Question

If fringe width is \(0.4\) mm, the distance between fifth bright and third dark band on the same side in interference pattern of Young's double slit experiment is (in mm)

• A. \(1\)
• B. \(2\)
• C. \(3\)
• D. \(4\)

Hint:

Bright fringes lie at n times the fringe width and dark fringes at (2n - 1) times half the fringe width, so subtract the two positions.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
In Young's experiment the \(n^{th}\) bright band is at \(x_n=n\beta\) and the \(n^{th}\) dark band is at \(x_n'=\dfrac{(2n-1)\beta}{2}\), measured from the centre.

Step 2: Fifth bright band
\(x_5=5\beta=5\times0.4=2\) mm.

Step 3: Third dark band
\(x_3'=\dfrac{5\beta}{2}=\dfrac{5\times0.4}{2}=1\) mm.

Step 4: Distance
On the same side the separation is \(2-1=1\) mm, which is option (A).

Final Answer:
The fifth bright and third dark bands are 1 mm apart. \[ \boxed{\text{(A) }1} \]