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# Relationship Between U and V For a Convex Lens

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Introduction

SC 1 Relationship between u and v for a convex lens Prediction I think that when the length of 'u' increases (object distance), the length 'v' will decrease. (image distance.) Only when the object is greater than the focal length of the lens, is a real image is produced. If the object distance is nearer the focal length than a virtual image is produced. The virtual image has a negative distance from the lens, which means it can't be focused onto the screen. When plotting my results on graph, I will expect them to produce a curved line for u over v, producing a reciprocal graph. However a straight line when plotting 1/u over 1/v. Scientific Ideas This formulae for the focal length of an object: 1/focal length = 1/object distance + 1/image distance The following formulas are rearranged from the one above. This will help me throught my experiment, and with my scientific ideas. u = object distance f = focal length v = image distance (20.0 cm) (15.0 cm) (60.0 cm) f = 1 / (1/u + 1/v) 15 = 1 / (1/20 + 1/60) (FOCAL LENGTH) f = (uv) / (u + v) 15 = (20*60) / (20 + 60) u = 1 / (1/f - 1/v) 20 = 1 / (0.06 - 0.016) (OBJECT DISTANCE) u = (vf) / (v-f) 20 = (60*15) / (60-15) v = 1 / (1/f - 1/u) 60 = 1 / (0.06 - 0.05) (IMAGE DISTANCE) v = (uf) / (u-f) 60 = (20*15) / (20-15) FOCAL LENGTH = 15 cm u (cm) v (cm) 10.00 - 30.00 20.00 60.00 30.00 30.00 40.00 24.00 50.00 21.43 60.00 20.00 70.00 19.09 80.00 18.46 90.00 18.00 100.00 17.65 110.00 17.37 120.00 17.13 130.00 16.96 140.00 16.80 150.00 16.67 160.00 16.55 170.00 16.45 180.00 16.36 190.00 16.29 Above shows a table that I have produced from the previous equations. ...read more.

Middle

* I will take care with the lenses so they don't break in the dark, which could cut somebody when broken. * Lastly, I will take care when the lights are switched off and I am in the dark, so that I don't trip up and hurt myself. Apparatus The instruments which I shall use in this experiment are: * I metre Ruler X2 * Convex lens * Lamp (12V) * Image Screen * D.C supply * Lens holder * Object window Method The experiment will be done on a table allowing a flat base, so that straight rays of light can travel to the convex lens and produce an image, along with providing an easy measuring surface. We will use a lamp as a bright object, so that an image can be easily produced on to the screen. A lamp will also be used in this experiment to transmit rays of light into the lens, and focus them to form a sharp image on the screen. To supply electricity to the lamp a D.C supply will be used. The D.C supply is kept at 12V (the brightest), so that the brightest image can be produced and easily focused. In front a window will be placed; this is so that the object distance can be easily located. Without the use of a window it will mean that only light rays go through the lens, and not produce a picture, meaning the object distance is harder to find. Then, the lens will be placed in a lens holder; the lens holder with the lens will be first placed 16.0cm away from the object. A convex lens will be used to focus the image on a screen, and not to divert the image like a concave lens. If a real image is formed, it will be focused onto a screen in front of the lens holder so that it can be seen on the screen. ...read more.

Conclusion

Using the formula, rearranged from the original, it shows that when u increases v decreases. However when a distance for u is put in, which is less than the focal point, it means a negative distance is given. This shows the image produced is, virtual. When the a virtual image is formed, one ray goes straight through the middle of the lens and another passes through the focal point and emerges parallel to the principal axis. To work out the focal length from a virtual image, the equation below is used: 1/v - 1/u = 1/f However to work out the focal length from a real image, the equation below is used: 1/v + 1/u = 1/f Using the Cartesian sign convention, the linear magnification is given by: V/U During the practical I made some errors, firstly I didn't use the same equipment throughout the practical. This is because I had to take the results down in four lessons. This meant that different instruments were used for the different days, which meant that the experiment could not to be a fair test. This means that my controlled variables weren't accurate. Lastly another mistake I made was that my work base (table) wasn't long enough for the distance v. The anomalies that I have discovered are, are from my results. These were found by looking at the expected results, worked out by the formula. Which showed that my average reading for v, when u was 20.0cm was 10cm out then expected. It also showed that my last few results were also out, but this time only by 1cm. However overall, my experiment shows that when the distance u increases, the distance v decreases. This meant my prediction was correct and proved. I found my results were fairly accurate, and close to my expected results using the lens formula. Evaluation My plan has worked out as expected this is because my method, readings, range, safety and equipment were used how I expected in my plan. ...read more.

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