Question

In young's double-slit experiment $\lambda =500nm,d=1mm,D=4m$. The minimum distance from the central maximum for which the intensity is half of the maximum intensity is ${}^{\prime }{x}^{\prime }\times {10}^{-4}m$. What is the value of ${}^{\prime }{x}^{\prime }$?

Answer 1

$I=I_{0}co{s}^2\frac{\delta }{2}$

$⟹\frac{1}{2}=co{s}^2\frac{\delta }{2}$

$⟹\delta =\frac{\pi }{2}$

Path difference $=\delta \times \frac{\lambda }{2\pi }=\frac{\lambda }{4}=\frac{yd}{D}$

Hence, $y=\frac{D\lambda }{4d}=5\times {10}^{-4}m$