Thin lenses and spherical mirrors are very useful optical elements. They can be used to form images of objects for a variety of applications. An example would be a telescope where the goal is to magnify the image of an object located very far from the optical device. The thin lens equation allows for a mathematical solution to the features of the resulting image for a system of optical elements.
Even the Hubble Telescope needed corrective lenses to see better.
Crazy Engineering: The Camera that Fixed Hubble
Watch the pre-lecture videos and read through the OpenStax text before doing the pre-lecture homework or attending class.
Optical elements such as lenses and spherical mirrors can be used to create a variety of image features. One way to understand the effects of the optical elements is to use Ray Tracing to locate the image. While that approach is qualitatively good for understanding the features of the light rays it sometimes lacks the precision of a mathamatical model. The thin lens equation provides a mathamatical model for studying lenses, spherical mirrors, and the images they form. The figure below shows the ray diagram for a converging lens. The distance to the object is $d_o$ while the distance to the image is $d_i$. The height of the object is defined as $h_o$ while the height of the image is $h_i$. The focal point is also defined as $F$ - the focal distance, which is the distance from the optical element to the focal point, is defined as $f$.
Converging Ray Diagram
Using those variables we can relate these variables with a few equations.
Thin Lens Equation
Magnification Equation
$M=\frac{h_i}{h_o}=-\frac{d_i}{d_o}$
Use of these equations requires careful consideration to a set of sign conventions. A summary of the sign conventions are below.
Thin Lens Equation
Magnification
Now, take a look at the pre-lecture reading and videos below.
