Determination of the Focal Length of a Convex Lens

Determination of the Focal Length of a Convex Lens Shaikh Ilyas AIM: To determine the focal length of converging lens and it’s radius of curvature. HYPOTHESIS: The relationship between u and v and the focal length f for a convex 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 image 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 convention have a positive image distance value; Virtual 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.[1] [2] BACKGROUND: For a thin double convex lens,refractionacts to focus all parallel rays to a point 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 formula Following graphic illustrates a simple lens model: [3] where, h= height of the object h’= height of the object projected in an image G and C = focal points f= focal distance u= Distance between the object and the focal point O= Centre of the lens v= Distance between the centre of the lens and image plane Assumptions Lens is very thin Optical axis is perpendicular to image plane Proving is true. Proof In ΔAHO, In ΔEDO, ∠´ (1) In ΔBOC, In ΔEDC, ∠´ (2) Equating equations (1) and (2), Dividing both sides by v, Hence the formula is proved. VARIABLES: Independent: Distance between the candle and the lens Dependent: Distance (v) from the image to the lens Control: This experiment was conducted in an almost dark room. Same sheet of paper used as the screen. A stable candle flame The time taken for a sharp and focused image to settle The 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 throughout this experiment I used candles of the same make and size. APPARATUS REQUIRED: 2 meter rules A white screen Candle Convex lens PROCEDURE: I 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 above by making the distances v and u the same. So the image observed on a plain white screen was focused and clear Recorded 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 v Repeated 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 A Part B: Firstly 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 clear Recorded 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 v Repeated 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 B DATA COLLECTION AND PROCESSING: Part A: Table 1: Data collected for convex lens A Table 2: Data collected for convex lens B Table 3: Data collected for convex lens C Table 4: Data collected for convex lens D Table 5: Data collected for convex lens E Part B: Table 6: Data collected for Trial 1 Table 7: Data collected for Trial 2 Table 8: Data collected for Trial 3 Using 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 A: Table 9:Data processing for convex lens A Standard deviation: ÃŽ ´m = = = 0.30967 Therefore, the focal length is 10.01+ 0.31 cm The % error = = 3.1% Table 10:Data processing for convex lens B Standard deviation: ÃŽ ´m = = = 0.47044 Therefore, the focal length is 10.26+ 0.47 cm The % error = = 4.6% Table 11:Data processing for convex lens C Standard deviation: ÃŽ ´m = = = 0.30500 Therefore, the focal length is 9.89+ 0.31 cm The % error = = 3.1% Table 12:Data processing for convex lens D Standard deviation: ÃŽ ´m = = = 0.32524 Therefore, the focal length is 10.15+ 0.33 cm The % error = = 3.2% Table 13:Data processing for convex lens E Standard deviation: ÃŽ ´m = = = 0.20508 Therefore, the focal length is 9.76 + 0.20508 cm The % error = = 2.1% Part B: Table 14: Data processing for Trial 1 Standard deviation: ÃŽ ´m = = = 0.43905 Therefore, the focal length is 19.85 + 0.44cm The % error = = 2.2% Table 15: Data processing for Trial 2 Standard deviation: ÃŽ ´m = = = 0.16976 Therefore, the focal length is 19.76 + 0.17 cm The % error = = 0.9% Table 16: Data processing for Trial 3 Standard deviation: ÃŽ ´m = = = 0.14809 Therefore, the focal length is 19.90 + 0.15 cm The % error = = 2.2% CALCULATIONS AND DATA PRESENTATION: Table 17: Data presentation for Convex lens A (cm)-1 (cm)-1 (cm)-1 <