0
$\begingroup$

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.

$\endgroup$

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

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Michael Seifert, tpg2114
If this question can be reworded to fit the rules in the help center, please edit the question.

1
$\begingroup$

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.

$\endgroup$
0
$\begingroup$

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.

Two lenses with different radii, same center thickness, and different edge thicknesses.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.