Question

Assertion : 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 YDSE:

Bright and dark fringes are equally spaced.
Fringe width depends only on \( \lambda, D, d \).

Answer 1

The Correct Option is A

Concept: In Young’s double-slit experiment (YDSE):

Fringe width: \[ \beta = \frac{\lambda D}{d} \]
Bright and dark fringes are equally spaced.

Step 1: Analyze Assertion (A). In YDSE:

Distance between two consecutive bright fringes = \( \beta \)
Distance between two consecutive dark fringes = \( \beta \)
Hence, fringe widths are equal. Assertion is true.
Step 2: Analyze Reason (R). The formula: \[ \beta = \frac{\lambda D}{d} \] gives the constant spacing between successive fringes. This applies equally to bright and dark fringes. Reason is true.
Step 3: Relation between A and R. Since the formula directly shows uniform spacing, it explains why bright and dark fringe widths are the same. Conclusion: Both Assertion and Reason are true, and Reason correctly explains Assertion.