[Optics] Concave-Convex lens radius

In summary, the question is asking for the optical power of a concave-convex eyeglass lens with a refractive index of 1.5 and radiuses of 12cm and 18cm. The solution involves using the equation 1/f = (n-1)(1/r1 - 1/r2), but the correct sign for the radiuses is unclear. Based on the provided pictures, it appears that both centers of the lens are on the left, which would make the radiuses negative. However, the solution uses positive radiuses, so it is unclear why. The solution will depend on how the radiuses are defined in the equation and in the question.
  • #1
decsis
1
0
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 learned 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?
 
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  • #2
It will depend on which is r1 and which is r2. How are they defined in the equation? Which is which in the question?
 

Related to [Optics] Concave-Convex lens radius

1. What is the difference between a concave and convex lens?

A concave lens is thinner in the middle and thicker at the edges, causing light rays to diverge. A convex lens is thicker in the middle and thinner at the edges, causing light rays to converge.

2. What is the radius of curvature of a concave-convex lens?

The radius of curvature is the distance between the center of the lens and the point where the curved surface meets the optical axis. For a concave-convex lens, the radius of curvature of the concave surface is negative and the radius of curvature of the convex surface is positive.

3. How does the radius of curvature affect the focal length of a concave-convex lens?

The focal length of a concave-convex lens is determined by the difference between the radii of curvature of its two surfaces. A smaller radius of curvature will result in a shorter focal length, while a larger radius of curvature will result in a longer focal length.

4. Can the radius of curvature of a concave-convex lens be changed?

Yes, the radius of curvature can be changed by altering the shape of the lens's surfaces. This can be done through grinding, polishing, or other manufacturing processes.

5. How does the radius of curvature affect the magnification of a concave-convex lens?

The magnification of a concave-convex lens is determined by the ratio of the image distance to the object distance. The radius of curvature can affect this ratio, as a larger radius of curvature will result in a smaller magnification, and vice versa.

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