What it shows
Rays from an object under water that meet the surface at more than the critical angle are totally reflected and cannot leave. A disc on the surface can hide a pin completely when its radius is large enough, which gives the refractive index.
The science
Light leaving water for air bends away from the normal. At the critical angle C the refracted ray runs along the surface; for larger angles the light is totally internally reflected, and sin C = 1 / n, where n is the refractive index of the water. A pin of length h hanging under a disc of radius r sends rays to the rim at an angle with tan = r / h; when the pin just disappears from above, that angle equals C, so sin C = r / √(r² + h²) and n = √(r² + h²) / r.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A tall, clear, straight-sided glass or a transparent plastic container
- A circular cork or foam disc about 5 cm across, with a pin pushed through its centre, point down
- Water
- A ruler and a fine pin
- A card with a hole to look through
- A piece of tape to hold the pin steady
Safety
For this project: An adult must handle the sharp pins and push them through the disc.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Fill the glass with water almost to the brim and let it settle.
Push the pin through the centre of the cork disc so that its point hangs down by about 3 cm; the head is on top and the disc floats on the water.
Look at the pin from above and from the sides; when seen from directly above the point is visible through the water.
Cut cards of increasing size, or use a larger disc, and keep trying until you find the smallest radius that makes the point of the pin vanish from every angle.
Measure the radius r of the disc and the length h of the pin below the disc with the ruler.
Repeat with pins of different length h and find the matching smallest r each time.
Calculate sin C = r / √(r² + h²) and n = 1 / sin C for each trial and take the average.
What you should see
For water, r / h turns out to be near 1.13, giving a critical angle of about 49 degrees and n about 1.33. The pin disappears whenever the disc radius is larger than this ratio times the pin length.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What is total internal reflection?
All the light is reflected back into the denser medium when it meets the boundary at more than the critical angle.
2What is the critical angle of water?
About 49 degrees, since sin C = 1 / 1.33.
3Why does the pin disappear?
Rays leaving the pin tip toward the rim of the disc reach the surface above the critical angle, so none of them reach the eye from outside the disc.
4Name a use of total internal reflection.
Optical fibres, prism binoculars and diamond’s sparkle.
Take it further
Use salt water of a known strength and show that the critical angle becomes smaller because n has increased.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
Free ebooks for this project
Science projects
Science Projects for Class 9 and 10
Models and experiments for high-school physics, chemistry and biology
Science projects
Investigatory Projects for Class 11 and 12
Topics, method and report structure for physics, chemistry and biology