# Arrow that changes direction home experiment

I saw this cool optical effect in a experiment on Youtube:

Could anyone explain to me why the arrow points in the opposite direction?

I have read something about the refraction index of the glass and water, but it's not clear to me how those cause the effect.

A convex lens produces an image that is inverted. If we put the object at twice the focal length then the image is the same size as the object but the other way up.

This is what is happening in the video. When the glasc is empty it does not act as a lens so the light passes straight through and we see both arrows unchanged. When the glass is filled with water the glass+water acts as a cylindrical convex lens, and this produces an inverted image. The glass has been carefully positioned so that the object is twice the focal length away from the glass, so the inverted image is about the same size as the object.

• Just a small comment. When the glass is empty, the arrows are changed. You can see clearly at the beginning of the video that the arrows become smaller when the glass is introduced. It might be nice to add this to the explanation. – Hernan Apr 8 '15 at 17:25

Yes, this a pretty and very simple experiment. And the explanation likewise.

It is indeed about refractive index. The glass seen from above (empty to the left):

The refractive index $n$ (or index of refraction) is a material proporty. It is the relation between the speed $v$ of light in the material as to that in vacuum $c$:

$$n=\frac{c}{v}$$

Each material has it's own value, $n_{air}$, $n_{glass}$, $n_{water}$.

• A ray of light from low to high index of refraction bends inwards (incident angle is larger than refraction angle).
• A ray of light from high to low index of refraction bends outwards (incident angle is smaller than refraction angle).

For air$\to$glass the light bends. For glass$\to$air on the inside, it bends back. The ray is shifted a bit to the side but still towards you. Same but opposite situation when it hits the other inside of the glass. The ray is then back where it started.

With water in the glass, for air$\to$glass the light still bends inwards. For glass$\to$water it bends even more. It will reach the other side of the glass. For water$\to$glass it bends a bit back. For glass$\to$air it bends all the way back. Direction is the same but the ray is shifted to the side.

The change in glass is cancelled out on each side. But the change in water is not.

• So I've seen similar demonstrations where red and blue text are placed behind a cylindrical lens, and only one set of text is inverted. Does this have to do with the index being different for different wavelengths? – docscience Jan 26 '15 at 17:22