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 β = `(lambda D)/d`, where symbols have their usual meanings.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

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

• Assertion (A) is true, but Reason (R) is false.

• Both Assertion (A) and Reason (R) are false.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

Explanation:

The position of the n^th bright fringe is y_n = `(n lambda D)/d`

position of the n^th dark fringe is `y_n^' = (2n - 1)(lambda D)/(2 d)`

The fringe width (β) is defined as the distance between two consecutive bright fringes:

β = y_n+1 − y_n

= `((n + 1) lambda D)/d - (n lambda D)/d`

= `(lambda D)/d`

Similarly, the distance between two consecutive dark fringes:

β = `y_(n+1)^' - y_n^'`

= `((2n + 1) lambda D)/(2 d)`

= `(lambda d)/d`

Since both expressions give the same value, the fringe widths for bright and dark fringes are equal.

∴ Both Assertion and Reason are true, and the Reason correctly explains why the fringe widths are equal by deriving the common expression for β.