An object is placed on the principal axis of a lens of power -10.0 D, at a distance of 30 cm from it. The image is formed at a distance of _______ from the lens and is ______.

The correct answer is 7.5 cm; virtual.

Key Points

• The power of the lens is -10.0 D, which indicates it is a diverging lens.
• The formula for the focal length (f) of a lens is given by f = 1/P, where P is the power. Thus, f = -0.1 m or -10 cm.
• Using the lens formula (1/f = 1/v - 1/u), where u is the object distance (in this case, -30 cm), we can find the image distance (v).
• Substituting the given values, we get 1/(-10) = 1/v - 1/(-30). Solving this gives v = -7.5 cm, indicating the image is virtual.
• Thus, the image is formed at a distance of 7.5 cm from the lens and is virtual.

Additional Information

• Lens Power
  • The power of a lens is measured in diopters (D), and it is the reciprocal of the focal length in meters.
  • A positive power indicates a converging lens, while a negative power indicates a diverging lens.
• Lens Formula
  • The lens formula is 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance.
  • This formula helps in determining the position and nature (real or virtual) of the image formed by the lens.
• Virtual Image
  • A virtual image is formed when the outgoing rays from a point on the object appear to diverge from a point behind the lens.
  • Virtual images cannot be projected on a screen as they are formed by diverging rays.
• Diverging Lens
  • A diverging lens spreads out light rays that are initially parallel, causing them to diverge away from a common point.
  • These lenses are thinner at the center and thicker at the edges.