A convex lens forms a real image of an object with magnification m₁ . The lens is moved towards the object to obtain another real image of magnification m ₂ . The image distance is increased by x . The focal length of the lens is

Step-by-step solution

For a real image by a convex lens, magnification m = v |u| , giving v = f(1+m) . Initial image distance: v₁ = f(1+m₁) Final image distance: v₂ = f(1+m₂) Given v₂ - v₁ = x : f(1+m₂) - f(1+m₁) = x f(m₂ - m₁) = x f = x m₂ - m₁