Understanding Lens Magnification: Analyzing m = +2

The question asks about the characteristics of an image formed by a lens when the magnification (\(m\)) is given as +2. Magnification is a key property that describes the image's orientation and size relative to the object.

What is Lens Magnification?

Magnification (\(m\)) for a lens is defined as the ratio of the image height (\(h_i\)) to the object height (\(h_o\)). Mathematically, it is expressed as:

\(m = \frac{\text{Image Height}}{\text{Object Height}} = \frac{h_i}{h_o}\)

The value and sign of the magnification provide specific information about the image characteristics.

Interpreting the Magnification Value (m = +2)

Let's break down the given magnification value, m = +2:

• Sign Interpretation: The sign of the magnification indicates the orientation of the image.
  • A positive sign (like the '+' in +2) signifies that the image is erect. This means the image is oriented in the same direction as the object (e.g., both are upright).
  • A negative sign would indicate an inverted image.
• Magnitude Interpretation: The numerical value (absolute value) of the magnification indicates the relative size of the image.
  • Here, the magnitude is \(|m| = |+2| = 2\).
  • Since the magnitude is greater than 1 (\(2 > 1\)), the image is magnified, meaning it is larger than the original object.
  • A magnitude less than 1 would mean a diminished (smaller) image, and a magnitude equal to 1 would mean an image of the same size.
• Image Nature (Virtual vs. Real): For lenses, an erect image (positive magnification) is generally a virtual image. Virtual images are formed where light rays only *appear* to converge and cannot be projected onto a screen. They are typically formed on the same side of the lens as the object. In contrast, inverted images (negative magnification) are usually real images.

Summary of Characteristics for m = +2

Combining these points for a magnification of m = +2:

• The image is erect (due to the positive sign).
• The image is larger than the object (due to the magnitude being 2).
• The image is virtual (because it is erect).

Therefore, the correct description of the image is erect, virtual, and larger than the object.