# Diffraction, resolution and polarization

##### Waves through a gap in a barrier

Here is a film of a rippletank with a barrier with a gap in it. What do you observe?

Single slit diffraction pattern.

An oscillation is a system in which a mass moves towards an equilibrium point. Examples of oscillations are a spring pushing and pulling a mass, a ball bobbing on water, a coin rolling up and down the inside of a curved bowl, and a skateboarder on a half-pipe.

Oscillation occurs when the force is zero at the mid-point (equilibrium), and if the mass moves away from the equilibrium point, a force increase proportionally to the distance away it is. As the spring stretches, the force pulling the object back to the mid-point increases.

All oscillations have cycles, which have a period and frequency.

## Pendulums

A pendulum is an example of an oscillation with a period and frequency.

An oscillation is a motion which is self-replicating. It may be, as in the case of a spring, due to elastic potential converting to kinetic energy, and back again. Or it may be, as in the case of a pendulum, due to kinetic energy converting to gravitational potential, which then reconverts to kinetic.

Pendulum: can you time the period and calculate the length of the string?

The period of an oscillation is the time interval between two positions that are identical in space. This means that a period of a pendulum consists of two swings.

The frequency, λ, of a pendulum is the number of double swings (back and forth) per second, and is expressed in Hertz (Hz).

The mass and amplitude of swing has no effect on the period of a pendulum. Instead, only the length of the string will determine the period of oscillation for a any mass.

### The Maths

The period T of a pendulum of length L is:

\$\$T = 2π √{L/g}\$\$

Note: the value of π/√g is 0.987, or very close to 1. Therefore, an approximation of the time it takes a pendulum to make a single swing (half a period) is simply √L.

A pendulum 1.0m long has a period of 2 secs, or 1 second a swing. This is how Galileo 'swung' the pendulum clock industry into being!

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#### Daniel Bernoulli

1700 - 1782

Daniel Bernoulli was a major scientist and mathematician of the 18th century, a friend and associate of Leonard Euler, and a member of the illustrious Bernoulli dynasty of mathematicians.

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Capitalism is the astounding belief that the wickedest of men will do the wickedest of things for the general good of everyone.