An optical system is constructed by placing three thin lenses coaxially in contact. The focal lengths of the three lenses are f , f 2 , and -f , respectively. If the lateral magnifications produced by these individual lenses are m₁ , m₂ , and m₃ , what is the equivalent power and the total lateral magnification of the system?

Step-by-step solution

The equivalent power of a combination of thin lenses in contact is the sum of their individual powers. P = P₁ + P₂ + P₃ P = 1 f₁ + 1 f₂ + 1 f₃ Substituting the given focal lengths f₁ = f , f₂ = f 2 , and f₃ = -f : P = 1 f + 2 f - 1 f = 2 f For a system of lenses in contact, the total lateral magnification is the product of the lateral magnifications produced by the individual lenses. M = m₁ m₂ m₃ = m₁ m₂ m₃ Answer: 2 f and m₁ m₂ m₃