Two thin biconvex lenses have focal lengths f₁ and f₂ . A third thin biconcave lens has focal length of f₃ . If the two biconvex lenses are in contact, then the total power of the lenses is P₁ . If the first convex lens is in contact with the third lens, then the total power is P₂ . If the second lens is in contact with the third lens, the total power is P₃ , then

Step-by-step solution

According to cartesian sign conversion, Focal length of first biconvex lens =f₁ Focal length of second biconvex lens =f₂ Focal length of third biconcave lens =-f₃ Focal length of combination of first and second lenses is 1 f = 1 f₁ + 1 f₂ = f₁+f₂ f₁ f₂ As, power of lens, P₁= 1 f = f₁+f₂ f₁ f₂ Similarly, power of combination of first and third lenses is P₂= 1 f = 1 f₁ - 1 f₃ = f₃-f₁ f₁ f₃ and for combination of second and third lenses is P₃= 1 f = 1 f₂ - 1 f₃ = f₃-f₂ f₂ f₃