When a convex lens is immersed in a liquid, its focal length is given by:
1/fl = (nl - 1)(1/R1 - 1/R2)
where:
A convex lens will behave as a plane glass plate when its focal length approaches infinity (fl = ∞) or when 1/fl = 0. This is possible only when:
nl = 1
Since nl = ng/nl (where ng is the refractive index of the glass and nl is the refractive index of the liquid), the condition for the lens to behave as a plane glass plate is:
ng = nl
It means the refractive index of the lens (glass) must be equal to the refractive index of the liquid.