# the power of a lens and radius of curvature relation

Optical power of the lens depends on the radius of curvature R 1 and R 2 of its spherical surface and the refractive index n of the material from which the lens is made by expressed by the formula $(\frac{1}{r1} + \frac{1}{r2} ) (n-1)$ the question is what's the difference between the two radii, aren't they one?

• Draw an exaggerated picture where one side is flat and the other is curved. – AHusain Mar 17 '17 at 22:52
• elaborate please – sarah Mar 17 '17 at 23:07
• +sarah both the sides don't have to be symmetrical. They can have different "bulginess" or radii of curvature. One side will protrude more and other side will protrude less. This would create two radii of curvature. – Pritt Balagopal Mar 18 '17 at 7:14

According to the lens maker's formula,

$\frac{1}{f}=(\frac{n_2}{n_1}-1)(\frac{1}{R_1}-\frac{1}{R_2})$,

Here, $n_2$ is the refractive index of the lens and $n_1$ is the refractive index of the medium from which the light is incident on the lens. The medium surrounding the lens must be the same for this formula to work.

$R_1$ and $R_2$ are the radius of curvature of the curved surfaces of the lens from which the light enter the lens and emerges out of the lens respectively.

Sign Conventions play an important role here.

For a convex lens, $R_1$ is +ve (if light is incident from the left) and $R_2$ is -ve. In the above image, as you can see, the radius of the curvature of the convex lens' left curved surface $(R_1)$ lies in the direction of the incident ray, so it is +ve and the radius of curvature of the other surface $(R_2)$ points the direction opposite to the direction of incident ray, so its -ve.

So after applying the sign conventions for a convex lens, as explained above, we get the following formula,

$\frac{1}{f}=(\frac{n_2}{n_1}-1)(\frac{1}{R_1}+\frac{1}{R_2})$

This is just a rehash of Sammy Gerbil's answer with some illustrating graphics, since I have them on hand. Witness the three "radius" dimensions that define an object such as you are considering. $r_1,\, r_2$ are the two radius dimensions marked on the left hand projection.

I think you are confusing the radius of a circular lens with the radius of curvature of each face.

The radius of a circular lens is the same when measured from front and back, looking at the lens face on. The radius of curvature measures the bulge of the spherical faces as you look at the lens side on. The front and back surfaces of the lens can have a different radius of curvature.