### Ghost Writing Essays

I will set up the apparatus as shown in the diagram above. To decide which lens I am to use I will find the focal lengths of different lenses and us the lens that gives the easiest focal length to work with, this will be found out in my preliminary experiment.

In this experiment I will be trying to prove my hypothesis, to do that the results that I obtain have to help me find the magnifications of different lengths away from the focal length. The object will be put on the focal point for the first result then I will measure the diameter of the object, this should always be 2.0cm, and then I will measure the diameter of the image. I will record my results into a suitable table; all of my results must be to 1 decimal place apart from the results for the magnifications, which will be to 2 decimal places.

I will obtain results every 2.0cm and take four results so that I can take an average result for the object distance (U), for the width of the image and the magnification. I will obtain results every 2.0cm because the image size drastically changes at the beginning when moving it away from the lens just a little bit and less so later on when got past 2F(twice the focal length), therefore a small gap between results is vital or else when coming to make a graph of the results will cause major parts of the magnification change to be lost.

I will choose a suitable range of results from performing the preliminary experiment.

Variables

My independent variable will be moving the object.

My dependant variable will be the lens.

There are two common types of lenses convex (converging) lenses and concave (diverging) lenses.

As you can see by looking at these diagrams a convex lens can make a real or a virtual image and a concave lens can only make a virtual image. I am using a convex lens in this experiment so that I can measure the size if the image and to be able to do that my image needs to be real, but only a convex lens produces a real image. My image needs to be real because one cannot touch or project a virtual image on to a screen and to measure the image one would need to touch the image.

Concave lenses are lenses that are thinner at the center than at the edges, bend light rays so that they diverge, and so produce only virtual images. The image is formed on the same side of the lens as the object; it is upright and is always diminished. The distance of the object from the lens controls the size of the image: the closer the object is to the lens, the larger the image.

A convex lens is thicker at the center than at the edges. When an object is placed beyond the focal length of a convex lens, the lens bends the light rays from the object so that they converge and form a real image on the opposite side of the lens. If the object is placed within the focal length of the lens, however, an enlarged virtual image is formed behind the object, on the same side of the lens. In general, in this case, the closer the object is to the lens, the less the image is enlarged.

These are descriptions of the two lenses and how they work, this will hopefully explain why I am using a convex lens and why I am not taking any measurements between the focal point and the lens, if not this is because it gives a virtual image and a virtual image cannot be measured.

So I have hopefully explained why in my experiment I will use a convex lens, but I have not yet said why I believe the convex lens will cause the magnification of the image to decrease as the object moves further away from the focal point of the lens. So now I will do that.

Here are some ray diagrams, the object in each is 2.0cm tall and the focal length of the lens in each diagram is 4.0cm.

In the first ray diagram the object is between the focal point and the lens this giving a virtual image. This is of little use to me for I would not be able to measure the image in real life but I can explain why, the reason being one cannot touch or project a virtual image onto a screen, therefore I would be unable to measure the image for I would not be able to touch it. This is also a diagram of how a magnifying glass works.

Ray Diagram 2 shows the object on the focal point, when constructing a ray diagram of this 2 parallel lines are given this then means that the image is magnified, but to an amount that one would find it immeasurable.

Ray Diagram 3 shows the object between the F (focal point) and 2F (double the focal length). This gives a real, magnified and inverted image this is smaller that the previous one but one could easily measure it.

Ray Diagram 4 shows the object on 2F this then gives a real, same size and inverted image. This should now indicate that as the object has been moved further away from the focal point the size of the images have decreased and when the magnification is worked out the magnifications should also decrease. This should now mean the any images after this should not be magnified or the same size but diminished.

Ray diagram 5 shows a real, diminished and inverted image, as I thought. Now if I work out the magnification for each of the diagrams they should gradually decrease.

There are two ways of working out the magnification one simple way and one more complicated way, which is supposed to be more accurate. A ray diagram is not required for the complicate method but a ray diagram is required for the simpler method, so if the ray diagram is inaccurate then the answer for the magnification using the simpler method should in theory be as inaccurate also.

