PhysicsICSE Class 10 · Lenses

Ray Diagrams for Convex and Concave Lenses: Principal Rays and Images for Every Position (ICSE Class 10)

Q: Which rays should I use in a lens ray diagram?

Any two of: a ray parallel to the axis (refracted through, or away from, a focus), a ray through the optical centre (undeviated), and a ray towards a focus (emerging parallel).

Q: Can a convex lens form a virtual image?

Yes. When the object is between the focus and the lens, the rays diverge after refraction, and their backward extensions meet on the object's side, giving a virtual, erect, magnified image.

Q: Why can a concave lens never form a real image of a real object?

It always makes the rays diverge, so they never meet after the lens. Only their backward extensions meet, on the object's side, giving a virtual image.

Updated 15 October 2026 · Fact-checked

Two of three principal rays locate any lens image: a ray parallel to the axis passes through (convex) or seems to come from (concave) the focus; a ray through the optical centre goes straight on; a ray aimed at the first focus emerges parallel. A concave lens always gives a virtual, erect, diminished image.

The parallel ray bends through F2 and the central ray goes straight; they cross below the axis, giving a real, inverted, smaller image.

Illustration drawn for QuestionBuddy.

Understand Ray Diagrams for Convex and Concave Lenses

Lenses as prisms. A convex lens behaves like a set of prisms with their bases towards the centre, so it bends rays towards the axis (converging). A concave lens is like prisms with bases outward, so it bends rays away from the axis (diverging).

Terms. Optical centre O; principal axis; principal foci $F_{1}$ (object side) and $F_{2}$ (other side); focal length $f$ = OF; $2 F$ points at twice the focal length; focal plane through F perpendicular to the axis.

The principal (construction) rays.
1. A ray parallel to the principal axis: after a convex lens it passes **through $F_{2}$ ; after a concave lens it diverges as if coming from $F_{1}$ ** (on the object side).
2. A ray through the optical centre O passes undeviated.
3. A ray **through $F_{1}$ (convex) or directed towards $F_{2}$ (concave) emerges parallel** to the principal axis.
Any two of these locate the image of the top of the object.

Drawing rules examiners check. Same scale on both sides (equal OF and F–2F spacings); object as an upright arrow on the axis at the stated position; real rays solid with arrows; virtual extensions dashed without arrows; image drawn where the rays (or their extensions) meet.

Convex lens: images for all positions.

Object	Image position	Nature and size
At infinity	At $F_{2}$	Real, inverted, highly diminished (point)
Beyond $2 F_{1}$	Between $F_{2}$ and $2 F_{2}$	Real, inverted, diminished
At $2 F_{1}$	At $2 F_{2}$	Real, inverted, same size
Between $F_{1}$ and $2 F_{1}$	Beyond $2 F_{2}$	Real, inverted, magnified
At $F_{1}$	At infinity	Real, inverted, highly magnified
Between $F_{1}$ and O	Same side as object, behind it	Virtual, erect, magnified

As the object moves from far away towards $F_{1}$ , the real image moves away from the lens and grows.

Concave lens. For any position of a real object, the image is virtual, erect and diminished, between O and $F_{1}$ on the object side. For an object at infinity, it is at $F_{1}$ and highly diminished.

Magnifying glass (simple microscope). A convex lens of short focal length, with the object placed **between $F_{1}$ and O**, gives a virtual, erect, magnified image on the same side. A concave lens cannot be used because its image is always diminished. (For ICSE, locate the image and judge magnification from the ray diagram only.)

Changing the lens, not the object. With the object fixed, replacing a convex lens by one of greater focal length moves the object relatively closer to F (in units of $f$ ), so the real image forms farther away and larger.

Half the lens covered. Every part of a lens forms a complete image, so covering half of it gives the whole image, but dimmer.

Ray Diagrams for Convex and Concave Lenses: formulas and key facts

Lens formula (to check a diagram): $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$; Sign convention as in the lens-formula topic.
Magnification: $m = \frac{v}{u}$; |m| > 1 magnified; negative m real and inverted.

How to solve Ray Diagrams for Convex and Concave Lenses questions

Draw to scale, use two principal rays from the top of the object, and read off the image.

