Increasing lens power?

[LINK1290]

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A solution to one of the practice problems in my prep book states that "increasing the radius of curvature of one side will flatten the lens and reduce the amount that it refracts light, thus decreasing its power." However, the lens maker's equation shows that 1/f is proportional to (1/r1 - 1/r2), where r1 and r2 are radii of curvature of the lens. If, say, r2 was increased, that would make (1/r1 - 1/r2) larger, making 1/f (the lens power) larger. Does the solution in the book conflict with the lens maker's equation, or is there something simple I'm missing here?

 

[engineeredout]

A solution to one of the practice problems in my prep book states that "increasing the radius of curvature of one side will flatten the lens and reduce the amount that it refracts light, thus decreasing its power." However, the lens maker's equation shows that 1/f is proportional to (1/r1 - 1/r2), where r1 and r2 are radii of curvature of the lens. If, say, r2 was increased, that would make (1/r1 - 1/r2) larger, making 1/f (the lens power) larger. Does the solution in the book conflict with the lens maker's equation, or is there something simple I'm missing here?

If (1/r1 - 1/r2) is made bigger, f will be smaller, no? Remember that its 1/f that is getting larger, so f itself will get smaller.

 

[LINK1290]

Right, that's what I'm saying. If (1/r1 - 1/r2) is made bigger by increasing r2 (in other words, making one side of the lens flatter), then f is made smaller, and 1/f is made larger. Power is equal to 1/f, so power would increase by flattening one side of the lens. However, my book says that power is decreased by flattening one side of the lens. Where am I going wrong?

 

[neutropos]

Well, what if you increased r1?

 

[LINK1290]

Even if r1 is increased, the difference between r1 and r2 increases, which means that (1/r1 - 1/r2) grows larger in absolute value, and the magnitude of 1/f increases, right? Power would still increase.

 

[TieuBachHo]

A solution to one of the practice problems in my prep book states that "increasing the radius of curvature of one side will flatten the lens and reduce the amount that it refracts light, thus decreasing its power." However, the lens maker's equation shows that 1/f is proportional to (1/r1 - 1/r2), where r1 and r2 are radii of curvature of the lens. If, say, r2 was increased, that would make (1/r1 - 1/r2) larger, making 1/f (the lens power) larger. Does the solution in the book conflict with the lens maker's equation, or is there something simple I'm missing here?

I am thinking that you are missing the sign convention of radii. The radii of curvature of lens are opposite since they are on both sides. Thus the power should decrease as you increase the radius. Make sense?