Simple Method

Magnification = size of image

Size of object

Complicated Method

U = object distance

V = image distance

f = focal length

1=1+1

f U V

1-1=1

f U V

U-f=1

Uf V

Uf =V

U-f

Magnification=V

U

Using the Simple Method

Ray Diagram 1

4.2=2.1

2.0

Ray Diagram 2

Unable to work out for I have no result for the size of the image.

Ray Diagram 3

3.8=1.9

2.0

Ray Diagram 4

2.0=1.0

2.0

Ray Diagram 5

1.5=0.75

2.0

As you can see from my results the further the object was from the focal point the smaller the magnification got.

Using the Complicated Method

Uf=V

U-f

Magnification=V

U

Ray Diagram 1

2.0×4.0=-4

2.0-4.0

Magnification=-4

2.0

=-2

Ray Diagram 2

4.0×4.0=0

4.0-4.0

Magnification=0

Ray Diagram 3

6.0×4.0=12

6.0-4.0

Magnification=12.0

6.0

=2

Ray Diagram 4

8.0×4.0=8

8.0-4.0

Magnification=8

8.0

=1

Ray Diagram 5

10.0×4.0=6.7

10.0-4.0

Magnification=6.7

10.0

=0.67

From 2 different methods of working out the magnification I have got virtually the same results, which show the same trend that proves the hypothesis, moving the object further away from the focal point of a converging lens will decrease the magnification of the size of the image.

Preliminary work

Apparatus

In the preliminary work I have to find out which lens I will be using and why I have chosen to use that particular one. I will want the one with the most easily manageable focal distance. I know that once that I have chosen which lens I want, I cannot change half way through the experiment without retaking the result that I already have with the new lens. It is crucial for my lens to stay the same and for my object to be the same size, or else the results will not work out because the images will be of different sizes not following with the trend. Therefore my dependant variables will be the lens I use and the object that I use. My independent variable will be the object distance because that will be the only thing as part of the experiment that I will be changing.

Method

To find out which lens I want to use I will have to find out the focal lengths of them, because I want the one with the most easy to work with and of a reasonable size.

When I find out which lens I will use I will be able to find a suitable range of results and a suitable distance between each result.

I will need the apparatus as shown in the diagram above. The reason I am using the sun as a light source is because the rays of light from a light source are not parallel until the rays of light have travel a very far distance and because the light source being the sun is very far away the rays of light will be parallel. Only parallel rays of light will converge in a convex lens to give a focal point.

When the light converges in the lens I will try to get a sharp dot of light on the wall, I will measure the distance from the centre of the lens to the sharp dot of light this will be the focal light of the lens. This is because the sharp dot of focused light is the focal point and the distance from the centre of the lens to the focal point is the focal length.

I will record the result and decide which lens to use.

Results from Preliminary Experiment

Lens (thinnest-fattest)

Focal length

1

37.0cm

2

24.0cm

3

10.0cm

4

9.8cm

5

9.0cm

6

5.5cm

7

5.0cm

I will us the 3rd lens with a focal length of 10.0cm, I am using this because it is an easy number and I can get a reasonable amount of results between F, 2F and 3F. So I will go up to 30.0cm and in intervals of 2.0cm. I will take at least 4 records per measurement and then be able to work out all the magnifications the work out the average results.