1Draw the principal axis and the lens; mark $F_{1}$ , $2 F_{1}$ , $F_{2}$ , $2 F_{2}$ at equal spacings.
2Place the object arrow at the stated position.
3From its top draw a ray parallel to the axis and refract it through $F_{2}$ (convex) or away as if from $F_{1}$ (concave).
4Draw a second ray through O, undeviated.
5Where the refracted rays meet is the image (real); if they diverge, extend them backwards with dashes to meet (virtual).
6State position, nature (real/virtual, inverted/erect) and size (magnified, diminished, same).

Ray Diagrams for Convex and Concave Lenses in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

A slide projector

Suppose a projector lens has a focal length of 10 cm and the slide is placed 10.5 cm in front of it.

Where is the image formed, how large is it compared with the slide, and why are slides loaded upside down?

Try it first, then show the solutionSolution

Object just beyond $F_{1}$ : image far beyond $2 F_{2}$ , real, inverted, highly magnified. Check: $\frac{1}{v} = \frac{1}{10} - \frac{1}{10.5}$ , $v = 210$ cm, $m = - 20$ .
The image is inverted, so the slide is put in upside down to give an upright picture.

Answer: On a screen 2.1 m away, 20 times larger and inverted; hence slides go in upside down.

Memory hook: Just beyond F: far, big and upside down.

Burning a spot with sunlight

Imagine using a convex lens outdoors to focus sunlight onto a dry leaf.

Where must the leaf be held, and why does it heat up?

Try it first, then show the solutionSolution

The Sun is effectively at infinity, so its image forms at the focus $F_{2}$ .
The image is a tiny bright spot where the Sun's energy is concentrated.

Answer: At the focus, where the sunlight converges to a point.

Memory hook: Infinity in, focus out.

Tricks to remember Ray Diagrams for Convex and Concave Lenses

Short memory aids. Say each one aloud once, then use it on a question the same day.

Parallel–Focus, Centre–Straight
'P goes to F, C goes straight': a Parallel ray goes through the Focus; a Centre ray goes straight.
Use it when: Choosing two rays.
Closer object, farther and bigger image
For a convex lens, as the object walks in towards F, the image walks out and grows.
Use it when: Trend questions.
Concave: VED
Concave lens image is always Virtual, Erect, Diminished.
Use it when: Any concave lens case.
Real is solid, virtual is dashed
Arrows only on rays that light really travels along.
Use it when: Avoiding diagram penalties.

Ray Diagrams for Convex and Concave Lenses: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Object between F and 2F · 1 mark · MCQBoard level

An object is placed between $F_{1}$ and $2 F_{1}$ of a convex lens. The image is:
(a) between $F_{2}$ and $2 F_{2}$ , diminished
(b) at $2 F_{2}$ , same size
(c) beyond $2 F_{2}$ , real, inverted, magnified
(d) on the same side, virtual, magnified

Try it first, then show the solutionSolution

The refracted rays cross beyond $2 F_{2}$ , giving a real, inverted, enlarged image.

Answer: (c) beyond $2 F_{2}$ , real, inverted, magnified

Example 2: Describing the 2F diagram · 3 marks · Short answerBoard level

Describe how to draw the ray diagram for an object at $2 F_{1}$ of a convex lens, and state the position and nature of the image.

Try it first, then show the solutionSolution

Mark $F$ and $2 F$ at equal spacings on both sides; draw the object arrow at $2 F_{1}$ . (1)
From its top, draw a ray parallel to the axis, refracted through $F_{2}$ ; and a ray through O, undeviated. Both solid with arrows. (1)
They meet at $2 F_{2}$ below the axis: the image is at $2 F_{2}$ , real, inverted and the same size. (1)

Answer: Image at $2 F_{2}$ : real, inverted, same size.

Example 3: Concave lens image, drawn and checked · 3 marks · Short answerHarder board level

A diverging lens with $f = 15$ cm has a pin standing 30 cm away (at $2 F_{1}$ ). (a) Which two rays would you draw, and how do they behave? (b) Describe the image. (c) Check its position with the lens formula.

Try it first, then show the solutionSolution

(a) A ray parallel to the axis diverges as if from $F_{1}$ (extend backwards, dashed); a ray through O goes straight. (1)
(b) The dashed extension and the straight ray meet between O and $F_{1}$ : virtual, erect, diminished. (1)
(c) $\frac{1}{v} = - \frac{1}{15} - \frac{1}{30} = - \frac{3}{30}$ , $v = - 10$ cm; $m = \frac{1}{3}$ . (1)

Answer: Virtual, erect, one-third size, 10 cm from the lens on the object's side.

