0
$\begingroup$

In the context of spherical mirrors we have

  • $R > 0$ for concave mirrors
  • $R < 0$ for convex mirrors

But for curved refracting surfaces we have

  • $R < 0$ for concave mirrors
  • $R > 0$ for convex mirrors

Why is that so?

$\endgroup$
  • $\begingroup$ this is the convention that makes most sense in my opinion but quite many people use the opposite convention ($R<0$ for concave mirrors ans $R>0$ for convex mirrors). One should bear that in mind and always double check, and best is to always clarify (e.g. using vex and cav as abbreviations) $\endgroup$ – riddleculous May 11 '17 at 9:55
1
$\begingroup$

The general sign rule for the radius of curvature of a spherical surface is the following

When the center of curvature $C$ is on the same side as the outgoing light, $R> 0$ (the radius of curvature is positive), otherwise $R < 0$

Now in spherical mirrors we have

  • For concave mirrors, $C$ is always on the same side as the outgoing light, hence $R > 0$
  • For convex mirrors, $C$ is never on the same side as the outgoing light, hence $R < 0$

But in general curved refracting surfaces (i.e. not reflecting like mirrors) we have

  • For concave mirrors, $C$ is never on the same side as the outgoing light, hence $R < 0$
  • For convex mirrors, $C$ is always on the same side as the outgoing light, hence $R > 0$
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.