Reflection at a spherical surface

The focal length is taken positive in case of a concave mirror. F=|R|/2

ehild

 

The notes are wrong. Concave mirrors and convex lenses have positive focal distance while convex mirrors and concave lenses have negative focal distances.

 

I'm not sure that there is a universally agreed convention. The important thing is to pick a convention and ensure all your equations conform to it.

The convention used at http://en.wikipedia.org/wiki/Radius_of_curvature_(optics) and http://en.wikipedia.org/wiki/Focal_length seems good to me. You treat the incoming ray as coming from the negative side to the positive. The radius of the surface is always taken as the offset from the surface to the centre of curvature. So we have concave negative, convex positive whether it be a mirror, or the entry surface of a lens, but reversed for the exit surface of a lens.
Correspondingly, the focal length formula for a lens uses 1/R₁ - 1/R₂. Thus, for a biconvex lens we get a positive minus a negative, and the curvatures reinforce.

The error in the OP is the sign of S.

 

Yes there are alternative sign conventions but the one I described is the easiest.

 

How so?

 

Gaussian sign convention is easier for students that are being introduced to the subject because
* The equations used for mirrors and lenses become identical
* A minus sign for image location corresponds to a virtual image and the same thing is true for an object

The disadvantage is
* The sign convention for an object seems backwards (the left sign of the axis is negative, they are not used to that)

My experience is that students find the advantages to outweigh the disadvantages