Question

Assertion (A) : In Young's double-slit experiment, the fringe width for dark and bright fringes is the same. Reason (R) : Fringe width is given by \[ \beta=\frac{\lambda D}{d}, \] where symbols have their usual meanings.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Both Assertion (A) and Reason (R) are false.

Hint:

In Young's double-slit experiment, \[ \beta=\frac{\lambda D}{d}. \] The spacing between consecutive bright fringes and consecutive dark fringes is always the same and equal to \(\beta\).

Answer 1

The Correct Option is A

Concept: In Young's double-slit experiment, alternate bright and dark fringes are formed due to constructive and destructive interference of coherent light waves. The fringe width is defined as the distance between two consecutive bright fringes or two consecutive dark fringes. It is given by \[ \beta=\frac{\lambda D}{d}, \] where
• \(\lambda\) = wavelength,
• \(D\) = distance between screen and slits,
• \(d\) = separation between slits.

Step 1: Examine the Assertion. Positions of bright fringes are \[ y_n=n\beta. \] Positions of dark fringes are \[ y_n=\left(n+\frac12\right)\beta. \] The separation between two successive bright fringes is \[ \beta. \] Similarly, the separation between two successive dark fringes is also \[ \beta. \] Therefore, bright and dark fringes have the same width. Hence, the Assertion is true.

Step 2: Examine the Reason. The standard expression for fringe width is \[ \beta=\frac{\lambda D}{d}. \] This statement is correct. Therefore, the Reason is true.

Step 3: Check whether the Reason explains the Assertion. Since the same fringe width formula applies to the spacing of both bright and dark fringes, both have equal widths. Thus, the Reason correctly explains the Assertion.

Step 4: Final conclusion. \[ \boxed{\text{Assertion is true}} \] \[ \boxed{\text{Reason is true}} \] and \[ \boxed{\text{Reason correctly explains the Assertion}}. \] Therefore, \[ \boxed{\text{(A)}}. \]