Two coherent sources P and Q produce interference at point A on t… - Vidyadip

MCQ

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

(b) : For $n^{\text {th }}$ dark band, path difference i.e.,
$
Q A-P A=(2 n-1) \frac{\lambda}{2}
$
Here, $n=5, \lambda=6000 Å=6 \times 10^{-7} m$
$
\begin{aligned}
\therefore \quad & Q A-P A=\frac{9}{2} \times 6 \times 10^{-7} m \\
& =27 \times 10^{-7} m =2.7 \times 10^{-4} cm
\end{aligned}
$

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