Question

Two coherent point sources S1and S2 vibrating in phase emit light of wavelength delta. The separation between the sources is 2delta. The smallest distance from S2 on a line passing through S2 and perpendicular to S1S2. Where a minimum of intensity occurs is

Answer 1

Two coherent source S₁ and S₂ are shown in figure.Here P is the point where we have find path difference of source S₁ and S₂ . For minimum intensity of light , path difference must be equal to path difference for dark
e.g., ∆x = λ/2, 3λ/2 , 5λ/2 .....
consider ∆x =(2λ - λ/2) = 3λ/2
now, path difference = S₁P - S₂P
∆x = √{4λ² + x²} - x
3λ/2 = √{4λ² + x² } - x
3λ/2 + x = √{4λ² + x²}
taking square both sides,
9λ²/4 + x² + 3λx = 4λ² + x²
9λ²/4 + 3λx = 4λ²
3λx = 4λ² - 9λ²/4 = 7λ²/4
x = 7λ/12

Hence, smallest distance from source S₂ on line passing through S₂ and perpendicular to S₁S₂ is 7λ/12