🟢 Optics · Class 8–10 · Boards + IGCSE + Olympiad

Stand in front of a mirror. Walk back.

Why does your twin walk too? Light did not copy you — it only bounced. Move the ray below; wonder first, then the why.

One law
∠i = ∠r
One formula
1/v + 1/u = 1/f
One question
Where is the image?

Move the light — then ask why

Predict ∠r, lock it, then dial ∠i and watch the bounce. Plane / concave / convex · formula for curved · ∠i–∠r graph. 🟢 real reflection engine

Mirror Lab

∠i35°
∠r35°
Image v
m+1
Predict first: if ∠i is set, what is ∠r? (from the normal)

Guess, then change ∠i — the bounce waits until you commit.

Mirror
∠i = ∠r = 35° · plane · m = +1

Set the mirror and ∠i — the reflected ray must match ∠r = ∠i from the normal.

Mirror Challenge — hit the target

Aim the incident ray. The bounce obeys ∠i = ∠r. Can you hit the amber target in 3 attempts?

3-move bounce
Attempts left: 3

Drag the aim, then fire. Physics decides the bounce — not hope.

Impossible mirrors — what is wrong?

Each diagram breaks one law. Tap the broken idea. Expert thinking starts when something looks almost right.

What is impossible?

On a smooth mirror ∠i must equal ∠r from the normal. 30° in and 50° out cannot happen.

What is impossible?

Plane-mirror images of real objects are virtual — rays diverge. A screen behind the glass stays dark.

What is impossible?

For a real object, a convex (diverging) mirror only makes a diminished upright virtual image — never a real inverted one on a card.

Always · Sometimes · Never

Thinking beats memorising. Sort the universe of mirrors into three boxes.

Always true

  • ∠i = ∠r (from the normal) on each bounce
  • Incident ray, reflected ray and normal are coplanar
  • A mirror redirects light — it does not invent new photons

Sometimes true

  • Image is real (needs converging rays — usually concave)
  • Image is magnified (concave, object inside f)
  • You can catch the image on a screen

Never true

  • Plane mirror making a real image of a real object
  • Convex (usual) making an enlarged real image
  • Measuring ∠i from the glass and still calling it “incidence”

Ray Builder — draw the bounce

Incident ray and normal are fixed. Drag your reflected aim. Grade when you think ∠r matches the law.

You draw ∠r
Truth locked until Check

Set the bounce yourself — the engine grades honesty, not hope.

Design your own mirror

Pick a job. Dial kind, |u| and |f|. The formula tells you if you built the right tool.

Goal: virtual enlarged face
Not yet

For a shaving mirror: concave, object inside the focus → virtual, upright, |m| > 1.

Everyday detective — name that mirror

No upload needed — read the scene. What mirror (and image behaviour) is at work?

close face · huge upright
Spoon bowl, nose too close — image?

Concave + object inside focus → virtual, upright, magnified — makeup/shave territory.

CARwide lane · small cars
Wing mirror warning sticker — why?

Convex shrinks the scene for field of view — smaller look → brain thinks farther.

still lake · twin trees
Calm lake “mirror” — image type?

A flat water surface behaves like a huge plane mirror when calm — virtual twin below; wind → diffuse scatter.

What you'll learn

After the wow — what you can prove

This page covers the law of reflection (∠i = ∠r), plane mirrors, concave and convex spherical mirrors, the mirror formula 1/v + 1/u = 1/f, and magnification m = −v/u. By the end you'll be able to:

  • Measure angles from the normal — not from the glass itself.
  • Predict plane-mirror images — same size, upright, as far behind as the object is in front.
  • Use 1/v + 1/u = 1/f with the usual sign convention.
  • Tell real vs virtual — and when a concave mirror switches from enlarging to inverting.
  • Drive the Mirror Lab and match what the rays and formula predict.
Why it matters · where it's tested

The first chapter of ray optics everywhere

Mirrors open every light chapter — and "reflection of light" / spherical mirrors is a core Class 8–10 topic on every board. We go beyond the syllabus, but we never skip it:

CBSE · Class 8–10 — Light / Reflection ICSE — Reflection & mirrors IGCSE · Cambridge / Edexcel — Reflection AP Physics 2 — Geometric optics Olympiad — NSO · NSEJS foundations

Searched as: law of reflection, angle of incidence, plane mirror, concave convex mirror, 1/v + 1/u = 1/f, magnification, image distance.

