The focal length
of the lens was determined by the following formula:
Near the beginning of Heron civilisation it was discovered that a great number of heron had imperfect eyes. They could not focus properly on fish as they were trying to catch them. This proved to be a great disadvantage. One very intelligent heron one day came up with the idea of making a refracting lens to better focus images on the back of heron eyes. A lens was developed:
The focal length
of the lens was determined by the following formula:
1
+ 1
= 1
u
v
f
Where u and v are the distances shown on the diagram and f is the focal length of the lens.
The refracting power of the lens was thought at first to be mystical, but a well-known heron in the scientific community, Geuronicus, showed their application in many things.
Thanks to the marvels of the lens all herons that had difficulty seeing were now as advantaged as those who didn’t.
As the science of the Herons progressed it became quite
evident that they would
one day rule the universe. There time would definitely
come.
The Heron and the Diffraction Grating: A Parable
One day a young heron who had specialised in science
at heron university was at a
popular tourist location in the southern most continent
and decided to takes some
photos. He had previously heard of several prominent
heron physicist bending light
round edges. He suddenly thought to himself. What if
two waves overlap? Will their
relative amplitudes by added onto one another or otherwise?
He took his idea straight
to the proper authorities who experimented upon it thoroughly.
It turned out that when two waves overlapped their relative
amplitudes can be added
together. Superposed was the term coined. Further experimentation
was done on
diffracting light beams over lapping. Initially two slits
were used to diffract to beams
of light over each other. Superposition was seen on a
screen. After length calculation
formulas arised:
In this experiment there will be a bright fringe seen
where there is a difference of a
whole number of wavelengths. P is a bright fringe. \
S2P - S1P = nl
The distance between S1P and S2P are as follows:
(S2P)2 = d2 + (x1 + a/2)2 = d2 + x12 + ax1 + a2/4
(S1P)2 = d2 + (x1 - a/2)2 = d2 + x12 - ax1 + a2/4
\ S2P2 - S1P2 = 2ax1
so (S2P - S1P)(S2P + S1P) = 2ax1
In reality ‘a’ is very small compared to ‘d’ and if P
is near O then S2P and S1P are
each just greater than ‘d’.
\ S2P + S1P = 2d
It follows that:
(S2P - S1P)2d = 2ax1
\ S2P - S1P = ax1 / d
For the nth bright fringe at P we have
nl= ax1 / d
The next bright fringe after that, ie the (n+1)th, is
formed at Q where OQ = x2
S2Q - S1Q = (n+1)l
(n+1)l = ax2 / d
Subtracting nl=ax1/d from (n+1)l=ax2/d we get:
l= a(x2 - x1)/d
If y is the distance between two adjacent bright (or
dark) fringes then y=x2-x1 and so:
l= ay/d
If the wavelength and distance are constant then y µ
a-1.
If the wavelength and slit separation are constant then
y µ d.
If the slit separation and distance are constant then
y µ l.
The moral of this story is that you can think scientifically
and make great
breakthroughs even when on
4. A Diffracted Heron
It is said that when a heron comes of age their brain
has been diffracted. A similar
observation can be seen after a coherent light beam,
that is a light beam of only one
wave-length, has passed through a diffraction grating.
The image of bright fringes on
the screen show the complex neural picture on a herons
brain.
The light and dark fringes show the maximum and minimum
interference between the
light beams.
It was determined that where;
n is the order;
l is the wavelength of the
light;
d is the slit seperation; and
J is the angle from order n=0;
that
nl = d sin J
This equation can be used to find the wavelength of light.
The wavelength of light
between 590 and 610 have a special meaning for all the
people of Heri but they are
not allowed to say why to outsiders. If you ever hear
of this you must kill yourself.
5.Stationary Waves
The Story of the Heron who Forgot how to Fly
One day a young heron couldn’t fly. She tried as hard
as she could but just hadn’t
inherited one of the most sacred heron genetic memories.
To accommodate her large
brain she decided to enter a career as a scientist.
As she had to remain stationary on the ground all the
time it came as a great surprise
to her when she encountered stationary waves. ‘How simple!’
she thought.
A stationary wave is when two waves of equal frequency
and velocity and
approximately equal amplitude are travelling in opposite
directions. They appear to
be stationary, like the heron who couldn’t fly.
