Bouncing ball

This graph shows the motion of a ball held in a hand and then dropped so that it falls to the floor and repeatedly bounces. At A, it is in the hand, so it has zero velocity. As it falls, its velocity increases. At B, it hits the floor. It changes direction, but is still moving, so it has a velocity but it becomes negative. As it rises back up, it slows down due to gravity. At the top, it has velocity zero (C) before it falls again, with an increasing velocity to hit the ground at D etc. The gradient of a velocity-time graph gives you the acceleration, so here the gradient = 9.81 m/s/s/

This next graph is for a rocket. As it burns fuel, the thrust upwards is bigger than the weight downwards, so it accelerates. At C it runs out of fuel, so the weight starts to make it decelerate. It goes slower and slower until it stops at E, ready to fall back. E is the highest point that it reaches.

Multiple slit interference

This time we can't easily work out the fringe directions by marking out the points where the semi-circular ripples cross over. I've drawn ripples from four slits on my diagram but I could have added more. If I had done, the ripples from the top slit and the bottom slit would not even have overlapped. So what you have to do here is figure out directions in which there is constructive interference. We do this by drawing lines across the ripples in the way that Huygen's invented. This creates a wavefront where there will be constructive interference (you are joining up peaks and peaks!). To get the direction, draw a ray at 90 degrees to the wavefront. Notice that to reach the wavefront, the red wave has gone one wave further than the blue wave etc. Between the waves from one slit and the next on this wavefront, there is a path difference of one whole wavelength.

The next diagram shows the same situation with the ripples removed. Since the rays travel (almost) parallel, the marked section shows the path difference. If the path difference is an integer multiple of the wavelength, you will get constructive interference in that direction.

Finally we extract the bottom triangle, marked X on the previous diagram and label it up as shown to get the diffraction grating equation.

Diffraction with wider slits

These pictures show what happens if we repeat diffraction with wider slits. Notice that the waves no longer bend round as far. This means that the area of overlap in which interference can occur is reduced. This means fewer fringes are seen. (In the second picture, I've dotted the fringes that are lost). But notice that the fringes that remain still have the same spacing.

Slit separation and fringe width

You can use the Double Slit equation to prove that a smaller slit width results in a bigger fringe separation but these diagrams are a more "physics" way of doing it. Pick one wave a count the number of other waves that it crosses. The further apart the slits, the more waves it crosses so there are more places for constructive interference and thus more fringes in the same space. The closer the slits, the fewer times a wave overlaps another wave, so the directions of constructive interference are more spread out.