What are some ways of finding the center of curvature of concave and convex mirrors (spherical)?
For example, I can double the distance of focal length on the principle axis to find the center of curvature of concave mirror.
[Physics] Ways of finding the center of curvature
curvatureopticsreflectionvisible-light
Related Solutions
You find $s$ in the same way you found it for concave mirror, just keep in mind that for the convex mirror the image is always virtual(as explained nicely in the Wikipedia article on curved mirrors, it cannot be projected on a surface, unlike the real image), so in this case (by convention) $s'=-35cm$ and $f=-53cm$.
Not necessarily. The lens equation, as provided by Nordic, is
You can play around with the numbers, and a few things should become obvious.
1) If you increase the radius of one surface to a very large number, the lens becomes either a plano-convex or a plano-concave lens. For the moment, think only about a plano-convex lens, with R2 essentially infinite. Then
1/F = (n-1)(1/R1)
or F = R1 / (n-1)
where n is the refractive index.
2) So, for n < 2, the focal length of a plano-convex thin lens will be greater than the radius of curvature, and for n > 2, the focal length will be less.
Most optical materials have an index of refraction in the range of 1.3 to 1.7 for visible light, so for most lenses, the focal length will be greater than the radius of curvature. Diamond, though, has an index of refraction of about 2.4, so such a lens will reverse the usual order. And although it is reflective in the visible, germanium is transparent in the mid to far infrared, and has an index of refraction of about 4 at these wavelengths.
Best Answer
A concave mirror used for focusing light is parabolic, not spherical. There therefore isn't a "center of curvature".