Measuring hard things with easy experiments

Here are some links to experiments that allow you to measure impossibly-difficult-sounding things using everyday objects:

Measuring the thickness of a human hair using a laserpointer and a tape measure.

Tape a hair over the business end of a red laserpointer so it's roughly centered in the beam. Shine it onto the wall a few feet away. It should form a 'diffraction pattern' - a sequence of dark and bright areas in a line either side of the main beam. Measure the distance from the center of the main beam to the center of one of the dark spots (call this 'X'). Also, measure the distance from the wall to the hair (call that 'L').

Now do the calculations in two steps:

   a = arctan ( X / L )

...then we need the wavelength of the laser light - which because it's red must be around 700 nanometers.

   diameter of hair = 700nm / sin ( a )

So long as X and L are in the same units - the answer is in nanometers.

More details here:

    http://www.fysikbasen.dk/English.php?page=Vis&id=87

Measuring the speed of light using chocolate chips and a microwave oven

Take a bunch of chocolate chips and arrange them in a line - edge-to-edge across a dinner plate. Turn off the turntable in your microwave (or if you can't turn it off - you can turn the glass dish upside down to stop it rotating). Microwave the plate for 20 seconds - then QUICKLY open the door and look at the chips. You should find that some of them are melting and others are not. Measure the distance between the centers of the melted ones.

This distance is the distance between the peaks and toughs of the microwaves. Twice the distance you measured is one 'wavelength'. Microwave ovens operate at a frequency of 2.5 x 10⁹Hz because that's the frequency that water molecules absorb - which is how the oven cooks. If you know the frequency and wavelength of a wave, you can calculate it's speed:

  speed = frequency x wavelength

...the frequency is 2.5 x 10⁹ and the wavelength is twice the distance you measured. So now you can calculate the speed of light!

More details here:

  http://superpositioned.com/articles/2006/03/09/measure-the-speed-of-light-with-chips

Calculating PI with a box of toothpicks

Take a box of N toothpicks - each of length L. Find a floor with parallel lines on it - a tiled floor or one made of planks will do. (If you use tiles you need to pick one set of parallel lines to use. eg pick just the 'north-south' lines between them and ignore the east-west lines.) The distance between the parallel lines is D - and D must be bigger than L.

Now - dump out all of the toothpicks onto the floor from a good height so they land pretty much at random. Now, count the number of toothpicks that cross one of the lines on the floor...call that number 'C'.

OK - so all you need to do is to calculate:

  PI = 2 x L x N / ( D x C )

...tadaaaa! Of course you need to drop an awful lot of toothpicks to get a precise answer...especially if the distance between the lines on your floor is much bigger than the length of the toothpicks. Under good circumstances, you should be able to get within a few percent using a box of 100 toothpicks. Doing the experiment lots of times and averaging the results will help.

To understand why - look up "Buffons' Needle" in Wikipedia.