Only three ideas — everything else supports them

The chapter spine: 🟢 must-feel · helpers in muted rows
IdeaMeaningUnitWeight
∠i = ∠rTHE LAW — both from the normal°🟢
1/v + 1/u = 1/fTHE FORMULA — where the image sits1/m🟢
Where is the image?THE QUESTION — real / virtual · in front / behind🟢
f = R/2Helper — focus halfway to Cm🟡
m = −v/uHelper — size & often orientation🟡
signs · plane f→∞Convention & flat-mirror limit🟡

What's going on

Your twin walked back because the bounce law is mercilessly fair: whatever angle arrived, the same angle left. Curve the glass and the meeting place of the rays — the image — shifts. Same law. New geography.

What it is

Reflection is light bouncing off a boundary. Draw a dashed normal at right angles to the surface. The angle of incidence (∠i) and angle of reflection (∠r) are both measured from that normal — and they are equal. A plane bathroom mirror, a spoon, and a car wing mirror all obey the same bounce rule.

How mirrors shape images

A plane mirror puts a virtual image as far behind as the object is in front, same size, upright. A concave (converging) mirror can form real inverted images or magnified virtual faces for shaving. A convex (diverging) mirror always gives a smaller upright virtual image — wide field for traffic. The maths link is 1/v + 1/u = 1/f with f = R/2.

How it works in the lab

The Rays tab eases the incident ray to your chosen ∠i and mirrors the bounce so ∠r matches (motion-feel). Switch Plane / Concave / Convex, set |u| and |f|, and readouts follow the formula. The ∠i–∠r tab is a straight diagonal — the law drawn as a graph. 🟡 maths of the picture

Edge cases
  • Measured from glass? Wrong — always from the normal.
  • Object at focus (concave) → rays leave parallel; no sharp finite image.
  • Convex → f positive (New Cartesian); image always virtual, diminished.
  • Rough surfaces → diffuse reflection; law still true per tiny facet.
Three quantities & units
  • Angles (°) — ∠i and ∠r from the normal.
  • u, v, f (cm or m) — object, image, focal distances.
  • Magnification m — m = −v/u (sign often flags inversion).

Solve it with me, step by step 🟢 Class 8–10

Exams reward the method, not just the answer. Work it out one step at a time — read the thought, predict the line, then reveal it. Switch to practice to type your own numbers and check them.

See the maths

Drag the numbers — watch ∠r, v and m update.

🔢 ∠i = ∠r

Reflection law — both angles from the normal.
∠r
35°
∠i = ∠r = 35°

📏 1/v + 1/u = 1/f

Concave mirror — New Cartesian (u,f negative).
v
−60 cm
v from 1/v = 1/f − 1/u → −60 cm

🔎 m = −v/u

Magnification from object and image distances.
|m|
2.0
|m| = |v|/|u| → 2.0 (sign separate)

From bronze to JWST

Same bounce law. Wilder tools. Civilization is a gallery of mirrors.

~3000 BCE

Polished bronze & obsidian

Status and ritual first — a face in metal taught ∠i = ∠r long before symbols for it.

1st c. CE · Roman tin-glass

Looking glass goes public

Tin behind glass democratises the twin. Bathrooms are just late arrivals.

1608–1672

Telescope mirrors arrive

Newton’s reflector sidesteps colour fringes — concave gatherer + flat tip.

1800s–today

Silver, headlights, clinics

Dental folds, shop domes, sun furnaces — applied bounce everywhere.

1990 → 2021

Hubble → James Webb

Orbiting concave systems and golden hexes — 1/v + 1/u at cryogenic scale.

Physics illusions

The brain meets fair physics and calls it magic. Each trick is still ∠i = ∠r (or a stack of them).

