Question

For constructive interference to take place between two monochromatic light waves of wavelength \( \lambda \), the path difference should be

• A. \( (2n - 1) \frac{\lambda}{4} \)
• B. \( (2n + 1) \frac{\lambda}{4} \)
• C. \( (2n - 1) \lambda \)
• D. \( n \lambda \)

Hint:

Constructive interference occurs when the path difference between two waves is an integer multiple of the wavelength.

Answer 1

The Correct Option is D

For constructive interference, the path difference between the two waves should be an integer multiple of the wavelength, i.e., \( \Delta x = n\lambda \), where \( n \) is an integer. This condition ensures that the two waves reinforce each other, leading to a larger amplitude at the points of constructive interference. When the path difference is an integer multiple of the wavelength, the crests of the waves align with the crests, and the troughs align with the troughs, resulting in constructive interference.

Hence, the correct answer is (d).