# Mirrors and lenses under water

#### benw

I just have 2 questions.

If you use a mirror under water would the focal length change? And same question, but if you use a lens under water would the focal length change?

I was thinking, light rays travel slower in water, so then it difracts away from the normal more than if it was in air, which means the light rays converge at a different point?

#### krab

Science Advisor
benw said:
I just have 2 questions.

If you use a mirror under water would the focal length change? And same question, but if you use a lens under water would the focal length change?
No. Yes.

Lenses depend on refraction, which depends on the ratio of refractive indexes of the two media on either side of an interface. So for example, if you have a piece of plastic that has exactly the same refractive index as water, light would not bend at all when going through it under water. In fact, it would be invisible. Also, this is the reason your eyes cannot focus under water.

#### Leo32

To be 100% exact, "No" should read: "no when using front coated mirrors".

In your every day life, mirrors have a reflective layer at the back of a piece of glass. Just to make sure the cleaning lady doesn't scratch it off. Using such a mirror would change the focal length, as the light travels through glass, reflects of the reflective layer and then passes through the glass again. Going from water to glass and vice versa will happen differently in air or in water.

Just for the nitty gritty sake of it.

Greetz,
Leo

#### ceptimus

Even with a back coated mirror, I don't think the focal length would change, assuming the mirror glass is a uniform thickness.

The refraction on the way into the glass is cancelled out by the refraction on the way back out, so you end up with the angle between the incident and reflected beam being determined just by the the angle of incidence.

Although the reflection angle is unchanged by the refractive media, there is an offset between the point the ray strikes the mirror and the point it leaves from. This offset depends on the thickness of the mirror glass, and the difference in the refractive indices of the glass and the other medium. But I think this offset results in an aberation in the focus of the mirror, rather than a change in its focal length?

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