Special Relativity Math Thing (Fresnel's Drag Coefficient)

[Mark Zhu]

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.

 

[PeroK]

It doesn't make any difference. $\frac v c$ and $\frac v {nc}$ have the same order of magnitude.

 

[Mark Zhu]

What do you mean same order of magnitude? Isn't n the index of refraction?

 

[PeroK]

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.

 

[Mark Zhu]

Thank you for your help