Question

A convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens material. Then its focal length will

• A. increase
• B. remain unchanged
• C. become infinite
• D. become zero

Hint:

When a lens is immersed in a liquid with an identical refractive index, it becomes optically invisible inside that liquid! Because no light bends at the borders, it behaves exactly like a flat window pane, giving it a power of zero and a focal length of infinity.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The problem investigates the optical behavior of a convex lens when immersed in a fluid environment. The absolute refractive index of the liquid ($\mu_l$) is perfectly matched to the refractive index of the glass lens material ($\mu_g$). We need to determine the resulting net focal length ($f$) of the lens under these conditions.

Step 2: Key Formula or Approach:
The focal length of a lens immersed in any medium is quantified by the standard

Lens Maker's Formula: $$\frac{1}{f} = \left(\frac{\mu_g}{\mu_l} - 1\right) \left(\frac{1}{R_1} - \frac{1}{R_2}\right)$$ Where $\mu_g$ is the refractive index of the lens material, $\mu_l$ is the refractive index of the surrounding medium, and $R_1, R_2$ are the radii of curvature of the two lens surfaces.

Step 3: Detailed Explanation:
From the problem constraints, we are given that the refractive index of the lens matches the liquid: $$\mu_l = \mu_g \implies \frac{\mu_g}{\mu_l} = 1$$ Substitute this relative index ratio into the Lens Maker's Formula: $$\frac{1}{f} = (1 - 1) \left(\frac{1}{R_1} - \frac{1}{R_2}\right)$$ $$\frac{1}{f} = 0 \cdot \left(\frac{1}{R_1} - \frac{1}{R_2}\right) = 0$$ Taking the reciprocal of both sides to isolate the focal length $f$: $$f = \frac{1}{0} = \infty$$ Because the boundary interfaces create zero net refraction, light rays pass completely straight through the system without converging or diverging, which corresponds to an infinite focal length.

Step 4: Final Answer:
The focal length of the lens will become infinite, which corresponds to option (C).