Correct Option: (D) be compressed

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

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

$$\beta = \frac{\lambda D}{d}$$

Where:

• $\lambda$ = Wavelength of light in the medium
• $D$ = Distance between the screen and the slits
• $d$ = Distance between the two slits

When the apparatus is immersed in a liquid of refractive index $\mu$ ($\mu > 1$), the wavelength of light changes according to the relation:

$$\lambda' = \frac{\lambda}{\mu}$$

Step 2 (Step-by-Step Mathematical Working): [0.25 Mark]

Substituting the new wavelength $\lambda'$ into the fringe width formula to find the new fringe width $\beta'$:

$$\beta' = \frac{\lambda' D}{d}$$ $$\beta' = \frac{(\lambda / \mu) D}{d}$$ $$\beta' = \frac{1}{\mu} \left( \frac{\lambda D}{d} \right)$$ $$\beta' = \frac{\beta}{\mu}$$

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

Since $\mu > 1$, it follows that $\beta' < \beta$. Therefore, the fringe width decreases, meaning the fringe pattern will be compressed.

💡 EL10 Concept Insight:

Think of light waves like ripples in a pond; when they enter a denser liquid, they slow down and their "steps" (wavelength) get shorter. Because the waves are now packed closer together, the resulting interference pattern on the screen shrinks or "compresses."