Describe the characteristics of an image formed by a converging lens

3.2.3 Thin Lenses – Converging Lens Image Characteristics

What is a Converging Lens?

A converging (convex) lens is thicker at the centre than at the edges. It bends light rays toward a common point called the focal point.

🔍 Analogy: Think of a magnifying glass focusing sunlight to a single spot.

Key Image Characteristics

  1. Image Position (v) – The distance from the lens to the image. It depends on the object distance (u) and the focal length (f) via the lens formula:

    \$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\$

  2. Image Size (hᵢ) – Related to object size (hₒ) by magnification:

    \$m = \frac{hᵢ}{hₒ} = -\frac{v}{u}\$

    Positive m → upright image; negative m → inverted.

  3. Image Orientation – For a converging lens:

    • Object beyond 2f → inverted, reduced.

    • Object at 2f → inverted, same size.

    • Object between f and 2f → inverted, enlarged.

    • Object at f → no real image (rays parallel).

    • Object inside f → virtual, upright, enlarged.

  4. Real vs Virtual – If the image lies on the opposite side of the lens from the object, it is real and can be projected on a screen. If it lies on the same side as the object, it is virtual and can only be seen by looking through the lens.

Exam Tip Box

🔎 Remember: Use the sign convention: u is negative when the object is on the same side as the incoming light; v is positive when the image is on the opposite side. This helps avoid sign errors in the lens formula.

Lens Formula Table

ParameterSign ConventionTypical Value
Object distance (u)Negative if object is on the same side as the incoming light.-20 cm (object 20 cm from lens)
Image distance (v)Positive if image is on the opposite side.+30 cm (image 30 cm on other side)
Focal length (f)Positive for converging lenses.+10 cm

Practical Example

📐 An object is placed 30 cm from a converging lens with f = 15 cm.

Using the lens formula:

\$\frac{1}{15} = \frac{1}{-30} + \frac{1}{v}\$

Solving gives v ≈ -30 cm → the image is virtual, upright, and twice the size of the object.

🧠 Tip: Check the sign of v to decide if the image is real or virtual.

Common Mistakes to Avoid

  • Using the wrong sign for u or v.

  • Forgetting that magnification m = -v/u.

  • Assuming all images formed by a converging lens are inverted.

  • Mixing up object distance (u) with image distance (v) when interpreting diagrams.

Quick Revision Checklist

  1. Identify u, v, f and apply the correct sign.

  2. Calculate magnification m = -v/u.

  3. Determine image orientation from the sign of m.

  4. Decide if the image is real or virtual based on the sign of v.

  5. Check your answer against the expected image characteristics for the given object position.