Mini Physics
Part of Mini EducationSwitch subject
Search

Ray Diagrams For Converging Lens

Key idea: O Level converging-lens ray diagrams: the three principal rays and the image characteristics for common object positions.

  • SEC G3 Physics 2027
On this page

Learning objectives

  • Describe wave generation by vibrating sources, ropes and springs
  • Describe ripple-tank waves using wavefronts
  • Explain that waves transfer energy
  • Explain that wave energy transfer does not transfer matter
  • Use amplitude, frequency and wavelength to describe wave motion
  • Define and use wave speed and period and interpret wave graphs
  • Recall and apply wave speed = frequency × wavelength
  • Compare transverse and longitudinal waves and give examples
  • Explain sound production by vibration and the need for a medium
  • Describe sound using compressions and rarefactions
  • Relate sound loudness to amplitude and pitch to frequency
  • Explain reflected-sound echoes and use them to measure distance
  • Explain ultrasound use in sonar and soft-tissue scanning
  • Use the normal, angle of incidence and angle of reflection
  • Apply the law of reflection in constructions, measurements and calculations
  • Use the normal, angle of incidence and angle of refraction
  • Apply sin i divided by sin r as a constant for a fixed pair of media
  • Define refractive index as vacuum light speed divided by medium light speed
  • Explain the critical angle
  • Explain the conditions for total internal reflection
  • Apply total internal reflection to optical fibres and state advantages
  • Describe how a thin converging lens acts on a light beam
  • Define the focal length of a converging lens
  • Construct real and virtual image ray diagrams for a thin converging lens
  • Describe lens images as real or virtual, magnified or diminished, and upright or inverted

1. Definition

A. Ray diagrams (converging lens)

Ray diagrams for a converging lens are drawings that use a few standard rays to determine the position, size, and nature (real/virtual) of the image.

2. Key Ideas

  • You usually need only two rays to locate an image (where they meet).
  • Use solid lines for real rays and real images.
  • Use dashed lines only for extensions of rays (virtual rays/images).
  • Key terms:
    • focal length f
    • principal focus F
    • principal axis
    • optical centre
Prerequisite

Review converging lens terms first: Thin Converging Lenses.

3. Detailed Explanations

A. The three principal rays (rules)

You can use any two of these:

  1. Parallel ray: travels parallel to the principal axis → refracts through the focus on the far side.
  2. Central ray: passes through the optical centre → continues straight (approx.).
  3. Focal ray: passes through the focus on the near side (before the lens) → emerges parallel to the principal axis.

B. Common object positions and image characteristics (O Level)

Object positionImage positionImage natureOrientationSize
u > 2fbetween f and 2f (far side)realinverteddiminished
u = 2fat 2f (far side)realinvertedsame size
f < u < 2fbeyond 2f (far side)realinvertedmagnified
u = fat infinity (rays emerge parallel)no real image on a screen--
u < fsame side as objectvirtualuprightmagnified

C. How to draw a ray diagram (step-by-step)

  1. Draw the lens and the principal axis.
  2. Mark the focal points F and F' at distance f from the optical centre.
  3. Draw the object (arrow).
  4. Draw two principal rays from the top of the object:
    • parallel ray → through F'
    • central ray → straight (or use the focal ray instead of one of these)
  5. Where the rays meet is the top of the image:
    • if the real rays meet → real image
    • if they do not meet, extend backwards with dashed lines → virtual image

4. Common Mistakes

  • Forgetting to mark F and f before drawing rays.
  • Using dashed lines for real rays (dashed lines are for extensions only).
  • Mixing up “real/virtual”:
    • real image can be formed on a screen
    • virtual image cannot
  • Drawing the focal ray rule incorrectly (it must pass through F before the lens, then emerge parallel).

5. Exam Tips

  • Use a ruler and keep diagrams neat and to scale.
  • Two rays are enough, but drawing a third ray can help you check.
  • When asked for image characteristics, write four words in order:
    • real/virtual
    • upright/inverted
    • magnified/same/diminished
    • position (relative to f and 2f)

6. Worked Examples

Modelled example 1

Identify image characteristics

Core

Problem

An object is placed between f and 2f of a converging lens. State the image position, nature, orientation and relative size.
Study the worked solution

  1. Locate the ray intersection

    Method

    Draw a parallel ray through the far focus and a central ray straight through the optical centre.

