Light, Reflection and Refraction

A mirror can show an upright face or an upside-down one. A lens can enlarge a word or make a small inverted picture on a screen. The useful question is not simply “Which device is this?” It is: where do rays from one point go after meeting it? Follow that question and the image rules become consequences you can explain.

This guide follows Class 10 NCERT Science, Light – Reflection and Refraction, Chapter 9 in the 2026–27 reprint. The current CBSE curriculum includes spherical mirrors, refraction, spherical lenses, magnification and lens power; derivations of the mirror and lens formulae are not required. The guide also marks a small lens-combination extension. Check your own board’s prescribed text before treating this as its syllabus. NCERT chapter; CBSE Science curriculum.

What is Light?

Light is electromagnetic radiation; visible light is the part our eyes can detect. A lamp emits light. An ordinary book is visible because light falling on it is scattered towards our eyes. A transparent window transmits much of the light that reaches it. Reflection, transmission and absorption can occur together: a window can show a faint reflection while still letting you see through it.

For the mirrors and lenses studied here, we represent light by rays: lines showing its direction of travel. In a uniform transparent medium, these rays are straight. A ray is a model, not a thin material thread. A drawing usually shows only a few rays chosen from the many leaving an object point.

The speed of light in vacuum is approximately 3 × 10⁸ m s⁻¹. Light travels more slowly through ordinary transparent materials such as water and glass. Ray optics does not explain every optical effect. Bending and spreading around sufficiently small openings is diffraction; separation into colours is dispersion. They are different phenomena. Wave and quantum descriptions extend the ray model, but are not needed to solve the image problems in this chapter.

A black notebook absorbs much light. Why can you still see it?

It does not absorb all the light reaching it. Some reflected or scattered light reaches your eyes, and contrast with its surroundings helps reveal its outline. “Black” does not mean a perfect absorber under every condition.

Reflection of Light

Reflection sends light back into the medium from which it arrived. At the point where a ray meets a surface, draw a line perpendicular to the surface: the normal. Measure the angle of incidence i and angle of reflection r from this normal, not from the surface.

• i = r. An incident ray 30° from the normal leaves 30° from the normal.
• The incident ray, normal and reflected ray lie in one plane.

These rules also apply locally on a rough or curved surface. A rough surface has normals pointing in different directions, so a parallel beam is scattered into many directions. It has not stopped obeying reflection.

Plane mirrors and the meaning of virtual

Imagine rays leaving the top of a pencil, reflecting off a plane mirror and entering your eyes. Extend the reflected rays backwards on paper. Their extensions meet behind the mirror, even though the actual reflected light stays in front. This apparent source is a virtual image. For a plane mirror it is upright, the same height as the object, and as far behind the mirror as the object is in front.

The familiar lateral inversion is the change in handedness seen when comparing an object with its mirror image. A mirror does not physically move your right hand to the left; it reverses the direction perpendicular to its surface. Writing therefore appears reversed when you face the mirror.

A real image forms where actual outgoing rays from an object point converge. Put a suitable screen there and the image can appear on it. A virtual image cannot be caught directly on a screen at its apparent position. Both kinds can be seen: your eye can receive either converging/diverging bundles and form its own retinal image. Real/virtual describes ray convergence; upright/inverted describes orientation. In the single-device, real-object cases below these properties follow familiar pairings, but they are not interchangeable definitions.

A ray makes 20° with a plane mirror’s surface. What is its angle of reflection?

The normal is 90° to the surface. The incidence angle is 90° − 20° = 70°, so the reflection angle is also 70°. The reflected ray makes 20° with the surface.

Spherical Mirrors

A spherical mirror’s reflecting surface is part of a sphere. A concave mirror faces into the hollow; a convex mirror bulges towards the object. The inward and outward sides of a shiny spoon give a rough everyday comparison, although a spoon is not an ideal spherical mirror.

• Pole P: the midpoint of the reflecting surface.
• Centre of curvature C: the centre of the sphere of which the mirror is a part, not a point on its surface.
• Principal axis: the line through P and C.
• Radius of curvature R: the distance PC, with the appropriate sign when calculating.
• Principal focus F: near-axis rays parallel to the principal axis converge there after concave reflection, or appear to diverge from there after convex reflection.
• Focal length f: the signed distance PF. For the small-aperture spherical-mirror model, R = 2f.
• Aperture: the effective diameter of the reflecting part.

