1)

Two coherent sources P and Q produce interference at point A on the screen where there is a dark band that is formed between 4th bright band and 5th bright band. The wavelength of light used is 6000 Å . The path difference between  PA and QA is 


A) $1.4 \times 10^{-4}$ cm

B) $2.7 \times 10^{-4}$ cm

C) $4.5 \times 10^{-4}$ cm

D) $6.2 \times 10^{-4}$ cm

Answer:

Option B

Explanation:

 Path difference $\triangle $x is given by  $\frac{\lambda\delta}{2\pi}$

  [ where, $\lambda$= wave length of light , $\delta$ = phase difference ]

 for n= 4th dark fringe

                     $\delta$ =(2n-1)$\pi$

 $\Rightarrow$    $\delta = (8+1)\pi=9\pi$

 $\triangle x=\frac{\lambda 9\pi}{2\pi}=\frac{9}{2}\lambda=\frac{9}{2}\times6\times 10^{-7}$

$ 2.7 \times 10^{-6}$ m= $ 2.7 \times 10^{-4}$ cm