Question

Two coherent sources 'P' and 'Q' produce interference at point 'A' on the screen where there is a dark band which is formed between 4th bright band and 5th bright band. Wavelength of light used is $6000\mathring{A}$. 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 1

Answer: (B)

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

Given : $\lambda =6000\mathring{A}=6000\times {10}^{-8}cm$

$5^{th}$ dark band is formed between $4^{th}$ and $5^{th}$ bright band.

Path difference between PA and QA $\Delta x=(n-\frac{1}{2})\lambda$ where $n=5$

$\therefore$ $\Delta x=(5-\frac{1}{2})\times 6000\times {10}^{-8}=2.7\times {10}^{-4}cm$