Pepper's Ghost

A tilted pane mixes a reflected performer with the live stage — virtual image overlapping real space.

Theatre · plane bounce

Infinity mirrors

Two facing mirrors trap ray after ray; your eyes invent a tunnel of twins.

Multiple reflections

Mirror maze

Corridors of planes kill your sense of depth — every exit is a law repeated.

Orientation + pathfinding

Anamorphic art

A curved or angled reflection “decrypts” a warped painting into a sharp face.

Cylinder / cone mirrors

In the real world

James Webb · golden honeycombs

Eighteen hex mirrors align so starlight acts like one giant concave collector — the same 1/v + 1/u geometry, just colder and farther than any bathroom glass.

Pepper's Ghost & stage twins

A tilted sheet of glass mixes a reflected actor with the real stage — your brain meets a ghost that is only ∠i = ∠r in theatre clothing.

LiDAR · dental · solar furnace

Laser scanners time bounced pulses; dentists fold sight with tiny planes; solar furnaces aim sunbeams with hills of mirrors — civilization is applied reflection.

From plane to curve — same bounce 🟡

Drag the ladder — everyday mirrors that still obey ∠i = ∠r.

planeclosefarconvexpara

Bathroom plane

∠i = ∠r

Shape changes; ∠i = ∠r stays the habit.

Build it yourself — science-fair projects

Physics you can see. Each project shows reflection — and the measuring is what turns a demo into a science-fair winner.

🪞Beginner

Pin & plane mirror

Shows · ∠i = ∠r

Build: stand a pin in front of a plane mirror on paper; sight and mark incident and reflected rays with another pin.

Measure: angles from a drawn normal — they should match within a few degrees.

🥄Beginner

Spoon two ways

Shows · concave vs convex

Build: look into both sides of a polished spoon.

Measure: which side magnifies close-up? Which shrinks and widens the room?

📏Intermediate

Image depth check

Shows · plane image distance

Build: place an object at measured u from a plane mirror; use parallax or a second object behind a clear board to find image position.

Measure: image distance ≈ u — as far behind as in front.

🕯️Intermediate

Concave candle screen

Shows · real image

Build: a concave makeup mirror, a candle beyond f, a white card.

Measure: where a sharp inverted flame appears — that is a real image you can catch.

🚗Intermediate

Field-of-view race

Shows · convex wide field

Build: compare how much of a room a phone selfie camera sees via a plane vs a convex door mirror.

Measure: count distinct objects visible — convex should win on width.

📐Champion

Focal length of a concave

Shows · f ≈ R/2 / distant focus

Build: focus a distant window on a screen with a concave mirror; distance mirror-to-screen ≈ f.

Measure: several trials, average f, then compare with an estimate from a measured radius if you can.

Glossary — the 10 words that unlock it

Normal

What it means
A line at 90° to the surface at the point of incidence.
Why it matters
Angles of incidence and reflection are measured from it.
Example
The dashed line in every ray diagram.
Key question
Why not measure from the glass?

Angle of incidence

What it means
Angle between the incident ray and the normal.
Why it matters
Equals the angle of reflection.
Example
∠i = 35° in Mirror Lab.
Key question
What if ∠i is 0°?

Angle of reflection

What it means
Angle between the reflected ray and the normal.
Why it matters
Always ∠r = ∠i for a specular bounce.
Example
Same 35° out.
Key question
Can ∠r ever differ on a smooth mirror?

Plane mirror

What it means
A flat reflecting surface.
Why it matters
Virtual image, same size, upright, equal depth behind.
Example
Bathroom glass.
Key question
Is the image real?

Concave mirror

What it means
Reflecting surface caves toward you — converging.
Why it matters
Can form real or virtual images depending on u.
Example
Shaving / makeup mirrors.
Key question
What if the object is at F?

Convex mirror

What it means
Bulges toward you — diverging.
Why it matters
Always a diminished upright virtual image; wide field.
Example
Car side mirrors.
Key question
Why the "closer than they appear" warning?

