A concave mirror initially forms a real image of an object, magnified 2 times. When the object is moved 10 cm towards the mirror, a virtual image magnified 3 times is formed. The magnitude of the focal length of the mirror is

Step-by-step solution

Let the focal length of the concave mirror be f = -F (where F > 0 ). The magnification produced by a mirror in terms of focal length and object distance is given by m = f f - u . In the first case, a real image is formed with magnification 2 , so m₁ = -2 . -2 = -F -F - u₁ -2 = F F + u₁ -2F - 2u₁ = F u₁ = - 3F 2 . The initial object distance from the pole is |u₁| = 1.5F . In the second case, a virtual image is formed with magnification 3 , so m₂ = +3 . 3 = -F -F - u₂ 3 = F F + u₂ 3F + 3u₂ = F u₂ = - 2F 3 . The final