Obtaining evidence

Evidence obtained

The object has a diameter of 2.0cm

Focal length of lens/cm

Object distance/cm

Description of image

Diameter of image/cm

Magnification

10.0

10.0

Indescribable

Immeasurable

/

10.0

10.0

Indescribable

Immeasurable

/

10.0

10.0

Indescribable

Immeasurable

/

10.0

10.0

Indescribable

Immeasurable

/

10.0

12.0

Real, magnified & inverted

9.1

4.55

10.0

12.0

Real magnified & inverted

8.9

4.45

10.0

12.0

Real magnified & inverted

8.8

4.40

10.0

12.0

Real magnified & inverted

8.9

4.45

10.0

14.0

Real magnified & inverted

4.4

2.20

10.0

14.0

Real magnified & inverted

4.6

2.30

10.0

14.0

Real magnified & inverted

4.3

2.15

10.0

14.0

Real magnified & inverted

4.5

2.25

10.0

16.0

Real magnified & inverted

2.9

1.45

10.0

16.0

Real magnified & inverted

3.1

1.55

10.0

16.0

Real magnified & inverted

3.1

1.55

10.0

16.0

Real magnified & inverted

3.1

1.55

10.0

18.0

Real magnified & inverted

2.1

1.05

10.0

18.0

Real magnified & inverted

2.3

1.15

10.0

18.0

Real magnified & inverted

2.1

1.05

10.0

18.0

Real magnified & inverted

2.3

1.15

10.0

20.0

Real same size & inverted

2.0

1.00

10.0

20.0

Real same size & inverted

2.0

1.00

10.0

20.0

Real same size & inverted

2.0

1.00

10.0

20.0

Real same size & inverted

2.0

1.00

10.0

22.0

Real diminished & inverted

1.5

0.75

10.0

22.0

Real diminished & inverted

1.6

0.80

10.0

22.0

Real diminished & inverted

1.6

0.80

10.0

22.0

Real diminished & inverted

1.7

0.80

10.0

24.0

Real diminished & inverted

1.2

0.60

10.0

24.0

Real diminished & inverted

1.3

0.65

10.0

24.0

Real diminished & inverted

1.3

0.65

10.0

24.0

Real diminished & inverted

1.3

0.65

10.0

26.0

Real diminished & inverted

1.1

0.55

10.0

26.0

Real diminished & inverted

1.1

0.55

10.0

26.0

Real diminished & inverted

1.2

0.60

10.0

26.0

Real diminished & inverted

1.1

0.55

10.0

28.0

Real diminished & inverted

1.0

0.50

10.0

28.0

Real diminished & inverted

1.0

0.50

10.0

28.0

Real diminished & inverted

1.1

0.55

10.0

28.0

Real diminished & inverted

1.0

0.50

10.0

30.0

Real diminished & inverted

0.8

0.40

10.0

30.0

Real diminished & inverted

0.9

0.45

10.0

30.0

Real diminished & inverted

0.9

0.45

10.0

30.0

Real diminished & inverted

0.8

0.40

Average Results

Average focal length of lens/cm

Average object distance/cm

Description of image

Average diameter of image/cm

Average magnification

10.0

10.0

Indescribable

Immeasurable

/

10.0

12.0

Real, magnified & inverted

8.9

4.45

10.0

14.0

Real, magnified & inverted

4.5

2.25

10.0

16.0

Real, magnified & inverted

3.1

1.55

10.0

18.0

Real, magnified & inverted

2.2

1.10

10.0

20.0

Real, same size & inverted

2.0

1.00

10.0

22.0

Real, diminished, inverted

1.6

0.80

10.0

24.0

Real, diminished, inverted

1.3

0.65

10.0

26.0

Real, diminished, inverted

1.1

0.55

10.0

28.0

Real, diminished, inverted

1.0

0.50

10.0

30.0

Real, diminished, inverted

0.9

0.45

Analysis

In performing this experiment I have found that the larger the object distance the smaller the magnification became which was what I had hypothesised. Therefore my hypothesis was correct and I have proved it.

I can see from the graph that as the object distance increased the magnification decreased. The magnification dramatically dropped from 4.45 at 12.0cm al the way down to almost half of that at 14.0 cm and the magnification being 2.25. This was at the beginning of the experiment but as the experiment progressed the decrease in magnification every 2.0cm became less dramatic.

To see if there was any erratic behaviour between 12.0cm and 14.0cm I could have took a few more readings in this gap. And if there were no erratic behaviour in this dramatic drop this would then again confirm my hypothesis to be correct.

From looking at my graph the only thing that surprise me was that there was such a dramatic drop in the first few results then they started to even out as the experiment progressed. I personally thought that the results would give an even decline in magnification between them but after the first result but it took about three results until they evened out.

I got these results for several reasons. I know that a convex lens causes the magnification to decrease as the object is moved further away from the lens. This is because the size of the image decreases as the object distance is increased and when the magnification is worked out (V/U) the image distance decrease as the object distance increases giving a gradual smaller answer when using the equation and the answer being the magnification.

