How does the shape of a lens affect focal lengths?

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The shape of a lens significantly influences the convergence of light rays and their respective focal points. Inner rays typically converge at a shorter focal distance compared to outer rays, which require more bending due to the lens's curvature. This discrepancy arises from the ideal versus actual shapes of lenses, affecting how light is refracted. Understanding these differences is crucial for grasping lens design and optical performance. The discussion highlights the importance of lens geometry in determining focal lengths.
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Homework Statement


Why do two outer rays converge to a different focal point than the inner rays?


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The Attempt at a Solution



The distance to the focal point of the inner rays is shorter than the outer rays, the light has to bend a lot more for the outer rays
 
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I don't think you've really hit the nail on the head. Think about the ideal shape of a lens and the actual shape of a lens.
 

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