Deriving back focal length using Fermat's principle

In summary, Fermat's principle is a fundamental principle in optics that states that light always takes the path of least time between two points. This principle is used in optics to understand and predict the behavior of light in various systems. It can also be used to derive the back focal length of a lens by considering the path of light rays and determining the path that takes the least time. The main assumptions made when using this principle are that light travels in a straight line in a homogeneous medium and that the optical system is symmetric. The accuracy of this method depends on the precision of measurements and validity of assumptions. While Fermat's principle can be applied to any optical system, the complexity and accuracy of measurements may affect the accuracy of the result. Some
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Woolyabyss
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Homework Statement


The plano-convex lens has a diameter of 200 mm and the central thickness of 20 mm. The edge thickness is zero and the refractive index of glass is 1.5. Find the following parameters of the lens: (i) the back focal length

Homework Equations


N/A

The Attempt at a Solution


I've attached my attempt below. I'm assuming the time taken for light to travel from the tip to the focal length is equal to the time taken to travel to the center to the focal length.
 

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Looks right.
 
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What is Fermat's principle?

Fermat's principle is a fundamental principle in optics that states that light will always take the path that requires the least time to travel between two points. This principle is used to understand and predict the behavior of light in various optical systems.

How is Fermat's principle used to derive back focal length?

In optics, the back focal length is the distance between the last optical surface of a lens and the focal point. To derive the back focal length using Fermat's principle, we consider the path of light rays from the object to the image, and use the principle to determine the path that takes the least time. This path will correspond to the back focal length of the lens.

What are the key assumptions made when using Fermat's principle to derive back focal length?

The main assumption made when using Fermat's principle is that light travels in a straight line in a homogeneous medium. This means that the light rays do not refract or bend as they pass through different materials with varying refractive indices. Additionally, the principle assumes that the optical system is symmetric, and that all light rays follow the same path from the object to the image.

How accurate is the method of deriving back focal length using Fermat's principle?

The accuracy of this method depends on the accuracy of the measurements and assumptions made. If the measurements are precise and the assumptions are valid, the result obtained using Fermat's principle should be very accurate. However, in some cases, other factors such as aberrations in the lens may affect the accuracy of the result.

Can Fermat's principle be applied to any optical system to derive back focal length?

Yes, Fermat's principle can be applied to any optical system to derive the back focal length. However, the complexity of the system and the accuracy of the measurements may affect the accuracy of the result obtained. Additionally, certain optical systems, such as those with non-uniform media, may require additional mathematical methods to derive the back focal length.

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