Finding the power of a concave lens by a method of combination

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Aims

To find the power of a concave lens by a method of combination, using a convex lens with a power of 4.5D to 5.5D using a convex lens with a focal length of 10

TheoryThe power of the length is what opticians prefer to use as a measurement and is the reciprocal of the focal length in metres. The equation for this is

The focal length of a lens is simply the distance from the lens to the point of principle focus. The equation is rearrange from above by taking the reciprocal from each side

The process of calculating the exact power within the 4.5 D to 5.5 D margin will involve initially finding the focal length but in order to find the focal length I need to the power so therefore I will have to devise a means of doing this.

Theory 1)

Theory )

The above two theories are both capable of finding the focal length and the one which I will use is theory 1

When I have found both intercepts on each graph I will average them to find the focal lengths on, I will then divide by 1000 to get the power in dioptre of the Concave lens and combined lenses subsequently using the bellow rearranged formula I will be able to find the power of the convex lens.

Prediction

I predict that that when I have found the two intercepts and calculated the concave power it will fall within a margin of 4.5 D and 5.5 D

Apparatus

· Concave lens

· Convex lens

· Light source

· Meter ruler / mm

· Screen

· Power pack / 1 V

· Object- illuminated gauze

Diagram 1 - using single lens

Diagram using combination lenses

Safety

§ Sharp lenses

§ Hot lamp

§ Electric circuits

Variables

§ Amount of light

§ Power of convex lens

§ Focal length of convex lens

§ Distance between object and lens

§ Distance between lens and screen

Accuracy

Focus

§ (V) +- mm

§ (U) +- mm

Measuring

§ Ruler +- mm

Method

I. Set up the apparatus up as shown in the diagram and switch on the power pack to alight the bulb.

II. Now place the screen at any given place where a focus image will be able to appear on the screen.

III. Move the lens so that the object is clearly focused on the screen, now record the following into a suitable table

§ Position of lens

§ Position of screen

§ U distance between lens and object

§ T distance between lens and screen

IV. Repeat section II to III until a minimum of 6 readings has been obtained.

V. Now add the concave lens directly behind the convex and carry out stages II to IV. If possible repeat the whole experiment a number of time and divide your answers by how many times you carried the experiment out to find an average

Results table

LIGHT (CM) LENS (CM) SCREEN CM) U (CM) V (CM) 1/U (M-1) 1/V (M-1)

0 6 40 6 14 .85 7.14

0 50 14.4 5.6 6.4 .81

0 60 1. 46.7 7.5 .14

0 70 1.6 57.4 7.4 1.74

0 80 1. 67.7 8.1 1.48

0 100 11.5 88.5 8.70 1.1

0 10 11.4 108.6 8.78 0.

Combination lenses

0 6.4 85 6.4 48.6 .75 .05

0 1 5 1 64 . 1.56

0 8.8 105 8.8 76. .47 1.1

0 7.7 115 7.7 87. .61 1.15

0 6.8 15 6.8 8. .7 1.0

0 4. 170 4. 145.1 4.0 0.6

0 5.5 145 5.5 11.5 . 0.84

Analysis

From the above graph I found that the power of the single lens is .4D

And form the graph for the combined lenses I found that the power was 4.6D

Now to find the power I will use the equations I earlier mentioned in this essay.

Conclusion

In conclusion to my aim and prediction I fulfilled them both, the power I found fell at -4.6D.

The graphs show that as 1/U decreases 1/V increase, which illustrates that 1/U, is inversely proportional to 1/V.

Evaluation

On both graphs all the results lie on or extremely close to the line of best fit indicating that there was very little inaccuracies in the procedure experiment. This was because I closely followed my method and controlled my variables.

Uncertainties

Because nothing is 100% efficient there was errors encountered in my experiment.

The error margin I gave for 1/U was +- 0.4 mm

This was because the uncertainty of the ruler was +-0. and in the positioning of the lens was also +- 0. since measuring error in reading the scale I could not be exactly certain with the naked eye of the placement.

The error margin I gave for 1/V was +- 0.4 mm

This was because when focusing the image I could not be precise and may had been slightly out so I gave +- 0. error margin for this and with the error of the ruler which was as before +-0. adds up to the giver error above.

From the graph bellow it is possible that the lowest possible power for the single lens was

From the graph bellow it is possible that the highest possible power for the combined lens was

From the graph bellow it is possible that the highest possible power for the single lens was

From the graph bellow it is possible that the lowest possible power for the combined lens was

From the above findings the lowest possible power was

From the above findings the highest possible power was

Control of Variables

§ Amount of light was controlled by carrying out the experiment in a dark room, this is one of the reasons for the good set of results, because only the wanted light from the bulb was being projected on to the screen and no unwanted light from the surrounding contaminated the results.

§ Power of convex lens was kept the same by using the same lens throughout

§ Focal length of convex lens was kept the same by using the same lens throughout

§ Using the same ruler and clamping it down to keep it in a fixed position I controlled distance between object and lens. I also used a setsquare so that when measuring the length I had the lens at a right and to the ruler to improve accuracy.

§ Controlling the distance between lens and screen was the same as above, however to ensure I was in as much focus as I could be I spent enough time going in and out of focus to find the up most point of focus as possible with the eye.

Further proposals

The experiment was very human measured, electronic measuring equipment such as the Sonin 1000S Multi-Measure Combo Professional Electronic Distance Measuring Tool that is a fast and accurate tool would improve accuracy.

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