Question

In YDSE, $d=2mm,D=2m$ and $\lambda =500nm$. If intensities of two slits are $I_0$ and $9I_0$, then find intensity at $y=\frac{1}{6}mm$.

• A. $7I_0$
• B. $10I_0$
• C. $16I_0$
• D. $4I_0$

Answer 1

The correct option is A $7I_0$

Phase difference $=2\pi \frac{x}{\beta }=2\pi \frac{{10}^{-3}\times 2\times {10}^{-3}}{6\times 5\times {10}^{-7}\times 2}=\frac{2\pi }{3}$

Intensity at y $=I_o+{9I}_o+2\sqrt{{9I_o}^2}\cos \left(2\pi /3\right)=I_o+{9I}_o-3I_o=7I_o$