The correct option is D √α+1√α−1
Let Imax and Imin are the maximum and minimum resultant intensities, respectively, then,
ImaxImin=α
We know that, I∝A2
⇒AmaxAmin=√ImaxImin=√α
We know that,
Amax=A1+A2 and Amin=A1−A2
⇒√α=A1+A2A1−A2
after doing componendo-dividendo on both sides, we get,
A1A2=√α+1√α−1
Hence, (D) is the correct answer.