Question

In Young's double slit experiment, the fringe width is 0.4 mm. What is the distance between \(4^{\text{th}}\) dark band and \(6^{\text{th}}\) bright band on the same side of the interference pattern?

• A. \(0.5\) mm
• B. \(0.75\) mm
• C. \(1.0\) mm
• D. \(1.5\) mm

Hint:

Dark fringes are at (n - 1/2) beta and bright fringes at n beta.

Answer 1

The Correct Option is C

Step 1: Count in units of beta:
Dark fringe order 4 is at $3.5\beta$ and bright order 6 is at $6\beta$.

Step 2: Subtract:
$(6 - 3.5)\beta = 2.5\beta$.

Step 3: Number:
$2.5\times0.4 = 1.0$ mm, option (C).

Final Answer:
The separation is 1.0 mm. \[ \boxed{\text{(C) }1.0\ \text{mm}} \]