Two thin lenses, one convex of focal length magnitude f₁ and one concave of focal length magnitude f₂ , are placed in contact. What is the necessary condition for this combination to behave as a converging lens?

Step-by-step solution

The equivalent power of two thin lenses in contact is the algebraic sum of their individual powers: P_ eq = P₁ + P₂ . The power of a lens is the reciprocal of its focal length. For a convex lens, power is positive ( P₁ = 1 f₁ ), and for a concave lens, power is negative ( P₂ = - 1 f₂ ). Thus, the equivalent power of the combination is P_ eq = 1 f₁ - 1 f₂ . For the combination to behave as a converging lens, its equivalent power must be positive ( P_ eq > 0 ). 1 f₁ - 1 f₂ > 0 1 f₁ > 1 f₂ Since f₁ and f₂ are positive