Finding Point Q in a Parabolic Dish: Proving the Reflection Theory

In summary, the problem is to prove that all the reflecting light rays that hit the parabolic dish go through the same point Q in the Z axis. The problem can be reduced to 2 dimensions by starting with the parabola y = ax^2 and trying to find the angle of the line x = c that strikes the curve. However, this approach did not yield the correct angle and the solution may require the use of gradient magic. The final step is to find the point Q.
  • #1
gipc
69
0
I have the following "Parabolic Dish" z=c(x^2+y^2)
I have to prove that all the reflecting light rays that hit that dish go through the same point Q in the Z axis, and then I have to find said point Q.


I've thought of reducing the problem to 2 dimensions. Started with the parabola y = ax^2. Tried to find the angle that some line x = c strikes the curve but couldn't find the correct angle. Maybe do some gradient magic?


I'm unsure really, how to set it all together for a good proof, and how to finally find the point Q.

Please help :)
 
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  • #2


gipc said:
I have the following "Parabolic Dish" z=c(x^2+y^2)
I have to prove that all the reflecting light rays that hit that dish go through the same point Q in the Z axis, and then I have to find said point Q.


I've thought of reducing the problem to 2 dimensions. Started with the parabola y = ax^2. Tried to find the angle that some line x = c strikes the curve but couldn't find the correct angle. Maybe do some gradient magic?

I'm unsure really, how to set it all together for a good proof, and how to finally find the point Q.

Please help :)
I doubt that this is the complete problem as given. The incident rays would all need to be parallel to the z-axis.
 
  • #3


Ohh, yes, obviously they are indeed parallel :)
 

Related to Finding Point Q in a Parabolic Dish: Proving the Reflection Theory

What is the reflection theory in a parabolic dish?

The reflection theory in a parabolic dish states that incoming waves or rays of light will be reflected off the curved surface of the dish and converge at a single point known as Point Q.

How is Point Q located in a parabolic dish?

Point Q can be located by finding the focal point of the parabolic dish, which is the point where all incoming waves or rays of light will converge after reflecting off the surface of the dish.

What is the purpose of finding Point Q in a parabolic dish?

Finding Point Q is important in order to prove the reflection theory and demonstrate the effectiveness of a parabolic dish in focusing and amplifying incoming waves or rays of light. This principle is used in various applications such as satellite dishes, solar cookers, and telescopes.

What factors can affect the accuracy of locating Point Q in a parabolic dish?

The accuracy of locating Point Q can be affected by the shape and size of the dish, the distance of the dish from the source of the waves or rays of light, and any obstructions or imperfections on the surface of the dish.

How can the reflection theory be applied in other fields of science?

The reflection theory in a parabolic dish can be applied in other fields of science such as acoustics, where it is used to focus and amplify sound waves, and in optics, where it is used in the design of mirrors and lenses to manipulate light. It is also used in radar technology to detect and track objects.

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