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 Young's double-slit experiment, the fringe width is constant for both dark and bright fringes, and it is given by \( \beta = \frac{\lambda D}{d} \).

Answer 1

The Correct Option is A

In this question, we need to analyze the assertion and the reasoning given regarding Young’s double-slit experiment. Let's examine them one by one:

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.

Firstly, let's understand the concepts involved:

1. Fringe Width (\(\beta\)) Calculation: The fringe width (\(\beta\)) in Young’s double-slit experiment is the distance between two consecutive bright (or dark) fringes. It is expressed as: \(\beta = \frac{\lambda D}{d}\). Here,
   • \(\lambda\) = Wavelength of light used
   • \(D\) = Distance between the slits and the screen
   • \(d\) = Distance between the two slits
   This formula applies equally to both bright and dark fringes, resulting in identical spacing.
2. Conclusion Based on the Formula: This equation shows that the width of the fringes depends only on these parameters and not on the nature (bright/dark) of the fringe. Therefore, both dark and bright fringes have the same width.

Now, considering both the assertion and reasoning:

1. Assertion is True: In Young's double-slit experiment, indeed, the fringe width for both dark and bright fringes is the same.
2. Reason is True and Correct Explanation: The formula provided in the reason explains why the fringe width is identical for both types of fringes, making it the correct explanation for the assertion.

Based on the analysis, the correct answer is: Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).