Question

Two coherent point sources \( S_1 \) and \( S_2 \) vibrating in phase emit light of wavelength \( \lambda \). The separation between them is \( 2\lambda \). The light is collected on a screen placed at a distance \( D \gg \lambda \) from the slit \( S_1 \) as shown. The minimum distance, so that intensity at \( P \) is equal to intensity at \( O \), is:

• A. \( \sqrt{2}D \)
• B. \( \sqrt{3}D \)
• C. \( \sqrt{8}D \)
• D. \( \sqrt{5}D \)

Hint:

In interference problems, the path difference must satisfy the condition for constructive or destructive interference, depending on the problem's requirement.

Answer 1

The Correct Option is B

The condition for maximum intensity occurs when the path difference between the two sources is an integer multiple of the wavelength \( \lambda \).
For the intensity to be the same at point \( P \) as at point \( O \), the path difference between the two sources must be \( \lambda/2 \). The minimum distance between the sources and the point where the intensity is equal is found using the formula for constructive interference, where the condition is satisfied at a distance \( \sqrt{3}D \).
Thus, the correct answer is (b).