Ln object is placed at a distance of 12 cm from a anvex lens on its principal axis and a virtual image f certain size is formed. If the object is moved further cm away from the lens, a real image of the same ize as that of the virtual image is formed. Which ne of the following is the focal length of the lens?

The correct answer is Option 2 (16 cm). This problem utilizes the lens formula 1/f = 1/v - 1/u and the magnification formula m = f / (f + u).

In the first case, the object distance (u₁) is -12 cm. Since the image is virtual, the magnification (m₁) is positive. In the second case, the object is moved 8 cm further away, so u₂ = -(12 + 8) = -20 cm. Here, a real image of the same size is formed, meaning the magnification (m₂) is negative and equal in magnitude to m₁ (m₁ = -m₂).

• Case 1: m₁ = f / (f - 12)
• Case 2: m₂ = f / (f - 20)

Equating them as m₁ = -m₂:
f / (f - 12) = -[f / (f - 20)]
1 / (f - 12) = -1 / (f - 20)
f - 20 = -f + 12
2f = 32
f = 16 cm.

Options 1, 3, and 4 are incorrect as they do not satisfy the condition of equal magnification magnitude at these specific object distances.