    Reason

    For f < u < 2f, these refracted rays meet beyond 2f on the far side.

    Working

    Actual rays intersect beyond 2f.

  2. Read the characteristics

    Method

    Classify the image as real, inverted and magnified.

    Reason

    Actual ray intersection makes it real; the intersection is below the axis and the image arrow is taller.

    Working

    Beyond 2f; real; inverted; magnified.

Guided practice 2

Object within focal length

About 5 min

Problem

An object is placed within the focal length (u < f). Can the image be formed on a screen? Describe its position, orientation and size.

Decide from actual rays or backward extensions

Screen outcome

Hints

Hint 1: trace real rays first
The refracted rays diverge after leaving the lens.
Hint 2: extend backwards
Use dashed backward extensions to locate the apparent intersection.
View solution step by step

  1. Locate the apparent image

    Method

    Extend the diverging refracted rays backwards with dashed lines.

    Reason

    The actual rays do not meet, but their extensions meet on the object’s side.

    Working

    Backward extensions intersect on the near side.

  2. Classify the image

    Method

    State virtual, upright and magnified, and not projectable on a screen.

    Reason

    Only apparent rays intersect; no light actually converges at the image position.

    Working

    Same side; virtual; upright; magnified.

Common misconception 3

Object at 2f

Find and correct the mistake

Learner response

An object is at 2f. A student says every real image made by a converging lens is diminished. Diagnose the claim and state the complete image characteristics.

Use the symmetric 2f construction

Image size

View solution step by step

  1. Use the 2f ray geometry

    Method

    Locate the image at 2f on the far side.

    Reason

    The principal-ray construction is symmetric in object and image distances for this case.

    Working

    u = 2f → v = 2f.

  2. State the characteristics

    Method

    Classify the image as real, inverted and the same size.

    Reason

    The rays actually intersect and the image height equals the object height.

    Working

    At 2f; real; inverted; same size.

Examiner practice 4

Working backwards from the image position

3 marks

Examination question

A converging lens forms a real image between f and 2f on the far side. Identify the object-position range and state the image orientation and relative size. [3 marks]

Reverse the governed image case

View solution step by step

  1. Infer the object range

    1 mark

    Method

    Place the object beyond 2f.

    Reason

    That is the ray-diagram case producing a far-side image between f and 2f.

    Working

    u > 2f

  2. State remaining characteristics

    2 marks

    Method

    State that the image is inverted and diminished.

    Reason

    Actual rays meet below the axis with a smaller image height in this case.

    Working

    Real; inverted; diminished.

Challenge 5

Working backwards from the image nature

Minimal support

Reverse-classification transfer

A converging lens forms an image that is virtual, upright and magnified. Infer whether the object is at u < f, u = f or u > f, and explain using ray behaviour.

Work from image nature back to ray geometry

Hints

Hint 1: use virtual
Actual rays leaving the lens must diverge rather than meet on the far side.
Hint 2: locate the object
For a converging lens, that happens when the object is inside the focal length.
View solution step by step

  1. Infer the position

    Method

    Place the object within the focal length.

    Reason

    Only the u < f case makes the refracted rays diverge and their backward extensions meet on the object side.

    Working

    u < f

  2. Connect to the observed nature

    Method

    Use the backward-extension intersection to justify virtual, upright and magnified.

    Reason

    No actual rays meet at the apparent image position.

    Working

    Same-side apparent intersection → virtual image.

7. Mind Stretchers

Mind stretcher 1: Why “no image” at u = f?Extension

Why can’t you form a sharp image on a screen when the object is at the focal length (u = f)?

Show Answer

The rays leaving the lens are parallel, so they do not converge to a point on the far side. A screen needs converging rays to form a real image.

Mind stretcher 2: Predicting image changeExtension

You move the object from “beyond 2f” to “between f and 2f”. What happens to the image size and position?

Show Answer

The image becomes larger (magnified) and moves further away (beyond 2f). It remains real and inverted.

8. Practice and next step

Construct images for objects beyond 2F, between F and 2F, and inside F, then classify each image. Use lens applications as transfer practice or take the Light check.

Continue with the next resource in this course.

Course and syllabus information
Course
SEC G3 Physics
Edition
SEC G3 Physics 2027