Question

Find the nature and order of the interference at the point P :

• A. ${70}^{th}$ maxima
• B. ${80}^{th}$ minima
• C. ${60}^{th}$ maxima
• D. ${70}^{th}$ minima

Answer 1

The correct option is A ${70}^{th}$ maxima

The optical path difference ($\Delta x$) between the waves at $P$ is given by
$\Delta x=S_{2}P-S_{1}P=\frac{y_{1}d}{D_1}+\frac{y_{1}d}{D_1}$
$\Delta x=\frac{\left(1\right)\left(10\right)}{{10}^3}+\frac{\left(5\right)\left(10\right)}{2\times {10}^3}$
Therefore, $\Delta x=0.035mm$
Also, $\Delta x=n\lambda =0.035mm$
$⟹n=\frac{0.035\times {10}^{-3}}{5000\times {10}^{-10}}=70$
Hence a maxima of ${70}^{th}$ order is obtained at P.