At the beginning of this experiment I had a prediction being, I hypothesise moving the object further away from the focal point of a converging lens will decrease the magnification of the size of the image. From getting the results that I did I can say that my hypothesis was correct and by looking at my graph I can easily tell that this is a true statement. I backed up my hypothesis as to why I thought it would be correct and now I can say that increasing the object distance will decrease the magnification when using a convex lens.

Evaluation

The procedure used in this experiment was safe for nobody got hurt and it was fair because I kept my variables the same throughout the experiment.

My results are of a reasonable standard it seemed pretty pointless to go any further in range, because all the results thereon would continue to decrease and from what I had done in the experiment I had proved the hypothesis, which was the aim of the experiment. No anomalous results are evident which improves the accuracy and reliability of my results.

My results are reliable in the sense that there are no anomalous results, but how accurate are they? There is a way that I can work out how accurate my results are that is by a process called percentage difference.

I will work out the percentage difference of the magnification for each different object distances.

Object distance is 10.0cm

% Difference

Object distance 12.0cm

% Difference

Average magnification, 4.45

Furthest value away is 0.1 bigger

0.1/4.45 x 100=2.2

My results for 12.0cm are inaccurate to 2.2%

Object distance 14.0cm

% Difference

Average magnification, 2.25

Furthest value away is 0.1 smaller

-0.1/2.25 x 100=-4.4

My results for 14.0cm are inaccurate to 4.4%

Object Distance 16.0cm

% Difference

Average magnification, 1.53

Furthest value away is 0.08 smaller

-0.08/1.53 x 100=-5.2

My results for 16.0cm are inaccurate to 5.2%

Object Distance 18.0cm

% Difference

Average magnification, 1.10

Furthest value away is 0.05 bigger or smaller

+-0.05/1.10 x 100=4.5

My results for 18.0cm are inaccurate to 4.5%

Object Distance 20.0cm

% Difference

Average magnification, 1.00

Furthest value away is the same

0.00/1.00 x 100=

My results for 20.0cm are inaccurate to 0%

Object Distance 22.0cm

% Difference

Average magnification, 0.80

Furthest value away is 0.05 bigger or smaller

+-0.05/0.80 x 100=6.3

My results for 22.0cm are inaccurate to 6.3%

Object Distance 24.0cm

% Difference

Average magnification, 0.65

Furthest value away is 0.05 smaller

-0.05/0.65 x 100=-7.7

My results for 24.0cm are inaccurate to 7.7%

Object Distance 26.0cm

% Difference

Average magnification, 0.55

Furthest value away is 0.05 bigger

0.05/0.55 x 100=9.1

My results for 26.0cm are inaccurate to 9.1%

Object Distance 28.0cm

% Difference

Average magnification, 0.50

Furthest value away is 0.05 bigger

0.05/0.50 x 100=

My results for 28.0cm are inaccurate to 10%

Object Distance 30.0cm

% Difference

Average magnification, 0.45

Furthest value away is 0.05 smaller

-0.05/0.45 x 100=

My results for 30.0cm are inaccurate to 11.1%

As you can see my results become increasingly inaccurate as the experiment progressed but was completely accurate when the object distance was 20.0cm, which was in the middle of the experiment.

I could have done this experiment with different sized convex lenses instead of just using the one type, but for this I would have needed a lot more time. I could have done the entire experiment on the same day because the weather on different days can affect the accuracy of the results and dependant on how focused I was on different days could have affected the results but by looking at the results I believe I was on the ball throughout the experiment. Instead of having results in intervals of 2.0cm I could have decreased this to 1.0cm or even 0.5cm. I would not go any lower than this for my accuracy to decimals would not be very accurate. Having a smaller gap between results would allow my to have more results to help me in my graph for at the beginning I do no know what is exactly happening in between the dramatic decline in magnifications.

Two more possibilities when using the same basic equipment would to do more repeats because you can never have enough repeats and to have a larger range in results to possibly see if the magnification is ever equal to 0 or if the magnification eventually goes so far that the magnification stops decreasing.

As far as the use of the apparatus goes I could have changed the odd thing realistically. I could have changed the light source from a lamp which is not a light source that gives off parallel rays of light I could have used a light source that gave off parallel rays of light for example the sun, but that would not be a very good thing to use in England because the amount of sunlight given off always changes according to typical English weather.

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