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valeriy2222 said:It says you can not change with lenses the value L - radiance. Below I have an example where it proves that you can or where am I wrong? (I made L for 2D case, in 3D case everything the same - L2>L1)
"Something is conserved/invariant" does not mean "this has the same value everywhere, for all setups".valeriy2222 said:well, lagrange invariant says you can not.
Andy Resnick said:I don't understand what you are trying to show.
If the light source is the same - it is not in your setups. And only if your focussing is ideal.valeriy2222 said:Then if you want at least the same amount of light into a smaller area the angle of radiance must increase.
valeriy2222 said:you focus some light (Watt) in a specific area (m2) and get a angle of radiance(sr - steradian). Then if you want at least the same amount of light into a smaller area the angle of radiance must increase. That's the Etendue/optical throughput/optical invariant. However, in the examples I have provided, I focus more light in the same area with the same angle thus breaking the L rule or what am I missing?
The Lagrange (Optical) invariant is a mathematical value used in optics to describe the behavior of light waves. It is defined as the product of the refractive index of a medium and the sine of the angle between the incident and refracted rays.
The Lagrange (Optical) invariant is related to diffraction because it is used to determine the amount of diffraction that occurs when light passes through a diffracting element, such as a grating or a slit. It helps to predict the spacing and intensity of the diffraction pattern.
Violation in diffraction refers to a situation where the Lagrange (Optical) invariant is not conserved, meaning that the value of the invariant changes as light passes through a diffracting element. This can occur when the light beam is not fully collimated, or when the diffracting element is not perfectly aligned.
Violation in diffraction can be caused by several factors, including imperfect alignment of the diffracting element, variations in the refractive index of the medium, or non-uniformities in the incident beam of light. It can also be influenced by the size and shape of the diffracting element, as well as the wavelength of the incident light.
To minimize violation in diffraction, it is important to carefully align the diffracting element and ensure that the incident beam of light is as collimated as possible. Using a smaller diffracting element or a shorter wavelength of light can also help to reduce violation in diffraction. Additionally, using a medium with a more uniform refractive index can also help to minimize the effects of violation in diffraction.