Introduction The aim of the project is to see which factors affect the size of a shadow and then to look more closely at one of the factors to see how exactly it varies the size of a shadow. Variables that may affect the size of the shadow Although, I will investigate how one factor affects the size of a shadow, there are other factors that could be investigated. Here are some examples: 1) The distance between the light and the object From the ray diagrams I can see that as the distance from the object to the light source is doubled, the length of the shadow decreases. A distance of 4 cm produces a shadow of approximately 1.6-cm. Decreasing the distance to 2 cm (half the distance), the shadow size increases by one and a half times to produce a shadow of 2.3 cm. The three ray diagrams together show the increase of the distance between the object and light source, decreasing the length of the shadow.

2) The distance between the object and the screen The results from this are opposite varying the previous factor. In this case the length of the shadow increased as the distance from the edge of the object to the screen increased. I expected that as the distance dubled, the length of the shadow would double but according to the ray diagram that was not the case. The length of the shadow The results from this are opposite to varying the previous factor.

I expected that as the distance doubled, the length of the shadow would double but according to the ray diagrams, that was not the case. The length of the shadow increased by 1.6 times between changing the distance from 2 cm to 4 cm (ie: doubling the distance). For changing the distance to 6 cm increased the length of the shadow, which was expected, but I was surprised as it increased by more than I had expected. When the distance was 2 cm the length of the shadow was 1.1 cm. By tripling the distance to 6 cm, if I then tripled the length of shadow it would come to 3.3 cm. This was shown in the 3rd ray-diagram as 3.3 cm 3) The light source 'If the point source of light is replaced by a spread-out or extended source such as a table lamp, the edge of the shadow becomes fuzzy and indistinct.

Around the area of full shadow, there is a region of part shadow where only some of the light from the lamp has been stopped' (Quoted from 'Explaining Physics' from Stephen Pople') 4) The shape of the object For this I would keep the area the same but change the shape in order to keep the same object size. I will use a rectangle and a square. From these diagrams I can clearly see that there is an effect. The rectangle has a shadow just under two and a half times larger than the squared shape's shadow.

The vertical height of the rectangle is 2 cm and is 1 cm for the square. I think this could be a reason for the shadow length being bigger for the rectangle. 5) The angle at which the screen is This shows that by increasing the angle the screen is held at, increases the length of the shadow. As I have not measured the angles I cannot compare the increase of angle to the length of shadow in numerical form, but this could be further investigated.

6) The size of the object This is an obvious effect but it still is a factor as it affects the size of the shadow in a directly proportional way i.e. : the bigger the object, the larger the size of shadow. 7) The angle at which light hits the object This shows by increasing or decreasing the angle the length of the shadow increases. By increasing the angle to 20 o the length of shadow changes from 1.9 cm to 2.6 i.e. : it increases by 1.3 times. I have decided to investigate how varying the angle at which light hits the object affects the size of a shadow.

It is important that all the other factors are kept constant in all my experiments; otherwise I would not be finding the effect of the factors, but of a mixture of factors. Therefore these factors will be kept constant... The distance between the light and the object: I will keep this constant by moving the light in a semi-circle, where the distance between the light and the object will stay the same... The distance between the object and screen: The screen and the object will not be moved throughout all the experiments... The light source.

The shape of the object: The same object will be used each time... The angle at which the screen is: The screen will be clamped 90 o to the ground and will not he altered... The size of the object: The same object will be used each time. Prediction I predict that when the object is hit with light travelling 0 o to the object (as shown below), a shadow will form, which will be smaller than the shadow formed by light hitting the object at another angle.

As the angles get further away from the 0, the size of the shadow will increase. I think this due to the ray diagram drawn below. I also think that as the angle triples the size of the shadow will double. From information from the four ray diagrams I can draw up this very simple table which gives approximate values. Angle (o) Length of shadow (cm) 0 1.4 15 1.6 30 2.0 45 2.6 Decreasing the angle has an inverse effect on the length of the shadow. The difference between the length of shadow in angle 0 o and 15 o is only 0.2 cm.

Therfore in 15 o the length increases by 0.2 cm, but then the differences get bigger. Between 30 o and 45 o the difference is 0.7. Preliminary Experiment The reason for doing this was to find out what apparatus was suitable, how things would be best arranged, how results would be taken etc. I clamped a screen upright using a clamp stand. I selected a couple of different objects, which were different from each other to try them all out, and see which one I liked. I brought 12 V torch bulb and a 1.5 V torch bulb to try.

I set up the experiment as shown below: The object between the screen and the light. From this I realised that. A 12 V torch bulb would suit me better as the bright light created a darker shadow than the 5 V bulb, which was very dim. A darker shadow was more vivid than the fainter shadow, therefore easier to take measurements from...

