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2.8: Derivation of the Powers

  • Page ID
    8301
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    Up to this point I have defined what is meant by convergence, and I have defined power as the difference between the final and initial convergences. I asserted without proof formulas for the powers of a lens, a refracting interface, and a mirror. It is now time to derive them. Remember that in this chapter I am dealing with small angles only (indeed if angles are not small, a point object will not result in a point image) and consequently I am going to assume that any angle is equal to its tangent or to its sine, and I am going to write Snell’s law in the form

    \( n_1 \sin \theta_1 = n_2 \sin \theta_2\) or \(n_1 \tan \theta_1 = n_2 \tan \theta_2\) or \(n_1 \theta_1 = n_2 \theta_2\)

    as the spirit moves me and at my convenience.


    This page titled 2.8: Derivation of the Powers is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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