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

Step 1 (Governing Law & Formula): [0.5 Mark]

In Young's Double Slit Experiment (YDSE), the position of the $n^{th}$ bright fringe is given by $y_n = \frac{n\lambda D}{d}$ and the position of the $n^{th}$ dark fringe is given by $y_n = \frac{(2n-1)\lambda D}{2d}$. The fringe width ($\beta$) is defined as the separation between two consecutive bright or two consecutive dark fringes.

The standard formula for fringe width is:

Step 2 (Mathematical Working): [0.25 Mark]

• For bright fringes: $\beta_{bright} = y_{n+1} - y_n = \frac{(n+1)\lambda D}{d} - \frac{n\lambda D}{d} = \frac{\lambda D}{d}$
• For dark fringes: $\beta_{dark} = y_{n+1} - y_n = \frac{(2(n+1)-1)\lambda D}{2d} - \frac{(2n-1)\lambda D}{2d} = \frac{(2n+1)\lambda D - (2n-1)\lambda D}{2d} = \frac{2\lambda D}{2d} = \frac{\lambda D}{d}$

Step 3 (Final Concluded Answer): [0.25 Mark]

Since $\beta_{bright} = \beta_{dark} = \frac{\lambda D}{d}$, the fringe width is uniform for both bright and dark fringes. Thus, both (A) and (R) are true, and (R) correctly explains (A).

💡 EL10 Concept Insight:

Think of the interference pattern like a set of evenly spaced ripples on a pond; because the light waves spread out and overlap in a perfectly repeating pattern, the distance between any two "peaks" (bright spots) or "troughs" (dark spots) remains exactly the same throughout the entire screen.