Question

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

• A. become zero
• B. become infinite
• C. become small, but non-zero
• D. remain unchanged

Answer 1

The Correct Option is B

The problem deals with optics, specifically the behavior of a convex lens when it is immersed in a liquid with a refractive index equal to its own. To understand the outcome, let's explore the relevant optical principles.

A convex lens focuses light rays because of the difference in refractive index between the lens material and the surrounding medium. The degree of bending of the light rays, and hence the lens's focal length, is governed by the lens-maker's formula:

\frac{1}{f} = (n_{\text{lens}} - n_{\text{medium}}) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)

Where:

• f is the focal length of the lens.
• n_{\text{lens}} is the refractive index of the lens material.
• n_{\text{medium}} is the refractive index of the surrounding medium.
• R_1 and R_2 are the radii of curvature of the lens surfaces.

In the situation given:

- n_{\text{lens}} = n_{\text{medium}}

If we substitute into the formula:

\frac{1}{f} = (n_{\text{lens}} - n_{\text{medium}}) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) = 0\left( \frac{1}{R_1} - \frac{1}{R_2} \right) = 0

This results in \frac{1}{f} = 0, which implies f = \infty (infinite focal length).

Explanation: When the refractive index of the lens and the medium are equal, light does not bend upon entering or exiting the lens, effectively eliminating the lens's ability to focus light. Consequently, the lens behaves as if it has no optical power, resulting in an infinite focal length.

Therefore, the correct answer is the focal length will become infinite.