The small-aperture condition matters. A wide spherical mirror does not bring every parallel ray to exactly one point. In this chapter, use near-axis rays and the idealised focus; do not generalise the model to arbitrary large rays. OpenStax’s mirror discussion illustrates this limitation, using a different sign convention from the NCERT convention used below.

Construct an image with two rays

Start both rays at the same object point, usually the top of an upright arrow. A ray parallel to the axis reflects through F for a concave mirror, or appears to come from F for a convex one. A ray through C, or directed towards C behind a convex mirror, meets the surface normally and retraces its path. A ray through, or directed towards, F reflects parallel to the axis. A ray striking P reflects with equal angles to the principal axis.

Choose two of these rules. Where the actual reflected rays meet is a real image point. If the reflected rays spread apart, extend them backwards with dashed lines to locate a virtual image point. Solid arrows show light travel; dashed extensions do not.

The concave-mirror journey

Think of moving a real object from far away towards the mirror. Distances in this list are positions, before signs are assigned.

• Very distant object: its near-parallel rays form a small real inverted image near F. “At infinity” is an ideal limiting case.
• Beyond C: image between C and F, real, inverted and smaller.
• At C: image at C, real, inverted and the same size.
• Between C and F: image beyond C, real, inverted and larger.
• At F: rays from each object point leave parallel; there is no finite screen position giving a sharp image. This is described as an image at infinity.
• Between F and P: image behind the mirror, virtual, upright and larger.

As the object approaches F from outside, the real image moves farther away and becomes larger. Once the object is inside F, the rays no longer meet in front of the mirror. Their backward extensions explain the enlarged upright face in a concave shaving mirror.

A convex mirror, with an ordinary real object in front, forms a virtual, upright, smaller image between P and F behind it. As the object moves very far away, the image approaches F. Its wider field of view helps a driver or shopkeeper see more of the surroundings, at the cost of smaller images.

A concave mirror makes your face upright and larger. Where is your face?

Between the pole and focus. “Concave means inverted” is incomplete: orientation depends on object position. Move the object outside the focal length and the ideal mirror forms a real inverted image.

Mirror formula: let the signs describe the geometry

Use the NCERT Cartesian convention consistently. Place the real object to the left, with incident light travelling left to right. Measure axial distances from the pole: right is positive and left is negative. Heights above the axis are positive; below it negative. Therefore u is negative, a concave mirror has f negative, and a convex mirror has f positive.

Mirror formula: 1/v + 1/u = 1/f.
Mirror magnification: m = h′/h = −v/u.

Here u is object distance, v image distance, h object height and h′ image height. Use one distance unit throughout the formula. Magnification is a ratio with no unit. Its sign indicates orientation; its magnitude tells the size factor. For example, m = −2 means an inverted image twice the object’s height, not a “negative size”.

Worked check: a screen in front of a concave mirror

A 3 cm object stands 36 cm in front of a concave mirror of focal length 12 cm. Predict first: C is 24 cm in front, so the object is beyond C. The image should be real, smaller and between F and C.

Use u = −36 cm and f = −12 cm.
1/v = 1/f − 1/u = −1/12 + 1/36 = −1/18 cm⁻¹.
Thus v = −18 cm. Also m = −(−18)/(−36) = −0.5, and h′ = −0.5 × 3 = −1.5 cm.

A screen belongs 18 cm in front of the mirror. The image is inverted and half-height. Both the signs and the position agree with the prediction.

Try the convex case: f = +12 cm and u = −24 cm. Find v and m.

1/v = 1/12 − (−1/24) = 1/8 cm⁻¹. So v = +8 cm, behind the mirror. m = −8/(−24) = +1/3. The upright virtual image is one-third as tall, between P and F.

Refraction of Light

A pencil partly in water can appear displaced at the surface because light from its submerged part changes direction on its way to your eyes. The pencil need not bend. Refraction occurs as light passes between media with different propagation speeds. At oblique incidence this usually changes its direction.

Draw a normal at the boundary. When light passes into a medium of higher refractive index, the refracted ray bends towards the normal. Passing into a lower-index medium, the transmitted ray bends away from the normal. At normal incidence it continues straight, even though its speed changes. The advanced possibility of total internal reflection is outside the calculations here.

