Final answer:
The behavior of two equi-convex lenses in contact with water between them is complex and depends on multiple factors, such as curvature and refractive indices. The lensmaker's equation is used to determine focal lengths and powers in various lens configurations.
Step-by-step explanation:
When two equi-convex lenses with focal lengths of 20 cm and a refractive index of 1.5 are placed in contact, and the space between them is filled with water with a refractive index of 4/3, the combination does not necessarily work as a diverging lens with a doubled focal length as claimed in the question. The overall behavior of the lens system depends on the relative refractive indices and the curvature of the lenses. To determine the actual focal length of the combination, one needs to use the lensmaker's equation considering the refractive indices and radii of curvature.
For example, to find the focal length of a thin plano-convex lens, we use the lensmaker's equation considering the radii of curvature and index of refraction. Similarly, for diverging lenses, we know that the focal length and power of a diverging lens are defined to be negative. The same principle applies when determining the power of a combined lens system, where two lenses of focal lengths f₁ and f₂ are glued together with transparent material; the total power is the sum of the individual powers of the lenses.