My experiments focus is to obtain an accurate measurement for a specific lenss power.

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Quality of Measurement Coursework:

‘The power of a lens’

Andrew Ensten

Aim

My experiments’ focus is to obtain an accurate measurement for a specific lens’s power.

This will be achieved by focusing on the lens equation:

1/v (curvature of wavefront after lens) = 1/u (curvature of wavefront before lens) + 1/f (power of the lens/curvature added by lens).

By performing an experiment with a source of light, a lens, and a screen, I will obtain several 1/u and 1/v values. When these values are plotted on a 1/v against 1/u graph, they will hopefully give me an accurate estimation of the power of the lens by looking at the axes intercepts.

Equipment:

  • Power pack: For each experiment I kept the output setting to 9 Volts to control the power being delivered to the filament lamp (as power = current x voltage). Power is proportional to intensity and so a brighter/darker output could result in a different range where the created image is in focus.
  • 2x Wires: These took the electric current from the power pack to the light source I was using.
  • Filament lamp: I chose a filament lamp over other sources of light as it is easy to tell when its’ image is formed. This is because the filament is a very definable object.

I used it for my first, third and fourth experiments. With a constant voltage output; the intensity of light was relatively constant.

  • Light Emitting Diode: I used an LED for my second experiment. This also maintained a relatively constant intensity of light as the voltage setting on the power pack was not altered.
  • Lens: I used a convex lens with a diameter of 50mm and a claimed focal length of 150mm. It converges incoming light to a specific point based on its power. An image is formed at this point (in my case the filament of the lamp/when LED is most intense).
  • Lens holder: This is a vital piece of apparatus as it keeps the lens firmly in position. I placed this on top of a wooden block so the lens axis was at the same height as the centre of the light source, allowing an image to be formed.
  • Screen: This was simply a thin wooden block with white paper on the front of it. It is beneficial that the paper is white as it reflects most of the light cast on it. The result is a more defined image.
  • Wooden Ruler: The ruler was used to measure the U (distance between light source and lens) values and V (distance between lens and where image is formed) values.

It has a resolution of 1mm and therefore creates an uncertainty of +/- 0.5mm in my ‘U’ measurements. This turned out to be a very small percentage uncertainty in the U values ((0.5mm/200mm) x 100) gave the highest value of 0.25%. Such a small percentage is negligible and hence I have ignored uncertainties in U in my calculations.

Method:

  1. Firstly I placed the ruler horizontally on a desk starting at one end. The ruler was selotaped down at both ends so it didn’t move whilst experimenting.
  2. Next I connected the filament lamp to the power pack which was at a setting of 9 volts and plugged into a nearby socket. These components were placed on one end of the desk with the middle of the filament lamp aligned with “0” millimetres on the ruler.
  3. Then I put the lens in the holder and placed it on top of a wooden block. This was aligned to the desired ‘U’ starting point. (i.e. 500mm away from filament lamp)
  4. At this stage the equipment was set up for the first results. I moved the screen up and down the ruler (on the opposite side of the lens to the filament lamp) until the image is formed on the screen. I would then find the range of where the image is formed, and note down the minimum and maximum distances of this range.
  5. With the maximum and minimum V values figured out for a specific U value; I could then work out the mean of these and the uncertainty of V by halving the range.
  6. Next I would decrease U by a specific amount by moving the lens closer to the filament lamp. (e.g. from 500mm to 450mm) Then I would work out the V values for this particular U value.
  7. Finally I would repeat step 6 until I have data for a range of approximately 10 U values.


  1. 1/U and 1/V values must be calculated.

These represent the curvature of waves before and after.

Referring to the curvature equation, the V and U values are

essentially the radii of curvature (values stated in metres).

        

Safety:

While this is certainly not an experiment that requires a high level of caution, it can be slightly harmful if no care is taken.

The light sources used are quite bright. These should not be looked at directly for an extended period of time as it could cause damage to the eyes.

Furthermore a bright filament lamp can become rather warm, it is best to avoid touching it while in use.

Variables:

Independant variable:

This is the U and so 1/U value. It is varied by placing the lens at different distances away from the light source.

Dependant variable: This is the V and so 1/V value. Its value changes when the U value is varied and hence is dependant of it.

Controlled variables:

Voltage output: If I were to alter the voltage setting, the light source’s intensity will vary which could result in a change of where the image is formed.

Also I must use the same diameter and focal length lens; lenses with different focal lengths will of course have different powers.

First Experiment

  • Power pack set to 9 Volts
  • Using a filament lamp as light source
  • Distance the U value decreases per stage is 50mm

Join now!

First Experiment Results Analysis

The results from my first experiment have produced graphs which match a typical 1/v = 1/u + 1/f graph. This is because the equation is essentially a straight line; ‘y=mx+c’, and the actual graph is indeed a straight line.

It is a positive correlation where as 1/u curvature becomes less negative, 1/v becomes more positive.

Additionally as 1/V increases, the uncertainty in its measurement generally increases.

First Graph:

In order to intercept both axes in the same graph, I had to make the y axis the same scale as the x axis. This ...

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