Moving the object and changing it with other objects made me realise that a 2 D shade didn't stay upright very well. I decided not to opt for the scissors because as it was difficult to measure the size of the shadow. In the end I chose a 3 D rectangular block... Standing the block upright was a better than leaving it lying on its wider base as it was hard to see the edges of the shadow, when it was lying flat. Strategy Apparatus list: . A large screen.

A 12 V torch bulb and a power supply. A rectangular block. A sheet with a large protractor drawn on it indicating the angles I will place the light at I need to change the angle by 15 o each time i.e. : 15 o further away from the starting line each time. I will measure the length and width of the shadow in order to work out the areas. The ruler will be marked with cm's and mm's. I will measure to the nearest.

The light source. A large screen. A rectangular block. The light source. A large screen. A rectangular block.

I am going to prove that in the play Macbeth, a symbol of blood is portrayed often (and with different meanings), and that it is a symbol that is developed until it is the dominating theme of the play towards the end of it. To begin with, I found the word "blood", or different forms of it forty-two times (ironically, the word fear is used forty-two times), with several other passages dealing with the symbol. Perhaps the best way to show how the symbol of blood changes throughout the play, is to follow the character changes in Macbeth. First he is a brave honoured soldier, but as the play progresses, he becomes a treacherous person who has become identified with death and bloodshed and shows his guilt in different forms. The first reference of blood is one of honour, and occurs when Duncan sees the injured sergeant and says "What bloody man is that?" . This is symbolic of the brave fighter who been injured in a valiant battle for his country.

In the next passage, in which the sergeant says "Which smok'd with bloody execution", he is referring to Macbeth's braveness in which his sword is covered in the hot blood of the enemy. After these few references to honour, the symbol of blood now changes to show a theme of treachery and treason. Lady Macbeth starts this off when she asks the spirits to "make thick my blood", . What she is saying by this, is that she wants to make herself insensitive and remorseless for the deeds which she is about to commit. Lady Macbeth knows that the evidence of blood is a treacherous symbol, and knows it will deflect the guilt from her and Macbeth to the servants when she says "smear the sleepy grooms with blood". , and "If he do bleed, I'll gild the faces of the grooms withal, for it must seem their guilt". When Banquo states "and question this most bloody piece of work", and Ross says "is't known who did this more than bloody deed?" , they are both inquiring as to who performed the treacherous acts upon Duncan.

When Macbeth is speaking about Malcolm and Donal bain, he refers to them as "bloody cousins" A final way, and perhaps the most vivid use of the symbol blood, is of the theme of guilt. First Macbeth hints at his guilt when he says "Will all great Neptune's ocean wash this blood clean from my hand?" , meaning that he wondered if he would ever be able to forget the dastardly deed that he had committed. Then the ghost of Banquo, all gory, and bloody comes to haunt Macbeth at the banquet. The sight of apparitions represents his guilt for the murder of Banquo which he planned. Macbeth shows a bit of his guilt when he says "It is the bloody business which informs thus", he could not get the courage to say murder after he had killed Duncan, so he says this instead. Lady Macbeth shows the most vivid example of guilt using the symbol of blood in the scene in which she walks in her sleep.

She says "Out damned spot! Out I say! One: two: why then 'tis time to do't: hell is murky. Fie, my lord, fie, a soldier, and afeard? What need we fear who knows it when none can call out power to account? Yet who would have thought the old man to have had so much blood in him?" .

This speech represents the fact that she cannot wipe the blood stains of Duncan off of her hands. It is ironic, that she says this, because right after the murder, when Macbeth was feeling guilty, she said "A little water clears us of this deed". When the doctor of the castle finds out about this sleepwalking, he tells Macbeth "As she is troubled with thick-coming fantasies", . What this means, is that Lady Macbeth is having fantasies or dreams that deal with blood. Macbeth knows in his mind that she is having troubles with her guilt, but does not say anything about it. Just before the ending of the play, Macbeth has Macduff at his mercy, and lets him go, because of his guilt.

He shows that he is guilty, when he says "But get thee back, my soul is too much charg'd with blood of thine already". . Of which, Macduff replies, "I have no words, my voice is in my sword, thou bloodier villain than terms can give thee out". After the death of Macbeth at the hands of Macduff, the symbolic theme of blood swings back to what it was at the beginning of the play. It is the symbol of honour to Malcolm this time. The death of Macbeth is honoured feat that Macduff is congratulated for.

So as we have seen meaning of the symbol of blood change from honour to treachery, and then to guilt, after this, it returns to the symbolic meaning of honour once again after the villain that changed the meaning from honour to tyranny is killed. Due to these many changes, it has been proved that the symbol of blood has many different meanings which can be attributed to it throughout the course of this play.