# How to find the radius of curvature of plano convex lens? [closed]

The information available about the lens are

Refractive index n

Aperture diameter d

Maximum thickness of the lens t

Is it possible to calculate the radius of curvature of the lens using the above 3 information mathematically? (the focal length is not known) If yes please elaborate.

## closed as off-topic by Michael Seifert, tpg2114♦May 12 at 0:22

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You have to find the radius $$R$$ of the curved side which can be done using the intersecting chord theorem.

$$t(2R-t) = \left(\frac d 2 \right)^2$$

and then the lens maker's formula can be used to find the focal length.

If you have no other information, then you can not find the radius from the refractive index n, thickness t, and aperture diameter d. The reason is that two lenses could exist with all identical values of n,t, and d, but their edge thicknesses would not be the same. The edge thickness of the lens would vary with radius. A longer radius would be flatter, and give more edge thickness on the lens. A shorter radius would lead to a smaller value of edge thickness.

See the picture below. The lenses should be drawn as if they have the same center thickness, please excuse the hand sketch. If the focal length is known, then you could get some information on the radius.