Absolute refractive index n = c/v, where c is the vacuum speed and v the speed in the medium. It is dimensionless. “Optically denser” means higher refractive index for the light considered; it does not mean greater mass per volume. Air is often approximated as n = 1 in school calculations.

For a given colour and pair of ordinary transparent media, n₁ sin i = n₂ sin r. Equivalently, sin i / sin r = n₂/n₁ = v₁/v₂ for non-zero angles. The incident ray, normal and refracted ray lie in one plane. The full sine equation also handles normal incidence without dividing 0 by 0. OpenStax’s refraction explanation connects the bending rule with the speed ratio.

Worked check: index tells you speed, not a fixed turning angle

For glass with n = 1.50, v = c/n = (3.0 × 10⁸)/1.50 = 2.0 × 10⁸ m s⁻¹. If light enters this glass from air at 30°, sin r = sin 30°/1.50 = 1/3. Thus r is about 19.5°, smaller than 30°, as the towards-normal prediction requires. A different incidence angle gives a different refraction angle.

A rectangular glass slab: direction returns, position shifts

At the first face, an oblique ray from air bends towards the normal. At the second parallel face it returns to air and bends away. With the same medium on both sides, the emerging ray is parallel to the incident ray, but shifted sideways. This lateral displacement does not mean “no refraction”: two refractions produced it. At normal incidence there is no sideways shift. Non-parallel faces, as in a prism, need a different construction.

A ray enters glass straight along the normal. A classmate says its unchanged direction proves unchanged speed. What is wrong?

Direction and speed are separate. Normal incidence gives i = r = 0°, while n = c/v still describes a lower speed in ordinary glass. Refraction need not produce a visible bend at normal incidence.

Lenses: a new route to an image

A spherical lens is a transparent object bounded by two surfaces, at least one spherical. For ordinary glass lenses in air, a convex lens is thicker in the middle and converges parallel near-axis rays; a concave lens is thinner in the middle and diverges them. This action depends on the lens material relative to its surroundings, not shape alone in every possible medium.

The optical centre O is the reference point for the thin-lens model. Its principal axis joins the centres of curvature of its spherical surfaces. A lens has a principal focus on each side, F₁ and F₂. For a convex lens, rays parallel to the axis from the left converge at F₂ on the right. For a concave lens, they emerge as though from F₁ on the left. Unlike a spherical mirror, a lens does not generally have f = R/2.

Three useful rays

• A parallel ray passes through the far focus of a convex lens, or appears to come from the near focus of a concave lens.
• A ray through the near focus of a convex lens emerges parallel. A ray directed towards the far focus of a concave lens emerges parallel.
• A ray through O continues undeviated in the thin-lens approximation.

Use two rays from the same object point. Lenses transmit the rays to the other side; mirrors reflect them back. That physical difference is why an ordinary convex lens can form its real image on the opposite side from the object.

The convex-lens journey

• Very distant object: small real inverted image near F₂.
• Beyond 2F₁: real inverted smaller image between F₂ and 2F₂.
• At 2F₁: real inverted same-size image at 2F₂.
• Between F₁ and 2F₁: real inverted enlarged image beyond 2F₂.
• At F₁: outgoing rays from each object point are parallel; no finite sharp-screen image.
• Between F₁ and O: virtual upright enlarged image on the object’s side.

A concave lens, for a real object at a finite distance, forms an upright, smaller virtual image between O and the near focus on the object’s side. With a very distant object it approaches that focus.

How can the same convex lens work as a magnifier and form an inverted image?

The object distance changes. Inside the focal length, outgoing rays diverge and their extensions locate an enlarged upright virtual image. Outside the focal length, they can converge into a real inverted image on the far side.

Lens formula, magnification and power

Keep right positive and left negative, but measure from O. For light initially travelling left to right, an ordinary real object has u negative. A convex lens has f positive; a concave lens has f negative.

Lens formula: 1/v − 1/u = 1/f.
Lens magnification: m = h′/h = v/u.

Notice the differences from the mirror formula and mirror magnification. Do not attach a memorised minus sign without checking which device is present.

Worked check: a real lens image

Use a convex lens with f = +12 cm and an object at u = −36 cm, height 3 cm. The object is beyond 2F₁, so predict a smaller real inverted image.

1/v = 1/f + 1/u = 1/12 − 1/36 = 1/18 cm⁻¹.
Therefore v = +18 cm, m = 18/(−36) = −0.5, and h′ = −1.5 cm. The image is on the far side, between F₂ and 2F₂.

