Two concave lenses L₁ and L₂ are placed in contact with one another. If the gap between the two lenses is filled with a substance of smaller refractive index, the magnitude of the focal length of the combination

Step-by-step solution

When two concave lenses are placed in contact, they touch at their edges, leaving a gap in the middle that is thicker at the center and thinner at the edges. This gap has the shape of a biconvex lens. Let the powers of the two concave lenses be P₁ and P₂ . Since they are concave, their powers are negative ( P₁ The initial equivalent power of the combination (with air in the gap) is: P_i = P₁ + P₂ When the gap is filled with a substance of refractive index > 1 , it acts as a convex lens. Let the power of this liquid