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 the peak intensity is

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

Answer 1

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

$I=I_{max}{\cos }^2\left(\frac{\varphi }{2}\right)\frac{1}{2}={\cos }^2\left(\frac{\varphi }{2}\right)\Rightarrow \cos \varphi =0\Rightarrow \cos \varphi =0\Rightarrow \varphi =\frac{\pi }{2},\frac{3\pi }{2},\frac{5\pi }{2},\frac{7\pi }{2}\Rightarrow \Delta x=\frac{\lambda }{4},\frac{3\lambda }{4},\frac{5\lambda }{4}\Rightarrow \Delta x=(2n+1)\frac{\lambda }{4}$