Question

In the Young's double slit experiment using a monochromatic light of wavelength $\lambda$, the path difference (in terms of an integer n) corresponding to any point having half peak intensity is

• A. $(2n+1)\frac{\lambda }{2}$
• B. $(2n+1)\frac{\lambda }{4}$
• C. $(2n+1)\frac{\lambda }{8}$
• D. $(2n+1)\frac{\lambda }{16}$

Answer 1

The correct option is B $(2n+1)\frac{\lambda }{4}$

Sol$.\left(B\right)$
$\frac{I_{max}}{2}=I_m{\cos }^2\left(\frac{\varphi }{2}\right)$

$\Rightarrow \cos \left(\frac{\varphi }{2}\right)=\frac{1}{\sqrt{2}}$

$\Rightarrow \frac{\varphi }{2}=\frac{\pi }{4}$

$\Rightarrow \varphi =\frac{\pi }{2}(2n+1)$

$\Rightarrow \Delta x=\frac{\lambda }{2\pi }\varphi =\frac{\lambda }{2\pi }\times \frac{\pi }{2}(2n+1)=\frac{\lambda }{4}(2n+1)$