An object is placed at a distance of 12 ~cm from a convex lens on its principal axis and a virtual image of certain size is formed. If the object is moved 4 ~cm away from the lens, a real image of the same size as that of the virtual image is formed. The focal length of the lens in cm is

Step-by-step solution

Let f be the focal length of the convex lens. The object distance is u₁ = -12 cm . The lens formula is 1 v₁ - 1 u₁ = 1 f . For the virtual image, the magnification is m₁ = v₁ u₁ = v₁ -12 . Since the image is virtual, v₁ is negative, so m₁ is positive. Let the size of the object be h . Then the size of the image is h₁ = |m₁| h = | v₁ -12 | h = |v₁| 12 h . When the object is moved 4 cm away, the new object distance is u₂ = -16 cm . The new image distance v₂ is positive because the image is real. The magnification is