (Fresnel's Drag Coefficient)

  • #1
Mark Zhu
32
3
Homework Statement:
Because v<<c in this case, we can expand the denominator
(1 + x)^-1 = 1 - x + ... keeping only the lowest term in x
v/c. The above equation becomes...
Relevant Equations:
(1 + x)^-1 = 1 - x + ...
I am wondering if there is a typo in my textbook. Please see the attachment. The textbook says "...keeping only the lowest term in x = v/c." I am wondering if it should be "x = v/(nc)," as I circled in blue on the left side. It is a binomial expansion of the denominator. Shouldn't x be v/(nc) instead of v/c? The textbook says "...keeping only the lowest term in x = v/c." Thank you.
 

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Answers and Replies

  • #2
PeroK
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It doesn't make any difference. ##\frac v c## and ##\frac v {nc}## have the same order of magnitude.
 
  • #3
Mark Zhu
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What do you mean same order of magnitude? Isn't n the index of refraction?
 
  • #4
PeroK
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What do you mean same order of magnitude? Isn't n the index of refraction?
It's ##\frac v c## that is important. You probably have ##n \approx 1## in any case.
 
  • #5
Mark Zhu
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Thank you for your help
 

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