Question

Two coherent sources \(P\) and \(Q\) produce interference at a 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 path difference between \(PA\) and \(QA\) is \(x\times 10^{-4}\) cm. The value of \(x\) is

• A. \(1.4\)
• B. \(2.7\)
• C. \(4.5\)
• D. \(6.2\)

Hint:

A dark band between the 4th and 5th bright bands has a path difference of 4.5 wavelengths.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Bright bands occur at path difference \(n\lambda\) and dark bands at \(\left(n+\dfrac{1}{2}\right)\lambda\).
A dark band between the 4th and 5th bright bands lies at \(4.5\lambda\).

Step 2: Calculation
\(\Delta x=4.5\times 6000\,\text{\AA}=27000\,\text{\AA}\)
Since \(1\,\text{\AA}=10^{-8}\) cm, \(\Delta x=27000\times 10^{-8}=2.7\times 10^{-4}\) cm

Step 3: Compare the options
So \(x=2.7\), which is option (B).

Final Answer:
The value of x is 2.7. \[ \boxed{\text{(B) }2.7} \]