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 $4^{th}$ bright band and $5^{th}$ 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)

Given : $\lambda =6000\mathring{A}=6000\times 10^{-8}cm$
$5^{\text{th }}$ dark band is formed between $4^{\text{th }}$ and $5^{\text{th }}$ bright band.
Path difference between PA and QA $\Delta x=\left(n-\frac{1}{2}\right)\lambda$
where $n=5$
$\therefore \Delta x=\left(5-\frac{1}{2}\right)\times 6000\times 10^{-8}$
$=2.7\times 10^{-4}cm$