# Sign convention for lens [duplicate]

What will be the sign convention for radius of curvature of a concavo-convex lens ? I know for equibiconcave and equibiconvex separately but for mixed one I am not clear .

For example for the following what will be the sign convention for radius of curvature here:

• Which sign convention have you adopted when using the lens equation which incorporates the focal length, object distance and image distance? – Farcher Jul 9 '18 at 8:28
• It's the same: the direction in which the light travels is considered to be positive. Practically any ray diagram for concavo convex lenses or convexo concave or anything would indicate that. – user191954 Jul 9 '18 at 9:14
• I have added an example so that you can now understand what I am referring to . – tejaswini nayak Jul 9 '18 at 14:27
• More on sign conventions in optics. – Qmechanic Jul 9 '18 at 19:15

For thin lenses we can use the lens maker's equation:

$$\frac1f=(n-1)(\frac1R_1-\frac1R_2)$$

Where $n$ is the index of refraction of the material, $R_1$ is the radius of curvature of the side the light hits first, and $R_2$ is the radius of curvature of the side the light hits last.

For each $R$, the convention is such that we make $R>0$ if the light hits the curved surface before the center of curvature, and $R<0$ if the opposite is true.

Therefore, in your example with light approaching from the left, both $R_1$ and $R_2$ should be taken to be positive if you are using this formula. This results in a positive focal length.

I think a good rule of thumb though is that if the lens is thicker in the middle than on the edges it is a converging lens, and hence has positive focal length.

• Thank you for helping me understand this , I understood now – tejaswini nayak Jul 9 '18 at 14:47
• @tejaswininayak If it is the answer you were looking for you should mark it as the correct answer. – Aaron Stevens Jul 9 '18 at 14:55