Question

In Young's double slit experiment, two slits are illuminated with a light of wavelength \(λ\). The line joining \(A_1P\) is perpendicular to \(A_1A_2\) as shown in figure. If the first minimum is detected at P, the value of slits separation 'a' will be
(D = distance between source and screen)

• A. \(λ\text{D}\)
• B. \(\sqrt{λ\text{D}}\)
• C. \(\sqrt{\frac{λ}{\text{D}}}\)
• D. \(\sqrt{\frac{\text{D}}{λ}}\)

Hint:

The path difference at the first minimum is half a wavelength.

Answer 1

The Correct Option is B

Step 1: Binomial approach
$A_2P - A_1P = D\left(\sqrt{1+\frac{a^2}{D^2}}-1\right)\approx\frac{a^2}{2D}$.

Step 2: Equate
$\frac{a^2}{2D} = \frac\lambda2$ gives $a^2 = \lambda D$. Option (B).

Final Answer:
root of lambda D. \[ \boxed{\text{(B)}\ a=\sqrt{\lambda D}} \]