Snells Law: Light Ray Passes from One Medium - Research Paper Example

Running head: Light and lenses Student’s name Institution Course Professor Date of Experiment Date of Submission Abstract This report describes experimental procedures that were used to determine the minimum angle of deviation and the focal length of the object. The minimum angle of deviation was produced through refraction in the first part of the experiment. The lens Maker’s formula was utilized in the determination of focal length of the object especially by determining the refractive index of the materials used to manufacture prisms. The objective of these two experiments were to be familiar with equipment such as spectrometer, prisms, lenses, screen and torch. The results of the experiments were tabulated and were compared with the theoretical values. A graph was plotted in the first experiments as the results arrived at with the use of both normal lights and sodium lights were compared. Experimental and theoretical values were compared and an experimental error calculated. Table of Contents Abstract 2 1.0 Introduction 4 1.1 Theory 4 2.0Methodology 6 3.0Procedures 6 Part 1 6 Part two 7 4.0 Results and Calculations 7 Part one 7 Part two 11 5.0 Conclusions 12 6.0 References 14 1.0 Introduction The main objectives of these experiments were as follow To familiarize with the equipment used in the experiments and basic knowledge on thin lens optics To determine the minimum angle of deviation (D min) To determine the focal length of lens with the use of thin lens formula To determine the transverse magnification of the image and the refractive index of the prism. 1.1 Theory There are two commonly known lenses; convex and concave lenses. The convex lenses also referred to as diverging lens makes the incident ray to appear like they are diverging from the focal point. The concave lenses are also known as converging lenses makes all light rays incident to it and parallel to its principal axis to converge at a focal point (Rusty,2006:158). Lenses and mirrors have same parameters such as the principal axis, the focal length, the focal point and the centre of curvature. In addition, in lenses, the distance from the center of the lens to the focus is focal length, f. the focal lengths for diverging lens are negative while that of converging lens are positive. The thin lens formula can be expressed mathematically as Thins lens equation Where U – Object distance V - Image distance F – Focal length of a lens While using this formula, the real is positive convention is normally applied. Thus a negative sign indicate a formation of virtual image and a positive sign denote real images. Alternatively, the Lens Markers formula can be used to calculate the focal length of both the biconcave and biconvex lens. This formula can be expressed mathematically as Where -the refractive index of lens - The radii of curvature for both sides. The ratio formula is useful in the magnification of the lenses. The ratio of the height of the image to that of its objects is referred to as linear magnification. The ratio of speed of light in a vacuum to that of light in the medium gives the index refraction, n A monochromatic light get deviated from its path through some angle when it passes through a prism. Therefore, the refractive index of a prism can be calculated using the below mentioned equation. The Snell’s law denote that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant when a light ray passes from one medium to the other. This law can be expressed mathematically as 2.0Methodology Among the tools and equipment employed included; Optical bench Screen Metre rule Spectrometer with sodium light Retort stand Torch Len’s holder Lenses 3.0Procedures This experiment had two procedures, namely part one and part two. Part 1 In this experiment, first of all, the torch was positioned in a retort stand so that the apex of the triangle forms part of the objects points upwards. Then the thin lens were installed into a holder on the optical bench and aligned in torch-lens-screen manner. The minimum object distance, u was found for which a focused image on the screen can be located. This was attained accurately by fixing the screen at some suitable position and moving the lens till a focused image of the object appeared. In addition, both the image distance, v and the object distance, u were measured and with the use of Lens maker’s formula, the focal length of the lens could be determined. Comparison was made between the measured and the published lengths of the lens. With the use of this formula, the true transverse magnification of the lens was determined. Consequently, this result was compared with that of ratio magnification, . The above process was carried out to give additional values of object distance. A graph of 1/u against the experimentally obtained 1/v was plotted and the expected results compared with that of the Lens makers formula. The image quality in each was described qualitatively as the above procedure was repeated while using a thicker lens. Part two In this experiment, spectrometer with sodium light was utilized in both prisms. First of all, the minimum angle of deviation Dmin was determined. The refractive index (np) of the materials was determine especially if A is prism angle (600) then np= sin (Dmin + A)/2) Sin (A/2) 4.0 Results and Calculations Part one The results obtained were tabulated as shown Lens u(m) v(m) 1/v 1/u f(m) f(mm) Labelled f (mm) % difference Height (I)(m) Height (O)(m) mtrue m % difference 1 0.384 0.385 2.60 2.60 0.192 192.2 200 3.9% 0.025 0.028 0.89 1.00 10.9% 2 0.340 0.435 2.30 2.94 0.191 190.8 200 4.6% 0.035 0.028 1.25 1.28 2.3% 3 0.325 0.485 2.06 3.08 0.195 194.6 200 2.7% 0.038 0.028 1.36 1.49 9.1% 4 0.310 0.535 1.87 3.23 0.196 196.3 200 1.9% 0.043 0.026 1.65 1.73 4.2% 5 0.300 0.585 1.71 3.33 0.198 198.3 200 0.8% 0.051 0.028 1.82 1.95 6.6% 6 0.286 0.635 1.57 3.50 0.197 197.2 200 1.4% 0.055 0.028 1.96 2.22 11.5% 7 0.274 0.685 1.46 3.65 0.196 195.7 200 2.1% 0.063 0.028 2.25 2.50 10.0% From the values in the table above, the initial values were; Object distance, u= 0.384m Image distance, v= 0.385m With the use of Lens formula, 1/f = (1/0.394+ 1/0.385) 1/f=5.2016 f = 0.1922M In regards to the published value of the focal length of 200mm and that the calculated value of 192.2mm, then the percentage error can be determined as follows Percentage Error = (7.8/200)* 100% 3.9% The value of percentage error is quite reasonable. Consequently, The differences in the values i.e 0.893 and 1.003 can be attributed to experimental errors when taking the values of height and distances of the objects Part two The results were tabulated as shown below Prism Minimum deviation Ѳ1  Minimum deviation Ѳ2  Minimum deviation Ѳ3  Minimum deviation Average  Np Material & actual refractive index of prism Percentage error Glass 48.0 53.0 53.0 51.3 1.65 flint glass (n=1.62) 1.80% Plastic 36.0 22.0 36.0 31.3 1.43 fused silica (n=1.45) 1.30% In glass prism, Average minimum deviation (Dmin) = There is a likelihood that this material was made from a flint glass with a refractive index, n=1.62 for instance, their differences in values was (1.6516-1.62=0.0316) and could be attributed to parallax errors. The percentage error= In a plastic prism Average minimum deviation (Dmin) = There is a likelihood that this material was made from a fused silica with a refractive index, n=1.45 for instance, the difference is 1.45-1.4306=0.0194 Percentage error= 5.0 Conclusions These experimental procedures were able determine the minimum angle of deviation and the focal length of the object. The minimum angle of deviation was produced through refraction in the first part of the experiment. The lens Maker’s formula was utilized in the determination of focal length of the object especially by determining the refractive index of the materials used to manufacture prisms. The values of the image distance and the object distance were used in the calculation of true transverse magnification. The theoretical and experimental values were compared to elucidate any error during both experiments. Some of the errors witnessed were; parallax errors, approximations in calculations that involved large decimals figures and also errors through approximated centre of lens utilized impacted on both image and object distances. In order to reduce the percentage errors, there is need to observe and make readings at perpendicular positions and increase the number of attempts to enhance accuracy. 6.0 References Hernández, C. A. Physics Laboratory Experiments. New York: Cengage Learning, 2009. Rusty L. M. The basics of physics. New York: Group Greenwood Publishing, 2006. Read More