As stationary waves were very important in the culture
of the Herons the flightless
heron felt honoured. Stationary waves, unbeknown to the
musicians, had for long
been used in musical instruments. One such instrument,
the heronitar, had several
strings on it. When the string was plucked a stationary
wave was produced with
nodes and anti-nodes.
Stationary waves were also discovered in wind instruments.
It was found that at an
open end in a wind instrument was an anti-node and at
a closed end was a node. A
stationary wave with a node at one end and an anti-node
at the other with nothing
inbetween is called the first harmonic (1/4 l),
with 3/4 lwe have the second
harmonic and so on.
As this was found so refreshing to the heron who couldn’t
fly she gave up science and
became a musician. She took on human and placed herself
in the middle of the third
millenium. She is still known widely today.
6. The Polarised Herons
One day a large number of herons were flying on a planet with a very weak gravitational field. Due to this they were able to fly on many different planes. They continued on for a long time and had meaningless discussions about the meaning of life. Suddenly up ahead of them they saw a polarise thing. "Oh no!" they all shouted as they flew into it. Unfortunately herons on only one plane were allowed through so the number of herons that continued after that point were minimised. You could say that their intensity had decreased. Fortunately the herons that did get through were all on the same plane and their communicative abilities were optimised.
There was once a great heron physicist called Heronewton. He was known greatly for defining the laws of heron motion. He noticed first:
This made perfect sense and seemed so simple. Secondly
he found:
t
so F = ma
This formula changed the ways herons did lots of stuff. However the third law of heron motion was still to come:
3. To every force there is an equal and opposite force.
This seemed so simple, yet so important.
v = s/t
There are five other equations of linear motion which are:
v = u + at
s = ½(u + v)t
v2 = u2 + 2as
s = ut + ½at2
s = vt – ½at2
When a heron was in equilibrium there is no resultant force or resultant moment. It will obey Heronewton’s first law of motion and stay at rest or continue travelling at a constant velocity unless acted on by a force.
One day some prominent scientists wondered what would happened if rope was tied to a heron then to a post stuck firmly in the ground and the heron were to start flying. They found that the heron started going round in circles. This was no surprise to them and with their great heron minds worked out that the velocity was proportional to the radius of the circle and the angular velocity of the heron. When the angular velocity, w, is measured in radians per second, then this formula arises:
v = rw
From Heronewtons’s law of motion the scientists knew that the heron wouldn’t change direction unless acted on by a force and that the acceleration was in the direction of the force. This meant that there was acceleration towards the centre post to which the heron was attached with a rope.
a = w2r = v2/r
The force towards the centre of the circle is called the centripetal force, and because F=ma and a = w2r:
F = mw2r = (mv2)/r
Herohm was the first Heron scientist to come up with ideas about electricity. He said, "The current in a conductor is proportional to the PD across it, provided temperature remains constant".
An ohmic conductor obeys this law.
He also said – "Current is the rate of flow of charge."
We know (if A = cross sectional area, R = resistance and l = length):
If we introduce a constant for resistivity we get:
Resistivity is the resistance across opposite faces of a unit cubed: Wm
As the temperature rises the atoms vibrate more making it harder for the electrons to get through.
Super-conductivity is when the temperature drops to a point where all resistance disappears. This is called the transition temperature.
If something has no resistance it is completely energy efficient – there is no heating effect. Strength of electro-magnets depends on current, so huge electromagnetic fields mean big engines.
Thermistors obey a non-linear relationship of such that the change of resistance with temperature is far greater than with metals. Low temperatures mean high resistance. They have tetravalent bonds. When the temperature drops the electrons are held in position.
When a free electron goes near a hole it fills it. As the temperature increases the electrons start to break away. Electron – hole pairs are produced. Conductivity starts. By adding impurity atoms you can further alter the resistance of the material.
The emf of a cell is the p.d. across it when it is not giving out a current.
Emf is the energy per unit charge.
The great Heri civilisation came across some work on an uninhabited planet that had an author named Mr Kirchoff. It went as follows…..
Current going into a junction = current going out of a junction
In any closed loop in a circuit the algebraic sum of the emfs is equal to the algebraic sum of the products of IR
When the heron’s first made the useful invention of a capacitor it greatly increased the potential of their electronics industry.
The capacitance of a capacitor is the charge stored when the p.d. is 1V. It is measured in farads (F).
