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[Optics] Concave-Convex lens radius

  • Thread starter decsis
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Hi, I'm trying to solve the following problem:

"What is the optical power (in dioptres) of a concave-convex eyeglass lens (n = 1.5) with the radiuses r1 = 12cm and r2 = 18cm?"

The attempt at a solution:
I'm usually solving such questions with the following equation:

## \dfrac{1}{f} = (n-1)(\dfrac{1}{r_1}-\dfrac{1}{r_2}) ##

I am having problems though choosing the right sign for the radius. I'm using the following picture to get an idea how such a concave-convex lens may look like :

http://upload.wikimedia.org/wikipedia/commons/thumb/4/49/Linsenarten.svg/595px-Linsenarten.svg.png

It is in German though, as I'm from Germany and in the problem, the lense is literally called "Concave-Convex (German: Konkav-Konvex)", so I assume it looks like the 3th or 4th from the left.

I learnt that the radius is positive, if the center of the circle is in the right, and negative if it is in the left:

http://www.geometrische-optik.de/OPTIK-Texte-html/Bilder Kapitel7_Duenne Linsen/bikonvex.gif

And to me it looks like both centers are left, so the radi should be negative, even though in the problem is was written that they are positive and according to the solution (+1.39 dptr), the positive ones were used.

Can anyone tell me why?
 

haruspex

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It will depend on which is r1 and which is r2. How are they defined in the equation? Which is which in the question?
 

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