Convex and Concave Lens Ray Diagrams, All Cases

How to use this simulation

1. Choose a convex or a concave lens. The focal points F and the points 2F are marked on both sides.
2. Drag the blue object arrow along the axis, or use the object-distance slider.
3. Use the "Place the object" buttons to jump straight to each textbook case: very far, beyond 2F, at 2F, between F and 2F, at F, and between F and the lens.
4. Orange lines are incident rays and red lines refracted rays. When the refracted rays truly meet, the green image is solid (real); when only their dashed backward extensions meet, the image is dashed (virtual).
5. Read u, v, f, magnification, power and the nature of the image in the readings panel, then check them against the solved problems below.

Glasses, cameras and a magnifying glass: lenses are everywhere

Hold a magnifying glass in sunlight and focus the light onto a piece of paper, and the paper starts to smoke. Hold the same glass close to your eye over a line of ants, and the ants look huge. Same piece of glass, two completely different jobs. The difference is only how far the object is from the lens, and this whole page is about that one idea.

Spectacles, a phone camera, the school microscope, a cinema projector and the lens inside your own eye all obey the same small set of rules. Once you know them, three straight lines drawn with a ruler tell you where an image forms, whether it is upright or upside down, and whether it is bigger or smaller.

Ray diagrams often feel like something to memorise. They are not. Drag the object in the simulation a little at a time and you will see the image race away, flip over, vanish to infinity, and then reappear upright behind the object. By the end of this page you will know exactly why each of those things happens.

From zero: what a lens is and why it bends light

When light passes at an angle from one medium into another, for example from air into glass, it changes direction. That is refraction. Light travels more slowly in glass, so it bends towards the normal as it enters and away from the normal as it leaves.

A lens is a piece of glass or plastic with at least one curved (spherical) surface. Because the surface is curved, light hitting different parts of the lens bends by different amounts: a lot near the edges and hardly at all near the middle. That graded bending is what gathers parallel light to a point, or spreads it out.

There are two main kinds. A convex lens is thicker in the middle than at the edges. It brings parallel rays together at one point, so it is also called a converging lens. A concave lens is thinner in the middle than at the edges. It spreads parallel rays apart so they seem to come from a point in front of the lens, so it is called a diverging lens.

A quick memory trick: a convex lens bulges outwards and pulls rays in; a concave lens "caves in" and pushes rays out.

Key words you need

Before drawing anything, let us pin down the vocabulary. Definition questions in exams come straight from this list, and every symbol in the simulation is one of these.

The three golden rules for drawing rays

Countless rays leave the tip of an object, but to find the image you only need two whose paths you already know. The simulation draws all three so you can see that they meet at the same point; in an exam any two are enough.

Convex lens ray diagram: all six cases

This is the table that turns up in almost every exam. Each row also has an example worked out for the simulation's default lens (f = 10 cm) in the Cartesian sign convention. Press the "Place the object" buttons to check each row with your own eyes.

Concave lens ray diagram: always the same answer

A concave lens is simple. An object at infinity gives a point-sized image at the focus. An object anywhere between infinity and the lens gives an image between the focus and the lens, on the same side as the object. Every time the image is virtual, upright and smaller than the object.

Choose the concave lens and drag the object from far away right up to the lens. The dashed green image never crosses F and never flips. It grows a little as the object approaches but never reaches the size of the object. That wide, shrunken view is exactly what a door peephole gives you.

The lens formula: 1/v − 1/u = 1/f

Ray diagrams tell you where an image is; the lens formula lets you calculate it. In the Cartesian sign convention (used by NCERT and most international syllabuses), distances are measured from the optical centre: positive in the direction light travels, negative against it. A real object on the left therefore has a negative u, a convex lens has a positive f, and a concave lens a negative f.

Things to try in the simulation

Reading about lenses sticks for a week; doing it sticks for years. Try each of these in turn, and predict what will happen before you move anything.

• Put the object at 20 cm (2F). The readings show v = 20 cm and m = -1: an image exactly the same size as the object, just upside down.
• Drag the object slowly towards F. The image races to the right and grows; exactly at F the refracted rays leave parallel and the image is at infinity.
• Move just inside F. The image suddenly appears behind the object, upright and dashed. That is a magnifying glass.
• Increase the focal length: at the same object distance the image moves farther away. A fatter, more curved lens has a shorter focal length and more power.
• With the concave lens, put the object anywhere. The nature line never changes: virtual, erect, diminished.
• Switch on light pulses and slow the speed to 0.25×. Light travels from the object to the lens and then onwards. It never travels along the dashed lines; those only show where the eye thinks the light came from.

Solved problems (Cartesian convention)

Every number below is calculated from the formula, and the first problem is the simulation’s default setting. After each one, set the same values in the simulation and compare.

Convex lens vs concave lens

For every "state the differences" question, here is the whole comparison at a glance:

Common mistakes

Examiners see these again and again. Check your own answers for each one.

• Forgetting that u is negative in the Cartesian convention and getting v with the wrong sign.
• Taking the focal length of a concave lens as positive. Both f and P are negative for a concave lens.
• Using f in centimetres in P = 1/f. For dioptres, f must be in metres, or use P = 100/f with f in cm.
• Drawing rays without arrowheads, or drawing virtual extensions as solid lines. Virtual parts are always dashed.
• Saying the image is "at F" when the object is at F. The refracted rays come out parallel, so the image is at infinity.
• Calling a real image erect. A single lens always forms real images inverted.

Lenses in real life

The eye: the eye lens is convex and forms a real, inverted image on the retina, which the brain reads the right way up. The ciliary muscles change the lens thickness to change its focal length; that is accommodation.

Spectacles: with myopia (short-sightedness), distant objects focus in front of the retina, so a concave lens with negative power is prescribed. With hypermetropia (long-sightedness), near objects focus behind the retina, so a convex lens with positive power is needed. A prescription of −1.5 or +2.0 is the lens power in dioptres.

Cameras and phones: the scene is far away (beyond 2F), so a small, real, inverted image forms on the sensor. Focusing moves the lens slightly so that the image falls exactly on the sensor.

Magnifiers and microscopes: an object inside F gives an upright, magnified virtual image. A compound microscope uses two convex lenses one after the other.

Projectors: a small slide placed between F and 2F throws a large real image onto a distant screen.

Exam corner

Lenses appear every year in Grade 10 physics (the "Light: reflection and refraction" chapter) and again in Grade 12 ray optics, as well as in JEE and NEET. The questions follow a handful of patterns:

• Definitions: principal focus, focal length, optical centre, power of a lens and its SI unit.
• Ray diagrams: draw the image for an object at a given position, usually between F and 2F or inside F, and state its nature.
• Numericals: given u and f, find v, m and the image height, with correct signs (as in Problems 1–5 and 8).
• Power: find P from f, or combine two thin lenses in contact (Problem 6).
• Applications: which lens corrects myopia or hypermetropia, and why.

Quick revision

If you only read one section the night before the exam, read this one.

• A convex lens converges light; a concave lens diverges it.
• Three rays: parallel → through F; through O → straight on; through F → parallel.
• Lens formula 1/v − 1/u = 1/f (Cartesian); magnification m = v/u = h′/h.
• P = 1/f with f in metres, unit dioptre; positive for convex, negative for concave.
• Convex lens: object outside F → real and inverted; inside F → virtual, erect, magnified.
• Object at 2F → same-size image at 2F; object at F → image at infinity.
• Concave lens → image always virtual, erect, diminished, between F and the lens.
• The simulation's default lens (f = 10 cm) has a power of +10 D.

Frequently asked questions