Software for Teaching through Interactive Demonstrations about Converging Lenses

Pavlos Mihas

doi:10.22158/asir.v3n1p15

Abstract

<p><em>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.</em></p>

Highlights

The teaching of lenses can be facilitated when the student is having an image of what is being taught
We explore the ray diagrams and wave fronts
We introduce a step by step procedure to find the focal length and find the principal planes and the use of the focal length and principal points to construct the image

Summary

Introduction

The teaching of lenses can be facilitated when the student is having an image of what is being taught. When the user presses this button, the sheet “THICK LENS MODEL” appears (Figure 4). The user can press “parameters” follow a step by step exposition of the elements of paraxial theory For this purpose in this form there are two buttons: INCREASE NUMBER OF STEPS, DECREASE NUMBER OF STEPS. If he presses the button INCREASE THE NUMBER OF STEPS to 1, on the screen appears a ray parallel to the x-axis from the right side of the lens. For the step 1, the student can see that by decreasing the value of y for the parallel ray, the point of intersection of the emerging ray with the x- axis is very near the value of the left focus calculated according to the paraxial model. If t is the width of the lens and the radii of the surfaces are Rb (for the left surface) and Ra (for the right surface) :

Finding the Image

Experiments for Finding the Focal Length