Geometric constructions for image formation by a converging lens

Journal of Physics: Conference Series, 2020

This study aims to determine the effect Android Ray Optics Application toward student’s ability in analyzing image formation on lens and mirror. This research is a quasi-experimental research with pre-test-post-test control group design. The population in this study were all prospective elementary school teacher candidates of fifth-semester students of Universitas Muhammadiyah Mataram. The sampling technique used was purposive sampling and class A (30 students) as an experimental class and Class C (30 students) as a control class. Data were collected by a descriptive test about the analysis of images formations on flat mirrors, curved mirrors, and lenses. The data were analyzed by independent sample t-test and normalized Gain test. The results showed that after treatment, students in the experimental class has a higher ability in analyzing images formations than the control one (t-value = 9,660 & t-table = 2,002). It’s concluded that Ray Optics is effective in improving student’s ab...

Software for Teaching through Interactive Demonstrations about Converging Lenses , 2019

In this paper, Software is presented for teaching through interactive demonstrations about lenses. At first we explore lenses constructed by two spherical surfaces. We explore the ray diagrams and wave fronts. Then there is a page for understanding the thick lens model. We introduce a step by step procedure to find the focal length and find the principal planes and finally the use of the focal length and principal points to construct the image. There is a page for finding the position of the image not by the formula but by the method we use on an actual experiment: We move the screen back and forth until we can get the sharpest possible image. This is done by finding the minimum of a standard deviation of the position of the rays for a given position of the screen. Then there is a simulation of an experiment for finding the focal length. This uses a macro to simulate the finding of several image points b for several object points a. These values are used first in the graphical representation of the image point as a function of b and the image points as a function of a. With suitable least square fits we get two lines with parameters that give values for the focal length and principal plane. Then there is a simulation of two experiments of finding the focal length of a lens. The spreadsheet calculates the distance b vs a, the image y, and there ar graphs of y as a function of a and y as a function of b from which we find 1) a hyperbolic fit for y vs a and a linear fit for y vs b from which we calculate the focal distance, 2) it calculates 1/a and 1/b and then finds a linear fit and a parabolic fit for the data. Also we get the same parameters by finding the cuts of lines uniting the point (a,0) and (0,b).. 3) there is a plot of a+b vs a and then the points are fitted with a hyperbola whose asymptotes give the sum of focal length and principal planes. Then there is a page where we can see two lenses for which the shape can change to have a perfect focusing at a given distance. These two lenses are based on Huygens’ ideas, Spherical and Huygen Lenses.

Science & Education, 2011

There are two indisputable findings in science education research. First, students go to school with some intuitive beliefs about the natural world and physical phenomena that pose an obstacle to the learning of formal science. Second, these beliefs result from the confluence of two factors, namely, their everyday experience as they interact with the world around them and a set of operational constraints or principles that channel both perceptually and conceptually the way these experiences are perceived and interpreted. History of science suggests that the theories of early scientists through which they sought to explain physical phenomena relied mostly on ideas that closely fitted their experiences of the relevant phenomena. This characteristic of the early scientific ideas is the root of the epistemological difficulties that early scientists faced in their attempts to explain the phenomena. In this paper, we focus on the early theories in optics (from ancient Greek to the late Islamic scientific traditions) and argue that students face some of the same epistemological problems as early scientists in explaining vision and optical phenomena for the reason that students' intuitive beliefs are also closely tied to particular phenomena and as a result the underlying notions are fragmentary and lack the necessary generality that would allow them to cover many disparate phenomena. Knowledge of these epistemological problems can help the instructor to identify the key elements for a better understanding of the formal theory of optics and, in turn, lead to a more effective instruction.

Applied Science and Innovative Research, 2019

In this paper, Software is presented for teaching through interactive demonstrations about lenses. At first we explore lenses constructed by two spherical surfaces. We explore the ray diagrams and wave fronts. Then there is a page for understanding the thick lens model. We introduce a step by step procedure to find the focal length and find the principal planes and finally the use of the focal length and principal points to construct the image. There is a page for finding the position of the image not by the formula but by the method we use on an actual experiment: We move the screen back and forth until we can get the sharpest possible image. This is done by finding the minimum of a standard deviation of the position of the rays for a given position of the screen. Then there is a simulation of an experiment for finding the focal length. This uses a macro to simulate the finding of several image points b for several object points a. These values are used first in the graphical representation of the image point as a function of b and the image points as a function of a. With suitable least square fits we get two lines with parameters that give values for the focal length and principal plane. Then there is a simulation of two experiments of finding the focal length of a lens. The spreadsheet calculates the distance b vs a, the image y, and there ar graphs of y as a function of a and y as a function of b from which we find 1) a hyperbolic fit for y vs a and a linear fit for y vs b from which we calculate the focal distance, 2) it calculates 1/a and 1/b and then finds a linear fit and a parabolic fit for the data. Also we get the same parameters by finding the cuts of lines uniting the point (a,0) and (0,b).. 3) there is a plot of a+b vs a and then the points are fitted with a hyperbola whose asymptotes give the sum of focal length and principal planes. Then there is a page where we can see two lenses for which the shape can change to have a perfect focusing at a given distance. These two lenses are based on Huygens' ideas, Spherical and Huygen Lenses.

