Step 1: The situation.
A convex glass lens is dipped in a liquid. The liquid has exactly the same refractive index as the glass. We must find what happens to the focal length.
Step 2: Why refraction happens.
A lens bends light only because light changes speed when crossing from one medium to another. That change needs the two media to have different refractive indices.
Step 3: The lens maker's formula.
The focal length when a lens sits in a medium is
\[ \frac{1}{f} = \left(\frac{\mu_g}{\mu_l} - 1\right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \]
Here $\mu_g$ is the glass and $\mu_l$ is the liquid.
Step 4: Use the equal index condition.
Since the liquid matches the glass, $\mu_l = \mu_g$, so
\[ \frac{\mu_g}{\mu_l} = 1 \]
Step 5: See what happens.
Put this in the formula:
\[ \frac{1}{f} = (1 - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) = 0 \]
Step 6: Read the result.
If $1/f = 0$, then $f$ is infinite. Light passes straight through without bending, as if no lens were there. So the focal length becomes infinite, which is option (3).
\[ \boxed{f = \infty} \]