When capacitors are in parallel their combined resistance is equal to the sum of all the separate resistances 9(Ct = C1 + C2 + C3…..). When in parallel the p.d. across each one is the same and the total charge is the sum of all the individual charges.
When capacitors are in series, 1/Ct = 1/C1 + 1/C2 +1/C3…..). When in series the charges on each capacitor is the same and the total voltage is the sum of all the individual voltages.
Millennia ago in the early stages of heron civilisation the herons had developed a play toy for infants called a ‘round-a-bout’. On it a young heron sat and was spun round and round in circles. To this heron the laws of circular motion were obeyed precisely and the young heron’s intelligence increased in direct proportion to the time spent on the toy. However one day a prominent Heri scientist took her son to the play park and began to watch him on the round-a-bout. She watched in awe as her son’s displacement from the centre of the round-a-bout followed a sinusoidal pattern (against time). When she got home and had helped her son make some lovely sardine sandwiches she sat down at her desk and thought about the round-a-bout. She thought about acceleration and velocity and how it related to the displacement. She decided to call the ‘motion’ she was observing in that plane simple harmonic motion. She wrote:
…..when an object is in simple harmonic motion the acceleration is proportional to the displacement, in the opposite direction and towards a fixed point, the equilibrium…..
She determined that a = w2x where a is the acceleration, w is the angular frequency and x is the displacement. Also there was:
| Displacement | O | min | O | max | O |
| Acceleration | O | max | O | min | O |
| Velocity | min | O | max | O | min |
x = A sin wt
Where x is the displacement, A is the amplitude, w is the angular frequency and t is the time.
Also:
T = 1/f = 2p/w
Where T is the period of oscillation (360° on the sine wave), f is the frequency and w is the angular frequency.
For a simple pendulum:
T = 2pÖ(l/g)
Where l is the length of the pendulum and g the gravity of the planet (in kgN-1).
For a spring pendulum:
Where m is the mass of the spring system and k is the spring constant (in Nm-1).
In a system undergoing simple harmonic motion the total
energy in the system remains constant (i.e. KE + PE = constant), and the
KE = ½kx2 = ½Fx.
14 Colliding in Mid-Air
One day a heron was flying home after a long day at work. He was a scientist heron and was studying Heronewton’s law of motion. He was thinking about his motion in the air when suddenly out of no-where a considerably larger heron crashed right into him. He his surprise the two heron’s did not stop dead in mid-air but continued travelling, at a slower speed in the direction the big heron had been travelling. After they had finished apologising to each other they both carried on, on their journeys. When the scientist heron got home he thought to himself – "Why did we not stop completely. I know we were both travelling at the same speed, the only difference is that that other heron was heavier than I. Of Course! That must be it. We must both have had a momentum and his was greater than mine, so our combined mass would travel in that direction at a fraction of the speed that other heron was travelling at. The momentum before the collision was equal to the momentum after our collision. It was just in the opposite direction!"
With that in mind he went into work the next day and wrote a fifty-page research paper outlining his discovery. Without this important addition to their knowledge it would have been hard for the great Heri civilisation to progress to space travel, which it most certainly did a few hundred years later.
It was initially thought that there would be an element with a relative atomic mass of around five hundred that would be relatively stable.
It was discovered in the Heron Year 438629. Its actual chemical symbol (in human representative functions) is 492213Hr. This chemical was found by the technique commonly referred to as neutron capture, until a nuclear mass of 300 was achieved at which point fusion became necessary to further the reaction. The technique was refined for use of producing the element on an industrial scale. Unfortunately it had a half life of 20 seconds and was highly radioactive emitting alpha, beta, gamma, delta, epsilon and the less common form of zeta radiation. It released huge amounts of energy and powered ships to stars and found that it was very useful in the field of planet removals. However as it was so radioactive a safer chemical with equally efficient properties. The herons decided to use gravitons to build their element. As this was very hard it took years to perfect the technique. A third number also had to be used in the element symbol as to show the number of gravitons necessary to hold it together. The element Heronium then looked like this;
222222Hr222
This means there are 222 protons, 222 gravitons and 222 neutrons. The energy available from one mole of the new Hr was ten (universal standard) billion times as much as the old one. It was also unsplittable unless it came within close proximity of a black photon. This new element was the beginning of the end of the civilisation of the Heri as it was at first kept secret and used only in covert government projects. It was at this point in history when the people of Heri came against their worst enemy. The Planktacs.