Investigating How the Size of a Shadow Depends on the Angle at Which the Light Hits the Object


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Investigating How the Size of a Shadow Depends on the Angle at Which the Light Hits the Object



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 4cm produces a shadow of approximately 1.6-cm. Decreasing
the distance to 2cm(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. 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 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).

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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 2cm the length of the shadow was 1.1 cm. By tripling the
distance to 6cm,if I then tripled the length of shadow it would come
to 3.3cm.This was shown in the 3rd ray-diagram as 3.3cm

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 2cm
and is 1cm 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 20º the length of shadow
changes from 1.9cm 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 90º 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 0º 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 0º and
15º is only 0.2cm.Therfore in 15º the length increases by 0.2cm, but
then the differences get bigger. Between 30º and 45º 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 12V torch bulb and a
1.5V 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 12V torch bulb would suit me better as the bright light created
a darker shadow than the 5V 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 2D 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 3D 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 12V 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 15º each time i.e.: 15º 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 .


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