# Change in focal length of lens inside water

I read it on Yahoo Answers (link below) that the power of lens changes when the lens is placed inside water. But then, if we consider the formula f=c/2 , the radius if curvature of the lens still remains same, then, how can the focal length change?

While considering the definition (point where light rays meet) we see that the focal length changes. But while considering the formula (f=c/2) focal length doesn't change.

Can anyone please explain this and please do mention whether the focal length actually changes or not.

• possible duplicate of Eyes open under water – DumpsterDoofus Mar 8 '14 at 15:01
• No the answer isn't there in those answers. :) – Harshal Gajjar Mar 8 '14 at 15:15
• Because the curvature of the lens is not the only aspect determining the focal length. The materials of lens and surroundings need also be taken into account. Which is done in the yahoo reference as in the reference given by DumpsterDoofus. And yes it changes – KvdLingen Mar 8 '14 at 15:31
• The lens bends light by refraction. Refraction depends on the indicies of refraction on both sides of the boundary. In other words, the accepted answer on @DumpsterDoofus' proposed duplicate contains the heart of the answer in the first sentence. – dmckee Mar 8 '14 at 15:48
• @HarshalGajjar: The answer is in there, read it again. – DumpsterDoofus Mar 8 '14 at 16:12

The formula $$f=\frac{c}{2}$$ where $c$ is the radius of curvature is for mirrors, not lenses.

The reason you are getting a wrong result is that you are applying a formula designed for mirrors to a lens.

Incidentally, the formula $f=\frac{c}{2}$ is still valid for mirrors underwater.

• Then is there no relation between C and F of lens? Also, in all my classes, I, used this same relation even for lens and got the correct answer, was that just coincidence? Thanks in advance. :) – Harshal Gajjar Mar 8 '14 at 16:57
• Thanks for feedback. I don't see how $f=c/2$ could apply to lenses. Where does the index of refraction enter the formula? Also, do you have a reference for the formula? I've searched online, but I've never seen it applied to lenses, only mirrors. Usually the Lensmaker's Equation is used for lenses, see en.wikipedia.org/wiki/Lens_(optics)#Lensmaker.27s_equation. – DumpsterDoofus Mar 8 '14 at 17:01
• Whenever C was given I used to just divide it by 2 to get the focal length. :) Anyways now I got my mistake, thanks. :) – Harshal Gajjar Mar 8 '14 at 17:32

Air, water and glass have different refractive indexes. This is a name given to a property of materials that affects the direction of a ray of light crossing a boundary between two materials. It is related to the speed of light in those materials.

This angle of refraction affects the focal length of a lens.

If you drop a glass lens into a liguid with the same refractive index, the lens no longer focuses light at all.

Image from gr5.org

• So is the formula f=c/2 wrong? – Harshal Gajjar Mar 8 '14 at 16:19
• As long as you do take in account the refractive indices, yes it is wrong. – KvdLingen Mar 8 '14 at 16:30

The focal length of a lens changes when the optical medium changes because focal length of any lens depends on the refractive index of the optical medium.

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