SIMPLIFIED: Geometric Optics

Link to article: https://physics.bu.edu/~duffy/semester2/c28_lenses.html 

Note: The image above is from the original article.

The article linked above talks about mirrors and lenses. I am not going to get into the mirror and lens equations, but rather, this simplified article is going to act as a cheat sheet for solving mirror and lens problems. 

When studying mirrors and lenses, you will frequently run into problems along the lines of  “if I have a mirror and the focal point is here and the object is here, where is the image going to be?”. Most of the time, you would have to draw out a ray diagram, which means you will lose testing time, be prone to making a mistake, and drawing the ray diagrams out is just tedious. Therefore, I have made the following table for you:

Where the object is:	At Infinity	At F	Past C	At C	Between F & 0	Between F & C
Convex Lens	At F, real, shrunk	At infinity, real, magnified	Real, shrunk	Real, same size	Real, magnified	Virtual, magnified
Concave Mirror	At F, real, shrunk	At infinity, real, magnified	Real, shrunk	Real, same size	Real, magnified	Virtual, magnified
Concave Lens	At F, virtual, shrunk	Virtual, shrunk	Virtual, shrunk	Virtual, shrunk	Virtual, shrunk	Virtual, shrunk
Convex Mirror	At F, virtual, shrunk	Virtual, shrunk	Virtual, shrunk	Virtual, shrunk	Virtual, shrunk	Virtual, shrunk

**A couple of notes: real images are ALWAYS inverted, virtual images are always behind the mirror and have a negative value for distance, and for lenses specifically, virtual images form on the same side as the lens. F represents the focal point, and C represents the center of curvature. 

Here is how to read this chart: The very top row describes where the OBJECT is. Then, each corresponding box describes where the image will be, if the image will be magnified or shrunk, and if the image will be real or virtual. Here is an example: If the OBJECT is past C for a concave lens, then the resulting image will be virtual and shrunk (this example should explain how to use the chart).