Applied Science and Innovative Research, 2019

In this paper, Software is presented for teaching through interactive demonstrations about lenses. At first we explore lenses constructed by two spherical surfaces. We explore the ray diagrams and wave fronts. Then there is a page for understanding the thick lens model. We introduce a step by step procedure to find the focal length and find the principal planes and finally the use of the focal length and principal points to construct the image. There is a page for finding the position of the image not by the formula but by the method we use on an actual experiment: We move the screen back and forth until we can get the sharpest possible image. This is done by finding the minimum of a standard deviation of the position of the rays for a given position of the screen. Then there is a simulation of an experiment for finding the focal length. This uses a macro to simulate the finding of several image points b for several object points a. These values are used first in the graphical representation of the image point as a function of b and the image points as a function of a. With suitable least square fits we get two lines with parameters that give values for the focal length and principal plane. Then there is a simulation of two experiments of finding the focal length of a lens. The spreadsheet calculates the distance b vs a, the image y, and there ar graphs of y as a function of a and y as a function of b from which we find 1) a hyperbolic fit for y vs a and a linear fit for y vs b from which we calculate the focal distance, 2) it calculates 1/a and 1/b and then finds a linear fit and a parabolic fit for the data. Also we get the same parameters by finding the cuts of lines uniting the point (a,0) and (0,b).. 3)there is a plot of a+b vs a and then the points are fitted with a hyperbola whose asymptotes give the sum of focal length and principal planes. Then there is a page where we can see two lenses for which the shape can change to have a perfect focusing at a given distance. These two lenses are based on Huygens' ideas (a preprint exists in https://www.researchgate.net/publication/322302527_Spherical_lenses_and_Huygens'_lens?_sg=afv5RV2zzgNXkpkwD-GkA5bFhOCe_gUk-zc1hKeFRQ8GE7IYfzNWVjzoHdibFtsUYG-F0-MzCvhn144VnYj5LyqZV817ao1RdVitW9qB.KOs9BSuYkYtrji9qHmqB8_fOUF4LBrFaixxy-g-zy29AdDNZ3VXnq8Z8Fr-dsjksZBLnZtOIKiv7JkiQSzxTEQ)

Studies in Philosophy of Science and Education, 2020

We, as budding researchers, try to present science in the form of comics. We present the theory of optics by Christiaan Huygens and Sir Isaac Newton in a short comic strip. As we know, the Huygens principle explains that each wavefront can be considered to produce new wavelets or waves with the same wavelength as the previous one. A wavelet can be likened to a wave generated by a rock dropped into the water. The Huygens principle can be used to explain the diffraction of light in small slits. When passing through a small gap, the wavefront will create an infinite number of new wavelets so that the waves do not just flow straight, but spread out. By doing so, Huygens discovered his telescope. In this paper, we then illustrate his telescope through a simple comic.

European Journal of Physics, 2008

A historical discussion of the theories which deal with the formation of real images in mirrors and lenses is presented in this paper. Speculations on mirrors See endnote 1 appeared as early as Plato. Euclid’s, Hero’s and Ptolemy’s approaches to visual rays are described. The theory on burning mirrors starts with Diocles and later was continued by the Arabs. Al Haytham extensively studied the reflection of light rays on concave mirrors. Huygens tried to find a shorter way to do the calculations. With lenses Kepler gave a new way of finding the position of images by using approximations. Huygens also gave a solution for the shape of a ‘perfect’ lens. Huygens’ principle on waves can be combined with Fermat’s principle to explain the formation of images. These theories can be used in education to help students better understand the formation of images, the propagation of waves and the properties of lenses.

Journal of the Washington Academy of Sciences, 2008

The properties of real and virtual images formed by lenses and mirrors are reviewed. Key ideas are summarized in tables and rules of thumb. Simple conceptual problems illustrate the utility of the results. The practical significance of virtual objects is illustrated by the construction of a noninverting optical microscope.

2023

Computing locations and extent of images, except in the most trivial configurations or special cases, is a complex task. Even rays emanating from a point source and passing through an optical system generally fail to converge at a single image point, highlighting the care needed to establish image locations. We use three approaches to study image formation in a simple configuration, that of a point source following reflection from a spherical concave mirror. We calculate the caustic surfaces and compute cross sections of flux densities on image surfaces, and compare the results with experimentally generated light intensity fields. One of the two caustic surfaces is linear while the other forms a surface. The latter, undergoes a metamorphosis from a distorted cone to an open surface as the source is moved away from the axis. Cross sections of the caustic surfaces with an image plane are found to coincide with peaks in the flux density. Experimental studies validate these conclusions.

Physics 310 them. The path is called a ray of light, and a bundle of such rays constitutes a beam of light.