Question

In Young's double slit experiment, if the distance between the first dark fringe and the second bright fringe on the same side of the central maximum is \(1.5\,\text{mm}\), then the distance between the first dark fringe on one side and the second bright fringe on the other side of the central maximum is

• A. \(2.5\,\text{mm}\)
• B. \(1.5\,\text{mm}\)
• C. \(3.0\,\text{mm}\)
• D. \(2.0\,\text{mm}\)

Hint:

In YDSE, \[ \boxed{ \text{Bright fringes: }y_n=n\beta, } \] and \[ \boxed{ \text{Dark fringes: }y_n=\left(n+\frac12\right)\beta. } \] Always mark the fringe positions on the screen before calculating the distance.

Answer 1

The Correct Option is A

Step 1: Write the positions of the required fringes. In Young's double slit experiment, - First dark fringe: \[ y_{D1}=\frac{\beta}{2}, \] - Second bright fringe: \[ y_{B2}=2\beta, \] where \(\beta\) is the fringe width.

Step 2: Use the given information. The distance between the first dark fringe and the second bright fringe on the same side is \[ 2\beta-\frac{\beta}{2} = \frac{3\beta}{2}. \] Given, \[ \frac{3\beta}{2}=1.5\,\text{mm}. \] Hence, \[ \beta=1\,\text{mm}. \]

Step 3: Find the required distance. The coordinates are \[ -\frac{\beta}{2} \] for the first dark fringe on one side and \[ +2\beta \] for the second bright fringe on the opposite side. Therefore, the required distance is \[ 2\beta+\frac{\beta}{2} = \frac{5\beta}{2} = \frac52\times1 = 2.5\,\text{mm}. \] Hence, \[ \boxed{2.5\,\text{mm}.} \] Therefore, the correct option is \(\boxed{(A)}\).