Explanation:

When a lens is immersed in a transparent liquid, it can become invisible under the condition of having the same refractive index as the surrounding liquid.

Refractive Index:
The refractive index is a measure of how much a material bends or refracts light. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. The refractive index determines how much light rays are bent when they pass from one medium to another.

Immersion in a Transparent Liquid:
When a lens is immersed in a transparent liquid, such as water or oil, the light rays entering the lens from the surrounding medium will experience refraction at the lens-medium interface. The direction of the light rays changes due to the change in the refractive index at the interface.

Same Refractive Index:
If the refractive index of the lens material is the same as that of the surrounding liquid, then there is no change in the direction of the light rays at the lens-medium interface. This means that the light rays passing through the lens will continue to travel in a straight line without any deviation.

Consequence:
As a result, when the refractive index of the lens is the same as that of the surrounding liquid, the lens becomes invisible. Light passes through the lens without any refraction or bending, making it indistinguishable from the surrounding medium.

Example:
For example, if a lens made of glass (with a refractive index of 1.5) is immersed in a liquid with the same refractive index of 1.5, the lens will appear invisible when viewed from the outside. The light rays will pass through the lens without any noticeable change in their direction.

Conclusion:
In conclusion, when a lens is immersed in a transparent liquid and it becomes invisible, it is because the refractive index of the lens is the same as that of the surrounding liquid. This condition ensures that light rays passing through the lens do not experience any refraction or bending, making the lens indistinguishable from the surrounding medium.