Deriving back focal length using Fermat's principle

AI Thread Summary
The discussion focuses on calculating the back focal length of a plano-convex lens with specific dimensions and refractive index. The lens has a diameter of 200 mm, a central thickness of 20 mm, and an edge thickness of zero, with glass having a refractive index of 1.5. The user attempts to apply Fermat's principle, assuming equal travel time for light from the lens tip and center to the focal point. The calculations and reasoning are presented, but further clarification or validation of the approach may be needed. The thread highlights the application of optical principles in determining lens parameters.
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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