## Total Internal Reflection in a Stream of Water

### Experiment number : 1765

• #### Goal of experiment

This experiment demonstrates a total internal reflection and shows the principle of optical fibres.

• #### Theory

Refraction of light at the interface of two media is described by Snell’s law

$n_1 \sin⁡ \alpha=n_2 \sin⁡ \beta,$

wherre $$\alpha$$ is the angle of incidence, $$\beta$$ angle of refraction and n1, n2 are refractive indices of the media. In order to observe the total reflection, the light must pass from an optically denser medium to an optically thinner medium. The propagating wave refracts away from the normal and with increasing angle of incidence the angle of refraction increases. When we reach the critical angle, the refraction angle reaches the largest possible value of 90°. The critical angle is therefore the largest angle of incidence at which refraction occurs. At larger angles of incidence the refraction does not occur and the ray is reflected at the interface. We call this a total internal reflection. On this phenomenon optical fibres are based. In the figure below there is a ray passing in an optical fibre.

• #### Tools

Laser pointer, plastic bottle, milk, container for water, nail.

• #### Procedure

1. Using the nail, make a hole in the bottle about 5 cm above the bottom.
2. Place the bottle on an elevated place and fill it with water.
3. Place the container under the bottle, so that it catches the water spilling out from it.
4. Point the laser beam horizontally through the bottle, so that it comes through to the hole.
5. Observe the beam in the spilling water.
• #### Sample result

Video below illustrates the experiment performation.

• #### Technical notes

• For easier penetration of the bottle with a nail, heat the nail above a candle.
• The hole should be wider that the width of the laser beam, so that no unwanted refraction occurs. Above that, the laser beam can pass through the stream of water and you should be able to see some points of refraction, which visualises the demonstrated phenomenon.
• When filling the bottle, it is recommended to seal the hole and the bottle so that the water does not spill until the experiment is prepared.
• The effect can be improved by adding a few drops of milk into the water, which makes the laser beam more visible.
• #### Pedagogical notes

• In this experiment, not only the reflection of the laser beam occurs. There is also a refraction of the beam out from the water stream; otherwise we would not be able to see the beam.