CBSE Class 12-science Answered

Two Waves that originates from different slits superimpose on each other. These are called interfering waves.

Consider an arbitrary point P on screen, which is at a distance D from slit s.

Let q be an angle between MO and MP.  Let S₁N be a normal on S₂ and PS₁ = PN.

Suppose S₁ and S₂ are two fine slits, a small distance d apart.  The two waves starting from each other from S₁ and S₂ superimpose upon each other, resulting in an interference pattern on screen.

The path difference of these two waves is S₂N.  The intensity of light at a point on the screen will depend upon the path difference between the two waves arriving at that point. If S₂N contains an integral number of wavelengths then two waves produces constructive interference, producing maximum intensity of light at P. If S₂N contains odd number of wavelength, then two waves produces destructive interference, producing minimum intensity at P.

From the figure we have,

PE = x – d/ 2

PF = x + d/ 2

(S₂P) ² - (S₁P) ² = [D ² + (x + d/2) ²] - [D ² + (x - d/2) ²]

(S₂P) ² - (S₁P) ² = 2xd