Next time you wonder where you are, here are a few points for your consideration.

How many dimensions would you say this graph projects?  What does it remind you of?  Is math a description of the universe or part of the universe itself?

Sometimes when we see something it reminds of other similar things.  For example, clouds can sometimes remind us of something completely non-cloud related.  Drag the blue slider in the graph below.   What past experiences or impressions of parts of nature are triggered in your mind by what you see? How do those memories or thoughts make you feel?

If you are looking at this blog-post, I will assume you have some sort of interest in curved mirrors.  Don't we all?  Who hasn't noticed how one's image on the inside of a shiny spoon looks different depending on how far away from one's eye one holds the spoon and whether one is looking at the inside or outside of the spoon? And talk about a simple experimental setup!  Physics is happening at nearly every breakfast table where cold cereal is eaten, tea is stirred, or sugar is sprinkled! 

This is an aspect of the behavior of light that fascinates nearly every curious mind at least some point in their life. It certainly fascinates me! Even though I know a few equations that help me understand the phenomenon to a deeper level than before, there is always more to learn! 

​I created the first version of this graph below during twenty minutes, a small part of one of my tutoring sessions with a local high school physics student.   It has already helped me gain a deeper understanding of the mirror equation, especially to visualize which circumstances lead to which results.
Take a look!  The best part about it is, it is interactive!   That's right!  You can drag the red dot marked "top of object" all over the graph to represent making an object bigger or smaller and closer or farther from a mirror, all at once!  

So what did you think of this graph?  If you have ever taken a physics course in which you encountered the mirror equation, you probably recognize this as a interactive version of the "ray diagram".   The straight lines trace the paths of the rays of light bouncing off of a spherically curved mirror from an object as viewed from the side.  Light travelling through a uniform material (or in a perfect a vacuum, the absence of all material) travels in a straight line.

Whether prepping for finals, or just seeking a little help with a subject in which you are struggling, call me today and mention this ad for 10% off your first session!