MHT CET · Physics · Wave Optics
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 \(6000\)Å. The difference between \(P A\) and \(Q A\) is
- A \(1.4 \times 10^{-4}\text{ cm}\)
- B \(2.7 \times 10^{-4}\text{ cm}\)
- C \(4.5 \times 10^{-4}\text{ cm}\)
- D \(6.2 \times 10^{-4}\text{ cm}\)
Answer & Solution
Correct Answer
(B) \(2.7 \times 10^{-4}\text{ cm}\)
Step-by-step Solution
Detailed explanation
Here \(\Delta x=\frac{\lambda \delta}{2 \pi}\)
For \(n=4^{t h}\) dark b and \(\delta=(2 n+1) \pi \Rightarrow \delta=(8+1) \pi=9 \pi\)
\(\Delta x=\frac{\lambda .9 \pi}{2 \pi}=\frac{9}{2} \times \lambda=\frac{9}{2} \times 6 \times 10^{-7}=2.7\) \(\times 10^{-6} m\)
\(=2.7 \times 10^{-4} cm\)
For \(n=4^{t h}\) dark b and \(\delta=(2 n+1) \pi \Rightarrow \delta=(8+1) \pi=9 \pi\)
\(\Delta x=\frac{\lambda .9 \pi}{2 \pi}=\frac{9}{2} \times \lambda=\frac{9}{2} \times 6 \times 10^{-7}=2.7\) \(\times 10^{-6} m\)
\(=2.7 \times 10^{-4} cm\)
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