Let the intensity due to each individual slit be I0.
The resultant intensity IR at a point where the phase difference is ϕ is given by:
IR=I1+I2+2I1I2cosϕ
Given that I1=I2=I0 and the resultant intensity IR=I0, we can substitute these values into the equation:
I0=I0+I0+2I0⋅I0cosϕ
I0=2I0+2I0cosϕ
I0=2I0(1+cosϕ)
1+cosϕ=21
cosϕ=−21
The minimum phase difference satisfying this condition is:
ϕ=32π
The relationship between phase difference ϕ and path difference Δx is:
ϕ=λ2πΔx
Substituting the value of ϕ:
32π=λ2πΔx
Δx=3λ
Given the wavelength λ=6000 A˚:
Δx=36000=2000 A˚
Answer: 2000