Question

describe two example Of extremum principle in action (or in real world) and state what quantities are maximized or minimized.

Answer 1

The Extremum Principle in Optics:

Fermat's principle, also known as the principle of least time, is the link between ray optics and wave optics. Fermat's principle states that the path taken by a ray between two given points is the path that can be traversed in the least time. here, time is minimized.

The Extremum Principle in Mechanics:

We define a quantity called action , where ds is the infinitesimal length along the trajectory of a particle of mass moving with speed v(s). For a particle with constant energy E, it can be shown that of all the possible trajectories between two fixed points, the actual trajectory is the one on which A defined above is an extremum (minimum or maximum). Historically this is known as the Principle of Least Action (PLA).