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Is it true that, twice the focal length of a convex lens is equal to the radius of curvature? Please give your opinion.

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    $\begingroup$ Do you mean an equiconvex lens? There are two radii of curvature. It's possible to have two different magnitudes (and even signs) for the radii and still have a positive lens. And this is not an opinion. It's a fact. $\endgroup$ – Bill N May 27 '18 at 12:49
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No. It is not true for a lens (except, possibly, rarely by numerical accident*). It is, though, true for a concave mirror (and no doubt for a convex mirror). For a (thin) converging lens in air or a vacuum, the relationship is this: $$\frac{1}{f}=(n-1)\left(\frac{1}{r_1}+\frac{1}{r_2}\right)$$ in which $r_1$ and $r_2$ are the radii of curvature of the two lens surfaces, counted positive if convex as seen from the outside, and n is the refractive index of the glass.

*For example, for an equiconvex lens ($r_1 = r_2$) what would n have to be in order for the focal length to be equal to $\frac{r_1}{2}$ ?

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  • $\begingroup$ I've just put right a typo: $n$ is the refractive index of the $glass$. $\endgroup$ – Philip Wood May 27 '18 at 13:53
  • $\begingroup$ "It is, though, true for a convex mirror." Only if n were 2. $\endgroup$ – my2cts May 27 '18 at 13:55
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    $\begingroup$ Thanks for giving the details. I also thought the same. My approach was this: Consider two identical equiconvex lenses, but made of two different materials. If one of the those two materials have greater 'bending power', the light will be bent more and so the focus will be nearer to the lens. Thus focal length will decrease. I think the same concept is explained by the above equation. Though we do not have that equation in high school classes. Thank you very much. $\endgroup$ – Nikhil Kumar May 29 '18 at 6:23
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    $\begingroup$ Well done! Lenses used to be taught in quite a lot of detail at high school level (at least they were in the UK). As an application of refraction, lenses are part of a subject called $geometrical\ optics$, which has been largely squeezed out of school syllabuses by more exciting topics! $\endgroup$ – Philip Wood May 29 '18 at 6:59

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