Determination of the Focal Length of a Convex Lens

Determination of the Focal Length of a Convex LensShaikh Ilyasintention To determine the focal space of converging electron lens and its radius of curvature.HYPOTHESIS The relationship amongst u and v and the focal continuance f for a bulging lens is given by . Where f is the focal length, u is the distance between the object and the lens v is the distance between the grasp and the lens. Real and Virtual Images Lenses produce images by refraction that are said to be either real or virtual.Real images are created by the convergence of rays and can be projected onto a screen real images form on the side of the lens that is opposite to the object and by pattern have a positive image distance pryVirtual images are formed by the apparent extrapolation of diverging rays and cannot be formed on a screen, whereas virtual images form on the same side of the lens as the object and have a negative image distance value.12 soil For a thin double convex lens,refractionacts to focus all par allel rays to a header referred to as the principal focal point. The distance from the lens to that point is the principal focal length f of the lens. Below is the derivation of the lens formulaFollowing graphic illustrates a simple lens model3where,h= height of the objecth= height of the object projected in an imageG and C = focal pointsf= focal distanceu= Distance between the object and the focal pointO= Centre of the lensv= Distance between the centre of the lens and image piece of paperAssumptionsLens is very thinOptical axis is perpendicular to image planeProving is true.ProofIn AHO, In EDO, (1)In BOC, In EDC, (2)Equating equations (1) and (2),Dividing twain sides by v,Hence the formula is proved.VARIABLESIndependent Distance between the candle and the lensDependent Distance (v) from the image to the lensControlThis prove was conducted in an almost dark room.Same sheet of paper used as the screen.A stable candle flameThe time taken for a discerning and focused image to settleThe size of the candle.METHOD FOR CONTROLLING VARIABLES Made sure that the room was sufficiently dark enough to carry out this experiment as smoothly as possible without any entrance of light from the outside. So I pulled down the blinds of the windows and also made sure that there was no draught present in the room that can make the candle flame unstable. Moreover, I waited for around 6-7 seconds for the image to be seen as sharp and focused. And passim this experiment I used candles of the same make and size.APPARATUS REQUIRED2 meter rulesA white screenCandleConvex lensPROCEDUREI divided this experiment in to 2 parts, A and B. In part A, I experimented using a single lens at a time, while in part B, I used 2 lens in contact at a time.Part A firstly I set up the apparatus as shown in Figure 1 higher up by making the distances v and u the same. So the image observed on a intelligible white screen was focused and clearRecorded the value of the lengths u and v and thereb y marking these maestro points using a chalk on the bench.Then I adjusted the length of u by moving it away from the lens by 5cm. Consequently, I adjusted the length of v until a sharp and focused image was seen.Recorded this distance of u and vRepeated step 3 4 for 7 different values of u by increasing the distance by 5 cm in each step. And recorded the values of u and v for every increment.Then I placed the candle and the screen back in their original marked positions.Finally, repeated the steps 1-8 by using different convex lenses A, B, C, D and E.Figure 1 Setup of the apparatus for Part APart BFirstly I set up the apparatus as shown in Figure 2 by making the distances v and u the same. So the image observed on a plain white screen was focused and clearRecorded the value of the lengths u and v and thereby marking these original points using a chalk on the bench.Then I adjusted the length of u by moving it away from the lens by 5cm. Consequently, I adjusted the length of v until a sharp and focused image was seen. Recorded this distance of u and vRepeated step 3 4 for 4 different values of u by increasing the distance by 5 cm in each step. And recorded the values of u and v for every increment.Repeated the above steps 1-5, thrice.Figure 2 Setup of the apparatus for Part BDATA COLLECTION AND PROCESSINGPart A panel 1 info hoard for convex lens A duck 2 Data collected for convex lens BTable 3 Data collected for convex lens CTable 4 Data collected for convex lens DTable 5 Data collected for convex lens EPart BTable 6 Data collected for run 1Table 7 Data collected for Trial 2Table 8 Data collected for Trial 3Using the formula, R = 2f I can calculate the value for the radius of curvature. The value of f can be found using the equation.Part ATable 9Data processing for convex lens A exemplification recreation m = = = 0.30967Therefore, the focal length is 10.01+ 0.31 cmThe % error = = 3.1%Table 10Data processing for convex lens BStandard deviation m = = = 0 .47044Therefore, the focal length is 10.26+ 0.47 cmThe % error = = 4.6%Table 11Data processing for convex lens CStandard deviation m = = = 0.30500Therefore, the focal length is 9.89+ 0.31 cmThe % error = = 3.1%Table 12Data processing for convex lens DStandard deviation m = = = 0.32524Therefore, the focal length is 10.15+ 0.33 cmThe % error = = 3.2%Table 13Data processing for convex lens EStandard deviation m = = = 0.20508Therefore, the focal length is 9.76 + 0.20508 cmThe % error = = 2.1%Part BTable 14 Data processing for Trial 1Standard deviation m = = = 0.43905Therefore, the focal length is 19.85 + 0.44cmThe % error = = 2.2%Table 15 Data processing for Trial 2Standard deviation m = = = 0.16976Therefore, the focal length is 19.76 + 0.17 cmThe % error = = 0.9%Table 16 Data processing for Trial 3Standard deviation m = = = 0.14809Therefore, the focal length is 19.90 + 0.15 cmThe % error = = 2.2%CALCULATIONS AND DATA PRESENTATIONTable 17 Data presentation for Convex lens A (cm)-1 (cm)-1 (cm)-1