In the following image:

enter image description here


$R1$ is positive as it is measured from the left surface and extends to the right.

$R2$ is negative as it is measured from the right surface and extends to the left.

As per:

For a double convex lens the radius R1 is positive since it is measured from the front surface and extends right to the center of curvature. The radius R2 is negative since it extends left from the second surface (Source).

So extending left is negative, extending right is positive, correct?

However, in this image:

enter image description here


Firstly they have R1 labelled on the opposite side to the first image.


$R1$ and $R2$ both extends to the left, so wouldn't these be negative?

Why have they labeled them positive?

This last image is for information of all the cases, just as an FYI: enter image description here


Firstly, lets define a reference system. Lets place the origin at the center of the lens and let right hand side be positive and left negative. The Lensmaker's formula works with this convention, although you can modify the formula and define your reference system accordingly.

In the first image $R_1$ is positive because if we draw a circle that the left surface (the first surface, hence the number $1$ used for it) is a part of, the center of the circle would be about $R_1$ distance to the right of the lens. Similarly, $R_2$ is negative because the center of the circle it is a part of, lies in the negative side of the axis.

Now, in the second image, the left surface is called $R_1$ because we are labeling the surfaces this way. Here both the left and right surfaces open to the right, i.e. if we draw a circle for each of them their centers would be along the (+)ve direction of the axis. Hence $R_1 > 0$ and $R_2 > 0$.

As a check, the last image is consistent with this convention.


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