Example 4: Changing only the lens · 3 marks · Short answerHarder board level

On an optical bench a candle stays fixed 40 cm from the lens holder, which first holds a convex lens with $f = 20$ cm. (a) Describe the image. (b) Only the lens is replaced by one of focal length 25 cm. Using the ray-diagram idea, predict how the image changes, then check with the lens formula.

Try it first, then show the solutionSolution

(a) Object at $2 F_{1}$ : image at $2 F_{2}$ (40 cm), real, inverted, same size. (1)
(b) Now $2 F = 50$ cm, so the object (40 cm) lies between $F_{1}$ and $2 F_{1}$ : image beyond $2 F_{2}$ , magnified. (1)
Check: $\frac{1}{v} = \frac{1}{25} - \frac{1}{40} = \frac{3}{200}$ , $v \approx 66.7$ cm; $m \approx - 1.67$ . (1)

Answer: (a) Same size at 40 cm (b) Image moves to about 66.7 cm and becomes magnified

Example 5: Walking the object towards F · 4 marks · Long answerHOTS / competency

A convex lens has a focal length of 10 cm. An object is moved from 30 cm to 20 cm, then 15 cm, then 12 cm from the lens. Find the image distance and magnification each time and describe the trend.

Try it first, then show the solutionSolution

30 cm: $v = 15$ cm, $m = - 0.5$ . 20 cm: $v = 20$ cm, $m = - 1$ . (2)
15 cm: $v = 30$ cm, $m = - 2$ . 12 cm: $v = 60$ cm, $m = - 5$ . (1)
As the object approaches $F_{1}$ , the real image moves away from the lens and grows rapidly; at $F_{1}$ it would go to infinity. (1)

Answer: v: 15, 20, 30, 60 cm; m: −0.5, −1, −2, −5; image recedes and enlarges.

Example 6: Case study: choosing a reading glass · 4 marks · Case-basedHOTS / competency

A grandmother wants a lens to read small print. She has a convex lens of focal length 8 cm and a concave lens of focal length 8 cm.
(a) Which lens should she use, and where should the page be relative to the lens?
(b) Describe the ray diagram that shows the image.
(c) State the nature of the image.
(d) Why is the other lens useless for this?

Try it first, then show the solutionSolution

(a) The convex lens, with the page closer than 8 cm, between $F_{1}$ and O. (1)
(b) A ray from the top of a letter parallel to the axis refracts through $F_{2}$ ; a ray through O goes straight. They diverge; extended backwards (dashed), they meet behind the letter, on the same side. (1)
(c) Virtual, erect and magnified. (1)
(d) A concave lens always gives a diminished image (m < 1), so print looks smaller. (1)

Answer: (a) Convex, page within 8 cm (b) Rays diverge; image found by backward extension (c) Virtual, erect, magnified (d) Concave gives a diminished image.

Where students lose marks in Ray Diagrams for Convex and Concave Lenses

The slips examiners see most often, and what to write instead.

Mistake: Arrows on virtual rays and dashed real rays
Real rays are solid with arrows; virtual extensions are dashed without arrows.
Wrong working
Dotted refracted rays, or arrowheads on dashed extensions.
Right working
Solid lines with arrows for light; dashes only for backward extensions.
Do this: Decide 'real or virtual' before drawing each line.
Usually costs: Reported by CISCE examiners for 2025 Q4(iii).
Mistake: Unequal scale on the two sides
The foci and 2F points must be equally spaced on both sides, or the image lands in the wrong place.
Wrong working
$O F_{1} = 2$ cm but $O F_{2} = 3$ cm; object not at 2F when asked.
Right working
Equal $O F$ and $F$ – $2 F$ spacings; object exactly at the stated point.
Do this: Mark the scale points with a ruler first.
Usually costs: Also reported for 2025 Q4(iii).
Mistake: Changing the wrong quantity
If a question says only the lens is replaced, the object distance stays the same.
Wrong working
Moving the object to keep it at the new 2F.
Right working
Keep $u$ fixed; with a larger f the object now lies between F and 2F, so the image is magnified.
Do this: Underline 'only' and list what stays fixed.
Usually costs: Reported for 2025 Q4(iii)(b).
Mistake: Explaining the concave reading lens by 'divergence'
The real reason is the size of the image: a concave lens always diminishes.
Wrong working
'A concave lens diverges light, so it cannot be used.'
Right working
'A concave lens always forms a diminished image, so it cannot magnify print.'
Do this: Answer in terms of image size.
Usually costs: Reported for 2024 Q3(i).

