Optics Equation: What Assumptions Lead to n1f1=-n2f2?

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In summary, the optics equation n1f1=-n2f2 is a mathematical expression that relates the refractive indices and focal lengths of two thin, symmetric optical systems operating in air or vacuum. This equation is important in designing and understanding optical systems and is derived from Snell's law. It cannot be applied to thick, asymmetric systems or systems operating in a medium with a different refractive index.
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I keep seeing this equation pop up and I have no idea what it is or where it comes from.

[tex]n_{1}f_{1}= -n_{2}f_{2}[/tex]

It looks like a take on snell's law, but what assumptions have to be made to get to this equation from snell's?
 
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The formula is related to an optical aberration called field curvature. See attachment.
 

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Thank you.
 

FAQ: Optics Equation: What Assumptions Lead to n1f1=-n2f2?

What is the meaning of the optics equation n1f1=-n2f2?

The optics equation n1f1=-n2f2 is a mathematical expression that describes the relationship between the refractive indices and focal lengths of two optical systems. It is based on the assumption that the optical systems are thin, symmetric, and operate in air or vacuum.

What are the assumptions that lead to the optics equation n1f1=-n2f2?

The assumptions that lead to the optics equation include:

  • The optical systems are thin, meaning that their thickness is negligible compared to their other dimensions.
  • The optical systems are symmetric, meaning that they have the same refractive index and focal length on both sides.
  • The optical systems operate in air or vacuum, which means that there is no change in refractive index or focal length as light passes through them.

Why is the optics equation n1f1=-n2f2 important in optics?

The optics equation n1f1=-n2f2 is important because it allows us to calculate the focal length of an optical system based on its refractive index and the refractive index of another system. This is crucial in designing and understanding the behavior of optical systems, such as lenses and mirrors.

Can the optics equation n1f1=-n2f2 be applied to all optical systems?

No, the optics equation n1f1=-n2f2 is only applicable to thin, symmetric optical systems that operate in air or vacuum. It cannot be applied to thick or asymmetric systems, or systems that operate in a medium with a refractive index different from air or vacuum.

How does the optics equation n1f1=-n2f2 relate to Snell's law?

The optics equation n1f1=-n2f2 is derived from Snell's law, which describes the relationship between the angles of incidence and refraction of light passing through two different media. By combining Snell's law with the assumption that the optical systems are thin, symmetric, and operate in air or vacuum, we can arrive at the optics equation n1f1=-n2f2.

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