A glass plate inside a colorless liquid becomes invisible because:
(A) the densities of both are same
(B) the refractive indices of both are same
(C) the colors of both are same
(D) liquid wets glass surface

Hint:We are supposed to tell why the glass plate is invisible. In order to do this, consider the various phenomena that will occur inside or outside the glass plate, the reflection and refraction at the interface of the glass plate and colorless liquid. Also look for the light rays inside and outside the glass plate. Create a situation such that the glass plate will be invisible.

Complete step by step answer:
Consider a glass plate inside a colorless liquid. There will be two kinds of lights, one that will reflect or refract on the outer surface of the glass plate and one that will reflect or refract on the inner surface. We are supposed to find conditions for which the glass plate is invisible.

The glass plate will not be visible if the light hitting the outer surface does not reflect and the light hitting the inner surface does not refract and enters the other medium. For this to happen, the refractive index of both the glass plate and the liquid must be the same.

Considering the refraction at the interface,
from Snell's Law, we will have $n\sin i = n\sin r$, as the refractive indices are considered to be the same. From here, we will get an angle of incidence that is equal to the angle of refraction, which means that the light rays will not deviate from its actual path and thus refraction does not occur. The light will not reflect as well because as there is no change in the refractive index, it will continue along its original path.

Therefore, a glass plate inside a colorless liquid becomes invisible because the refractive indices of both are the same.

Hence, theCorrect Option is (B).

Note:Always remember that when light hits a surface or interface between two mediums, two phenomena are possible, one is reflection and the other is refraction. For an object to be invisible, the refractive index of the object must be equal to the refractive index of the medium, so that the light will travel its original path without being affected.