Question

Derive the equation for analytical treatment of interference band.

Answer 1

We shall derive an expression for the resultant intensity at any point P of the screen due to the superposition of two waves of light. Let S be a narrow slit illuminated by a monochromatic light of wavelength ? (Figure 3), and S 1 and S 2 two narrow slits close together and equidistant from S. The wave of light from S arriving at S 1 and S 2 will always be in phase. Let a 1 and a 2 be the amplitudes of the two waves from S 1 and S 2 respectively. Then the displacement Y 1 due to one wave, from S 1, at any instant.

The displacement Y 2 due to other wave from S 2, at the same instant t. 

where ? is the phase difference between the two waves reaching at P, at an instant t.

According to the principle of superposition, the resultant displacement Y at P is merely the algebraic sum of the individual displacement Y 1 and Y 2, that is

where A and ? are new unknown constants.

Substituting equation (4) and (5) in equation (3), we get

obviously the resultant vibration at P is a simple harmonic of amplitude A and of phase ?.

Answer 2

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