Step 1 (Formula / Governing Law & Given Data): [0.25 Mark]
In Young's Double Slit Experiment (YDSE), the fringe width $\beta$ is given by $\beta = \frac{\lambda D}{d}$. The angular separation $\theta$ between consecutive bright fringes is defined as the ratio of fringe width to the distance of the screen from the slits:
$$\theta = \frac{\beta}{D} = \frac{\lambda}{d}$$Where:
- $\lambda$ = Wavelength of monochromatic light used.
- $D$ = Distance between the slits and the screen.
- $d$ = Separation between the two slits.
Step 2 (Step-by-Step Mathematical Working): [0.5 Mark]
We analyze the effect of the operations on the expression $\theta = \frac{\lambda}{d}$:
- Case (i): The screen is moved away from the plane of the slits. This changes $D$. However, the formula for angular separation $\theta = \frac{\lambda}{d}$ is independent of $D$. Therefore, $\theta$ remains constant.
- Case (ii): The separation between the two slits ($d$) is increased. Since $\theta \propto \frac{1}{d}$, as $d$ increases, the angular separation $\theta$ decreases.
Step 3 (Final Concluded Answer): [0.25 Mark]
Comparing the results: In case (i), $\theta$ remains constant; in case (ii), $\theta$ decreases. Therefore, the correct option is (C).
💡 EL10 Concept Insight: Think of angular separation as the "angle of view" from the slits; moving the screen back makes the fringes physically wider, but they also look smaller from the slits' perspective, so the angle stays the same. However, if you pull the slits further apart, the light rays have to bend less to create interference, which squeezes the fringes together and makes the angle smaller.