# Special Relativity Math Thing (Fresnel's Drag Coefficient)

• Mark Zhu
In summary, the conversation is about a possible typo in a textbook's equation for x, which the person believes should be x = v/(nc) instead of x = v/c. However, it is explained that both equations have the same order of magnitude and the value of n, the index of refraction, is approximately 1 regardless. The person thanks the expert for their help.
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.

#### Attachments

• Capture1.PNG
47.6 KB · Views: 90
It doesn't make any difference. ##\frac v c## and ##\frac v {nc}## have the same order of magnitude.

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

Mark Zhu said:
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.

## What is the Special Relativity Math Thing (Fresnel's Drag Coefficient)?

The Special Relativity Math Thing, also known as Fresnel's Drag Coefficient, is a mathematical equation used to calculate the drag force experienced by a moving object in a medium with a refractive index. It takes into account the effects of special relativity, such as time dilation and length contraction, on the drag force.

## How is Fresnel's Drag Coefficient calculated?

Fresnel's Drag Coefficient is calculated using the equation: Fd = ρv2c2sin2(θ)/2, where Fd is the drag force, ρ is the density of the medium, v is the velocity of the object, c is the speed of light, and θ is the angle between the direction of motion and the direction of the wave.

## What is the significance of Fresnel's Drag Coefficient in special relativity?

Fresnel's Drag Coefficient is significant in special relativity because it helps to explain the observed effects of relativity on the motion of objects in a medium. It takes into account the changes in time and space that occur at high speeds, and allows for more accurate calculations of drag forces in these situations.

## What are the limitations of using Fresnel's Drag Coefficient?

One limitation of using Fresnel's Drag Coefficient is that it only applies to objects moving at high speeds in a medium with a refractive index. It does not account for other factors that may affect drag, such as turbulence or surface roughness. Additionally, it assumes a perfectly flat and uniform medium, which may not always be the case in real-world situations.

## Are there any real-world applications of Fresnel's Drag Coefficient?

Yes, Fresnel's Drag Coefficient has practical applications in fields such as aerodynamics and astrophysics. It is used to calculate the drag forces experienced by objects moving through air or other fluids at high speeds, and can also be applied to the motion of particles in the Earth's atmosphere or in interstellar space.

• Aerospace Engineering
Replies
5
Views
681
• Introductory Physics Homework Help
Replies
3
Views
390
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
13
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
858
• Introductory Physics Homework Help
Replies
88
Views
6K
• Introductory Physics Homework Help
Replies
6
Views
849
• Special and General Relativity
Replies
6
Views
1K
• Introductory Physics Homework Help
Replies
7
Views
2K