Optics & Wave Phenomena

When both slits are open:

• Two waves interfere to form double-slit fringes where central fringe intensity is $I_{\max} = 4I_0$.
• Fringe width is $\beta = \frac{\lambda D}{d}$.

When one slit is closed:

• Double-slit interference ceases, and light undergoes single-slit diffraction through the remaining open slit of width $a$.
• The intensity at the centre of the screen drops from $4I_0$ to $I_0$ (decreases).
• The angular width of the central diffraction maximum is $2\theta = \frac{2\lambda}{a}$ (linear width $\beta_{\text{diff}} = \frac{2\lambda D}{a}$). Because slit width $a \ll d$, the central maximum width becomes much broader than the double-slit fringe width (increases).

When the Young's double slit apparatus is immersed in a medium of refractive index $\mu$, the wavelength of light decreases to:

Since fringe width $\beta = \frac{\lambda D}{d}$, the new fringe width in the medium becomes:

Given $\beta = 0.4\,\text{mm}$ and $\mu = \frac{4}{3}$: