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

- Assertion (A): In Young’s double-slit experiment, the fringe width for dark and bright fringes is indeed the same. This is because the distance between adjacent bright and dark fringes (fringe width) remains constant for a given setup.
- Reason (R): The fringe width is given by the formula \( \beta = \frac{\lambda D}{d} \), where:
- \( \lambda \) is the wavelength of light,
- \( D \) is the distance between the slits and the screen,
- \( d \) is the separation between the two slits.
This formula gives the distance between two adjacent fringes, and since dark and bright fringes are equally spaced, the fringe width is the same for both.
Thus, both the assertion and reason are true, and the reason correctly explains the assertion.
Final Answer: (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).