Optical systems

This page show the top view of an optical table. A metric optical table has a square grid of M6 threaded holes in it. These holes are used to mount optical components and are represented by the gray circles. The size of the table on your screen and the zoom factor can be adjusted. Optical systems consisting of lens, mirors, apertures, and eyes can be configured with this page. Press one of the '+' buttons to add a component. To display the controls for a component, press the corresponding button. There is a pull down menu under 'Optical components' that will load some typical optical systems. Details of the calculation can be found here.

Light Source
$x_o = $		[cm]
$y_o = $		[cm]
$\phi = $		[deg]

$\lambda ('s) = $ an array of wavelengths in nm
$380 < \lambda <780$

Optical components

Lenses:
Mirrors:
Eyes:
Apertures:

Table

Height:
Width:
Zoom:

<p>For a converging lens, the focal length is defined as the distance from the center of the lens to the point where parallel incoming rays are focused. This definition of the focal length is problematic because of chromatic aberration and spherical aberration. For real lenses chromatic aberration causes different wavelengths to focus at different points and spherical aberation causes rays that strike the lens far from the optical axis to focus at a different place that rays that strike the lens close to the optical axis. Chromatic aberration can be avoided by using only a single wavelength and spherical aberration can be minimized by using an aperture that only allows rays that make a small angle with the optical axis to strike the lens. If the lens is thin in the sense that the thickness of the lens measured along the optical axis $d$ is small compared to the focal length $f$ then the the lens-makers's formula can be used to calculate the focal length for a lens in air.</p>

$$\frac{1}{f} = (n_{\text{lens}}-1)\left( \frac{1}{R_{\text{left}}}-\frac{1}{R_{\text{right}}}\right)$$

<p>When the parameters of a lens are displayed and the update button is pressed, the lens-maker's formula is used to estimate the focal length. The approximate value of the focal length of the lens in air displayed at the right of the lens parameters. The actual distance from the middle of the lens at which the light rays focus may differ because $d$ may not be much smaller than $f$ or light rays might strike the lens at a large distance from the optical axis or at a large angle from the optical axis.</p>

<p>To determine the focal length experimentally, use rays from a distant source (like the sun) to focus the rays on a surface. The height of the lens when the smallest, brightest spot is produced is the focal length. </p>

<p>Diverging lenses have a negative focal length. If the diverging rays are extrapolated back to the other side of the lens the extrapolated lines meet at the focal point. In this case the image point is virtual.</p>

<p>An eye is an adaptive lens that focuses light on the retina at the back of the eye. For a person with normal vision, light rays coming from a source far away will focus at the retina when the eye muscles are relaxed. As an object is brought closer the eye muscles change the shape of the eye to keep the object in focus. The closest that an object can be to an eye and still be in focus is called the near point. The exact distance to the near point depends on the person but it is typically about 25 cm. In the controls for the eye, one of the parameters is $f$ which is the distance from the front of the eye to where parallel rays will be focused. The typical diameter for an eye is 2.4 cm so for someone with normal vision, $f$ can be adjusted from 2.4 to 2.295. The shift in the position of the focus is only about 1 mm so it is probably necessary to zoom in to see if the light is focused on the retina. </p>

<p>For a Keplerian telescope, the object is far away and the light rays entering the telescope are nearly parallel. These parallel rays form an image at the focal length of the objective lens. The eyepiece, also called the ocular lens, is then used to bend the light rays so that they are nearly parallel again so that they can be viewed by an eye. The length of the telescope is therefore about the sum of the two focal lengths. The magnification is $-f_1/f_2$ where $f_1$ is the focal length of the objective lens and $f_2$ is the focal length of the eyepiece. The focal length of the eyepiece is typically 1 - 2.5 cm so the magnification of a telescope that is $L$ centimeters long is between $L/4$ and $L$. Sometimes you see pictures of <a href="https://en.wikipedia.org/wiki/List_of_largest_optical_refracting_telescopes">very long telescopes</a> that were built to achieve a large magnification. The focus is adjusted by changing $L$.</p>

<p>It is probably necessary to zoom in on the eye to see when the telescope is focused. Change the angle $\phi$ of the incoming rays slightly and notice that the there is a larger angular deflection of the beam in the eye than of the incoming beam. By changing the angle of the incoming rays it can also be seen that the image is inverted by this telescope.</p>

<p>Galileo first built a telescope using a converging objective and a diverging eyepiece in 1609 and was able to achieve a magnification of about 30. He made observations of the moon and Jupiter's moons and published these in <a href="https://en.wikipedia.org/wiki/Sidereus_Nuncius"><i>Sidereus Nuncius</i></a>. The light rays entering the telescope are nearly parallel. The eyepiece is placed in front of the focal point of the objective so that the rays leaving the eyepiece are also nearly parallel. The length of the telescope is approximately the focal lengths of the two lenses but since the focal length of the diverging lens is negative, the length of the telescope is shorter than a Keplerian telescope. This configuration is often used in binoculars.The magnification is $-f_1/f_2$ where $f_1$ is the focal length of the objective lens and $f_2$ is the focal length of the eyepiece. The focus is adjusted by changing the distance between the lenses $L$.</p>

<p>It is probably necessary to zoom in on the eye to see when the telescope is focused. Change the angle $\phi$ of the incoming rays slightly and notice that the there is a larger angular deflection of the beam in the eye. A Galilean telescope does not invert the image.</p>

<p>In a simple microscope, the distance between the objective lens and the eyepeice is held fixed and the whole construction is moved up and down until the object is in focus. This happens when the image of the objective lens is at focal point of the eyepiece. The eyepiece will make these rays nearly parallel before they enter the eye. The objective lens of a microscope typically has a focal length between 0.2 cm and 4 cm.</p>

<p>Move the object radiating the light left and right until it is focused on the back of the retina. It will probably be necessary to zoom in on the back of the eye to see this. If you move the object slightly up and down in the $y$-direction you can see that the microscope inverts the image. As you move the light source, the apparent position of the light source is given by extrapolating the rays in the eye. To increase the magnification, make the focal length of the objective lens shorter. <input type="button" value="increase magnification" onclick="document.getElementById('txt1').innerHTML=lens_form(1); lens1.R1.value = 2; lens1.R2.value = -2; lenses[0].R1 = 2; lenses[0].R2 = -2; lenses[0].adjust_Rc(); set_focal_length(0); update(); MathJax.Hub.Queue(['Typeset',MathJax.Hub]); "> Refocus by moving the light source closer to the objective lens. </p>






	Physik für Geodäsie 511.018 / Physik M 513.805