Classical ellipsoidal scattering Impact parameter

In summary, the problem involves solving for the equation (x^2 + y^2)/a^2 + z^2/c^2 = 1 and finding the value of b(θ) using the given formula b(θ) = R / (f^2 * tan^2(θ/2) + 1)^0.5. The solution involves substituting the given values for f and z, and simplifying the equation using trigonometric identities. Further clarification on the problem is needed for a complete solution.
  • #1
insanelover11
1
0

Homework Statement


(x^2 + y^2)/a^2 + z^2/c^2 = 1

Homework Equations


[/B]

The Attempt at a Solution



the answer is :
b(θ) = R / (f^2 * tan^2(θ/2) + 1)^0.5
I can't understand how to calculate this.

My attempt :
(x^2 + y^2)/a^2 + z^2/c^2 = 1 from this.

b^2 + z^2/f^2 = a^2 , f = c/a, z = b*cot(∅)

b^2 *[ 1 + {1/f*tan(∅)}^2 ] = a^2

could you give a hand?...
 
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  • #2
:welcome:

Hello, it would be helpful, if you explained what is expected to be done. E.g. there is no "b" nor a "##\theta##" in the problem description. Also you should use more parentheses in case of a linear notation of quotients. Of course it would be far better, if you could use LaTeX code. For a brief introduction see: https://www.physicsforums.com/help/latexhelp/
(It's quite easy to make formulas a lot more readable.)
 

1. What is the classical ellipsoidal scattering impact parameter?

The classical ellipsoidal scattering impact parameter is a term used in physics to describe the distance between the center of an elliptical object and the path of a particle that is being scattered by the object.

2. How is the classical ellipsoidal scattering impact parameter calculated?

The classical ellipsoidal scattering impact parameter is calculated using a mathematical formula that takes into account the size and shape of the scattering object, as well as the velocity and direction of the scattered particle.

3. What does the classical ellipsoidal scattering impact parameter tell us about a scattering event?

The classical ellipsoidal scattering impact parameter provides information about the trajectory and outcome of a scattering event. It can help us understand the degree to which a particle will be deflected by the scattering object and the angle at which it will be scattered.

4. How is the classical ellipsoidal scattering impact parameter used in research and experiments?

The classical ellipsoidal scattering impact parameter is used in a variety of scientific studies and experiments, particularly in the fields of astronomy and particle physics. It allows researchers to make predictions and analyze the results of scattering events, which can provide insights into the properties and behavior of particles and objects.

5. Are there any limitations to using the classical ellipsoidal scattering impact parameter?

While the classical ellipsoidal scattering impact parameter is a useful tool in understanding scattering events, it does have some limitations. For example, it assumes that both the scattering object and the scattered particle are perfectly spherical, which may not always be the case in real-world situations.

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