Question

In Young's double slit experiment, the intensity on the screen at a point where path difference is l is K. What will be the intensity at the point where path difference is l/4 ?

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

Answer 1

Answer: (B)

$\frac{K}{2}$

Answer 2

Df = $\frac{2\pi}{\lambda}\Delta$ for path difference l, phase difference f₁ = 2p, for path difference $\frac{\lambda}{4}$, phase

difference f₂ = p/2, I = 4I₀ cos²$\frac{\varphi}{2} \Rightarrow \frac{I_{1}}{I_{2}} = \frac{\cos^{2}\frac{\varphi_{1}}{2}}{\cos^{2}\frac{\varphi_{2}}{2}}$

= $\frac{\cos^{2}\left( \frac{2\pi}{2} \right)}{\cos^{2}\left( \frac{\pi/2}{2} \right)}$ = 2 ̃ $\frac{K}{I_{2}} = 2$ ̃ I₂ = $\frac{K}{2}$