Under what condition does a biconvex lens of glass having a certain refractive index act as a plane glass sheet when immersed in a liquid ?

To determine the conditions under which a biconvex lens of glass behaves like a plane glass sheet when immersed in a liquid, we need to consider the relationship between the refractive indices of the materials involved. A biconvex lens typically has a positive focal length and can converge light rays. However, when it is submerged in a liquid, its optical properties may change depending on the refractive index of the liquid compared to that of the glass lens.

Refractive Index Considerations

The refractive index (n) is a dimensionless number that describes how light propagates through a medium. For a biconvex lens made of glass, let’s denote its refractive index as n_glass. When placed in a liquid with a refractive index n_liquid, the lens starts to act like a plane glass sheet under specific conditions.

Condition for Equivalence

For the biconvex lens to function as a plane sheet of glass, the refractive indices must be equal. This means:

• If n_liquid = n_glass, then the lens will behave like a plane surface.

When the refractive indices are the same, the light rays passing through the lens do not bend at the interface between the glass and the liquid, effectively negating the lens's converging properties.

Practical Implications

In practical terms, let’s consider an example. Suppose we have a biconvex lens made of glass with a refractive index of 1.5. If we immerse this lens in a liquid that also has a refractive index of 1.5, the lens will no longer converge light rays. Instead, it will allow light to pass through it unchanged, similar to how a flat sheet of glass would behave.

Why This Happens

This phenomenon occurs because refraction depends on the difference in refractive indices between two media. When the indices are equal, there is no effective change in speed or direction of the light as it crosses the boundary between the two materials. This is akin to walking on a flat road without any bumps or inclines; the surface feels uniform and straightforward.

Summary of Key Points

In summary, a biconvex lens behaves like a plane glass sheet when immersed in a liquid only if the refractive index of the liquid matches that of the glass lens. This condition results in the absence of any optical distortion, allowing light to travel through without bending. Understanding this relationship is crucial in optics, particularly in applications involving lenses and immersion media.