Two convex lenses, each having a focal length of 10 cm , are positioned at a separation of 15 cm with their principal axes coinciding. Compute the focal length of the equivalent lens. (Note that the sign of the focal length is positive even though the lens system actually diverges a parallel beam incident on it.)

Step-by-step solution

Given f₁ = 10 cm , f₂ = 10 cm , and the distance between the lenses d = 15 cm . The equivalent focal length F of two thin lenses separated by a distance d is given by the formula: 1 F = 1 f₁ + 1 f₂ - d f₁ f₂ Substituting the given values: 1 F = 1 10 + 1 10 - 15 10 10 1 F = 2 10 - 15 100 1 F = 20 100 - 15 100 1 F = 5 100 = 1 20 F = 20 cm