A

When a convex lens is placed in a medium whose refractive index is equal to that of the lens, the lens appears to be invisible and has no optical power. This is because the lens refracts light based on the difference in refractive indices between its material and the surrounding medium.
Step 1: Recall the lens maker's formula:
$$ f = \frac{R_1 R_2}{(n - 1)(R_2 - R_1)} $$
where $f$ is the focal length, $n$ is the refractive index of the lens material, and $R_1$ and $R_2$ are the radii of curvature of the lens surfaces.
Step 2: If the liquid's refractive index (n_l) is equal to that of the lens (n):
$$ n_l = n $$
Then the formula simplifies as follows:
$$ f = \frac{R_1 R_2}{(n_l - 1)(R_2 - R_1)} = \frac{R_1 R_2}{(n - 1)(R_2 - R_1)} $$
Since $n - 1 = 0$, the term becomes infinite.
Conclusion: Therefore, the focal length of the lens becomes infinite when it is submerged in a liquid with the same refractive index. Hence, the correct answer is Option A.