The angular width of fringes in Young's Double Slit Experiment (YDSE) is given by $\theta = \frac{\lambda}{d}$. Given: Initial angular width, $\theta_1 = 0.20^{\circ}$ Initial slit separation, $d_1 = 2 \text{ mm}$ Final angular width, $\theta_2 = 0.21^{\circ}$ Let the final slit separation be $d_2$. Since $\lambda$ is constant, we have $\theta \propto \frac{1}{d}$. $\Rightarrow \frac{\theta_1}{\theta_2} = \frac{d_2}{d_1}$ $\Rightarrow d_2 = d_1 \times \frac{\theta_1}{\theta_2}$ $\Rightarrow d_2 = 2 \times \frac{0.20}{0.21} = \frac{40}{21} \text{ mm} \approx 1.9 \text{ mm}$. Thus, the new separation between the slits should be $1.9 \text{ mm}$.