Question

In $YDSE,d=2mm,D=2m$ and $\lambda =500nm$. If intensity of two slits are $l_0$ and $9l_0$, then find the intensity at $y=\frac{1}{6}mm$.

• A. $7l_0$
• B. $10l_0$
• C. $16l_0$
• D. $4l_0$

Answer 1

The correct option is A $7l_0$

Given:

path difference $=\frac{yd}{D}$

$=\frac{1}{6}\times {10}^{-3}\times 2\times \frac{{10}^{-3}}{2}=1.66\times {10}^{-7}m$

phase Difference $=\frac{2\pi \Delta y}{\lambda }=2.08=0.664\pi =119.{52}^{\circ }$

therefore

I net $=Io+9Io+2\left(9Io2\right)\frac{1}{2}\cos \left(119.52\right)$

$=10Io-3Io$

$=7Io$