Optionals IAS Mains Physics: Questions 286 - 292 of 306

Hamilton’s Principle: This principle states that for a conservative holonomic system, its motion from time to time is such that the time integral (Known as action or action integral)

Where has stationary (extremum) value for the correct path of the motion?

The quantity is called as Hamilton’s principle function.

The principle may be expressed as

The Polarizability, , of an atom (or molecule) is defined as the dipole moment per unit local electric field at the atom (or molecule) i. e.

Thus polarizability is an atomic (or molecular) property where as dielectric constant is a macroscopic property which depends upon the arrangement of atoms or molecules within the crystal. If all the atoms (or

Let us consider the Zeeman splitting of the resonance lines and of sodium. These lines arise from the transitions.

and

The Zeeman levels, g-factors and the Zeeman shifts for the various terms involved in these transitions are as follows: we know that

Sign convention for lens (Converging/Diverging):

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For converging lens, focal length,

For diverging lens, focal length,

* Lens formula: 1

…………………… (i)

Here,

v = image distance from pole of lens

u = object distance from pole of lens

Given,

For first lens –

(Here, sign means image formed from len