With the mathematical knowledge yo have about angles and triangles can you guess the path that the crow selects? If you can’t, read the following.

The crow can pick the grain from any point on the ground. But the condition is selecting a point on the ground to reach point ‘B’ from point ‘A’ in least possible time. If we assume that the speed of the crow is constant, the path that crow selects should be the shortest. Let us find the shortest path.

Observe some of the paths in the figure-3.

Which among the paths ACB, ADB, AEB and AFB is the shortest path?

To compare the lengths of these paths, make the duplicates of them as shown in

figure-4.

In the figure CB = CG. The length of path ACB = AC+CB = AC+CG = ACG. Thus the length of the path ACG is equal to the length of the path ACB. similarly ,

length of the path ADB = length of the path ADG

length of the path AEB = length of the path AEG

length of the path AFB = length of the path AFG

If you observe the Fig-4 carefully, you will notice that, among the paths ACG, ADG, AEG and AFG the shortest path is AEG, because it is the straight line distance between points A and G. You can measure and check this using a scale. As AEG=AEB, path AEB is the shortest path to reach point B from point A. It would take the least time. So the smart crow will pick the grain from point E.

Observe the path AEB once again in figure-5.

If we draw a normal EEI at point E, we can easily find that angle AEEI (angle 1) is equal to angle EIEB (angle 2).

Like the crow in the above situation, light also selects the path which takes the least time to travel. This principle was first given by Pierre de Fermat, a French

lawyer and an amateur mathematician.

It is also applicable to reflection of light. When light gets reflected from a surface, it selects the path that takes the least time. That is why the angle of incidence is equal to the angle of reflection as shown in figure-5.

Now, before the detailed discussion on reflection, peform a fun activity

and refresh your previous knowledge.

## No comments:

## Post a Comment