## Sunday, March 18, 2007

### Similarity and Optics

It is purely geometry that we can determine properties of convex lenses and their images. In this case, it suffices to use congruency and similarity to show the relationship between object distance u, image distance v and focal length f. From there we can also determine the height of object h and height of image k .Consider the ray diagram below.

Triangles OCD and OBE are similar, hence h/k=u/v .
Also, triangles AOG and BEG are similar, hence f/(v-f)=h/k=u/v.

But h/k =u/v. Substitute this into the second equation will result in the neat formula:

1/f=1/u+1/v

## Saturday, March 17, 2007

### Confusion over abbreviations in kinematics

Consider the following abbreviations, s,d,v. What does each one mean in kinematics?
Firstly, students are often confused over "s". They might assume that "s" stands for speed, rather than displacement.

But really, why does "s" stand for displacement?

If anyone has an answer to the above question, do let me know.

As for "d", it would mean distance. For "v", it might mean speed or velocity depending on the context. When doing questions involving speed and velocity, these abbreviations would generally not lead to any confusion. Here is a question to think about:

Given a "s-t" graph, how do we know that it is a distance time graph or a displacement time graph?

Similarly, given a "v-t" graph, how do we know v stands for speed and not velocity? Why is there no ambiguity in either cases?