Keep f = +12 cm but move the object to u = −6 cm. What changes?

1/v = 1/12 − 1/6 = −1/12 cm⁻¹, so v = −12 cm. Now m = (−12)/(−6) = +2. The image is virtual, upright and twice the height, on the object’s side. It cannot be caught directly on a screen there.

For a concave lens, f = −12 cm and u = −24 cm. Check its image.

1/v = −1/12 − 1/24 = −1/8 cm⁻¹. Therefore v = −8 cm and m = (−8)/(−24) = +1/3. The result is upright, virtual and smaller, between O and F₁.

Power uses metres

Lens power measures convergence or divergence: P = 1/f, with f in metres. Its unit is the dioptre D, equivalent to m⁻¹. A convex lens has positive power; a concave lens negative power. Shorter focal-length magnitude means greater power magnitude, not necessarily a larger image in every arrangement.

A lens of f = +25 cm has f = +0.25 m and P = +4 D. A lens of P = −2 D has f = −0.50 m = −50 cm. Dividing by 25 without converting centimetres would give the wrong power in dioptres.

Extension: thin lenses in contact. In the ideal model, their signed powers add. A +4 D lens with a −1.5 D lens gives +2.5 D, equivalent to f = +0.40 m. Do not add focal lengths or apply this simple rule to lenses separated by an arbitrary distance. OpenStax’s lens treatment gives further ray-model context.

Discover it: predict before you reveal

Use the ray cards with this guide to compare three arrangements: a convex lens with an object outside its focus, the same lens with the object inside, and a concave lens. Before opening each explanation, predict the side of the image, its orientation and whether a screen can catch it. Trace the parallel ray and the centre ray; use dashed extensions only when actual rays do not meet.

Then draw a fourth arrangement yourself: put the object at twice the focal length of a convex lens. Decide where the two rays meet and check with the lens formula. Your goal is to make the diagram and calculation tell the same story.

Check your fourth arrangement

For f = +10 cm and u = −20 cm, 1/v = 1/10 − 1/20 = 1/20 cm⁻¹. Thus v = +20 cm and m = −1. The real image is inverted and the same size, at 2F₂.

For an ordinary-light observation, stand a pencil in a clear plastic cup of water on a stable surface and look from different sides. Compare its apparent direction above and below the water. Record what changes when your viewing angle changes, and whether the actual pencil is bent when removed. The curved cup wall also refracts light, so this observation is not a clean measurement of water’s refractive index.

Use ordinary room light only. Never look at the Sun through a lens, into a mirror reflecting sunlight, or at a laser. Do not focus sunlight or use flames for these activities. The ray cards provide the image experiment without bright-light or heating hazards.

Why it still matters

A camera must direct rays from each scene point towards the appropriate sensor point. A mirror for viewing traffic trades a smaller image for more of the scene. A magnifier puts the object inside a focal length. These are different design goals, so “more magnification” is not automatically “better optics”.

A useful diagnostic is covering half a convex lens in an ideal image-forming arrangement. You generally still obtain the whole image, but with less light: many parts of the lens receive rays from every object point. The top half does not exclusively make the top half of the image. Real systems may also show vignetting and other limits; the basic prediction belongs to the unobstructed paraxial model.

Continue to the human eye and the colourful world to see why the position of the retina changes the problem. The eye needs a sharp image on a fixed receiving surface, which makes focus adjustment essential.

Carry these checks into a new problem

• Draw the device, object and axis; predict the image before calculating.
• Measure incidence and refraction angles from the normal.
• Assign Cartesian signs from position, not from whether a distance “feels real”.
• Keep mirror and lens formulae distinct; use one distance unit, and metres for power in dioptres.
• Read real/virtual from actual rays versus extensions; read orientation and size from magnification.
• State the model: near-axis spherical mirrors and thin lenses, with real objects and ordinary transparent media unless specified otherwise.

Sources

NCERT Class 10 Science, Chapter 9, 2026–27 reprint supplies the chapter coverage and Cartesian convention. CBSE Science 2026–27 supplies the current stated curriculum. The explanations, numerical scenarios and discovery prompts here are original.

Additional physics checks: OpenStax College Physics 2e on mirrors, refraction and lenses. OpenStax uses a different distance-sign convention in its worked examples; do not mix it with the NCERT convention used in this guide.