Question

Two identical sources emitted waves which produces intensity of k unit at a point on screen where path difference is λ. What will be intensity at a point on screen at which path difference is λ/4

• A. $\frac{k}{4}$
• B. $\frac{k}{2}$
• C. k
• D. Zero

Answer 1

Answer: (B)

$\frac{k}{2}$

Answer 2

SBy using phase difference $\varphi = \frac{2\pi}{\lambda}(\Delta)$

For path difference λ, phase difference $\varphi_{1} = 2\pi$and for path difference λ/4, phase difference φ₂ = π/2.

Also by using $I = 4I_{0}\cos^{2}\frac{\varphi}{2}$ ⇒ $\frac{I_{1}}{I_{2}} = \frac{\cos^{2}(\varphi_{1}/2)}{\cos^{2}(\varphi_{2}/2)}$

⇒ $\frac{k}{I_{2}} = \frac{\cos^{2}(2\pi/2)}{\cos^{2}\left( \frac{\pi/2}{2} \right)} = \frac{1}{1/2}$ ⇒ $I_{2} = \frac{k}{2}.$