Exam tips

In 2025 Q4(iii), with only the lens replaced by one of greater focal length, the expected answer was that the image becomes magnified.
In 2024 Q3(i), the expected object position for a reading glass was 'within the focal length, between F and O'.
Two rays are enough; a third ray is a useful check but must be correct.
Always write the nature of the image beside the diagram: position, real/virtual, erect/inverted, size.

Practice questions on Ray Diagrams for Convex and Concave Lenses

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
A ray of light passing through the optical centre of a thin lens:
(a) passes through the focus
(b) emerges parallel to the axis
(c) goes straight on without deviation
(d) is reflected back
Hint
At the centre, the two faces are nearly parallel.
Answer
(c) goes straight on without deviation
Q2 · 3 marks · Short answerBoard level
State what happens after refraction through a convex lens to (a) a ray parallel to the principal axis, (b) a ray passing through the first focus, (c) a ray through the optical centre.
Hint
Three principal rays.
Answer
(a) It passes through the second focus $F_{2}$ . (b) It emerges parallel to the principal axis. (c) It goes straight on, undeviated.
Q3 · 2 marks · Short answerHarder board level
Where must an object be placed in front of a convex lens to obtain a real, inverted image of the same size? Where is the image?
Hint
m = −1.
Answer
At $2 F_{1}$ ; the image forms at $2 F_{2}$ .
Q4 · 2 marks · Short answerHarder board level
Describe the ray diagram and the image formed by a concave lens for an object at infinity.
Hint
Rays from infinity arrive parallel.
Answer
Parallel rays diverge after the lens; extended backwards (dashed) they meet at $F_{1}$ . The image is at $F_{1}$ , virtual, erect and highly diminished.
Q5 · 2 marks · Short answerHarder board level
Explain how a convex lens can be thought of as a set of prisms, and use this to explain why it converges light.
Hint
Which way does a prism bend light?
Answer
A convex lens is like prisms stacked with their bases towards the centre (a block in the middle). Each prism bends light towards its base, i.e. towards the axis, so the rays converge.
Q6 · 2 marks · Short answerHarder board level
Compare the images formed by a convex lens for an object (a) beyond $2 F_{1}$ , (b) at $F_{1}$ , giving position and nature.
Hint
Use the table of positions.
Answer
(a) Between $F_{2}$ and $2 F_{2}$ : real, inverted, diminished. (b) At infinity: real, inverted, highly magnified.
Q7 · 2 marks · Short answerHOTS / competency
The lower half of a convex lens is covered with black paper. Does the image of an object lose its lower half? Explain, using rays.
Hint
Rays from every point of the object pass through every part of the lens.
Answer
No. Rays from every point of the object still pass through the uncovered upper half and meet at the same image points, so the whole image forms, but it is dimmer because less light gets through.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Image for an object at infinity, convex lens?Show answer
At $F_{2}$ , real, inverted, point-sized.
2.Image for an object between F and O of a convex lens?Show answer
Virtual, erect, magnified, on the same side.
3.Nature of every image of a real object in a concave lens?Show answer
Virtual, erect, diminished.
4.What happens to a ray through the optical centre?Show answer
It passes undeviated.
5.Effect of covering half a lens on the image?Show answer
The full image forms but is dimmer.

Ray Diagrams for Convex and Concave Lenses: frequently asked questions

Which rays should I use in a lens ray diagram?

Any two of: a ray parallel to the axis (refracted through, or away from, a focus), a ray through the optical centre (undeviated), and a ray towards a focus (emerging parallel).

Can a convex lens form a virtual image?

Yes. When the object is between the focus and the lens, the rays diverge after refraction, and their backward extensions meet on the object's side, giving a virtual, erect, magnified image.

Why can a concave lens never form a real image of a real object?

It always makes the rays diverge, so they never meet after the lens. Only their backward extensions meet, on the object's side, giving a virtual image.