Question Analysis: Assertion (A) and Reason (R) type question.

Step 1 (Formula / Governing Law): [0.25 Mark]

The fringe width ($\beta$) in a Young's Double Slit Experiment (YDSE) is given by the formula:

Where:

• $\lambda$ = wavelength of monochromatic light
• $D$ = distance between the slits and the screen
• $d$ = separation between the two coherent sources

Step 2 (Step-by-Step Mathematical Working): [0.50 Mark]

Analyze the relationship between $d$ and $\beta$:

• From the formula, $\beta \propto \frac{1}{d}$. This implies that as the separation $d$ decreases, the fringe width $\beta$ increases.
• If the sources are "infinitely close" ($d \to 0$), then $\beta \to \infty$.
• When $\beta$ becomes infinitely large, the entire screen is covered by a single fringe (either bright or dark), making it impossible to distinguish individual interference fringes. Thus, the pattern is not observed.
• Reason (R) states $\beta \propto d$, which contradicts the derived relation $\beta \propto \frac{1}{d}$. Therefore, Reason (R) is false.

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

Conclusion: Assertion (A) is True, but Reason (R) is False.

💡 EL10 Concept Insight: Think of fringe width like the spacing between stripes on a shirt; if you push the two light sources closer together, the stripes get wider and wider until they are so huge that you can't see the pattern anymore, just one solid color!