Focal length f

What it means
Distance from pole to focus; f = R/2 for a sphere.
Why it matters
Sets the scale of image locations.
Example
|f| = 20 cm in the lab.
Key question
How does f relate to R?

Mirror formula

What it means
1/v + 1/u = 1/f with a sign convention.
Why it matters
Predicts where the image sits.
Example
u = −30, f = −20 → v = −60 cm.
Key question
What do the signs mean?

Magnification m

What it means
m = −v/u ≈ h′/h.
Why it matters
Size and often orientation of the image.
Example
m = −2 means twice as tall, inverted.
Key question
What does |m| < 1 mean?

Real vs virtual

What it means
Real: rays meet and can hit a screen. Virtual: rays only appear to meet.
Why it matters
Screens catch real images; you "see" virtual ones by looking into the mirror.
Example
Candle image on a card vs face in glass.
Key question
Can a plane mirror make a real image of a real object?
हिन्दी · key words Reflection · परावर्तन Normal · अभिलंब Mirror · दर्पण Focus · फोकस Magnification · आवर्धन

The questions people ask

Mirrors look simple until the first ray diagram. Straight answers:

What is the law of reflection?
What

The angle of incidence equals the angle of reflection, and both are measured from the normal — a line perpendicular to the surface at the hit point. The incident ray, reflected ray and normal also lie in one plane.

Why do we draw a normal?
Why

Angles measured along the glass confuse every diagram. The normal gives a fair, shared zero so ∠i and ∠r can be compared fairly on curved mirrors too — draw it at the point of incidence.

Is my face in the bathroom mirror a real image?
Scenario

No — it is virtual. Reflected rays diverge into your eyes as if they came from a spot behind the glass; nothing meets on a screen there. Real images form when rays actually converge and can light a card.

When does a concave mirror magnify?
How

When the object is between the pole and the focus, the image is virtual, upright and enlarged — the shaving-mirror case. Beyond the focus you get real inverted images whose size depends on exact u.

What does 1/v + 1/u = 1/f mean?
What

It links object distance u, image distance v and focal length f for spherical mirrors (with a chosen sign convention). Know two, solve for the third. Schools usually use the New Cartesian signs.

Why do car mirrors warn that objects are closer?
Scenario

Convex mirrors shrink the scene (|m| < 1) so cars look smaller and farther than they are. The warning reminds you the geometry traded size for a wider field of view.

How is f related to R?
How

For a spherical mirror under the usual school approximation, the focal length is half the radius of curvature: f = R/2. The focus sits midway from the pole to the centre of curvature.

Reflection vs refraction — difference?
Comparative

Reflection bounces light back into the original medium (∠i = ∠r). Refraction is light entering a new medium and usually bending (Snell's law). Most boundaries do a bit of both; mirrors are built to favour the bounce.

Common mistakes — and the fix 🟢 Class 8–10

Spot these before the exam does.

The slipThe fix
Measuring ∠i from the mirror faceAlways from the normal
Forgetting signs in 1/v + 1/u = 1/fPick New Cartesian (or your board's) and stick to it
Writing f = R instead of R/2f = R/2 for the spherical school model
Calling every image realPlane & convex (usual) → virtual; check if rays meet
Mixing |u| with signed u in m = −v/uUse the same signed u and v as the formula

Test yourself — a mixed set

Seven question formats, the way LLOS.ai serves them — multiple choice, multiple-correct, fill-in-the-blank, match, sequence, read-think-connect, and write-your-own. Every question has layered hints: a quick nudge, the reasoning, then a deeper connection — so a wrong answer opens a door, never a dead end. 🟢 received from a board-tagged question bank · seed toward 2,000

Pick your board — the set re-tunes to its wording and emphasis. Competitive draws the JEE / NEET / Olympiad lane.

Loading the question bank…
Question 1 of 16
Multiple choice

Key takeaways

  • ∠i = ∠r — always from the normal, in one plane.
  • Plane mirrors — virtual, upright, same size, equal depth behind.
  • 1/v + 1/u = 1/f and f = R/2 — spherical mirrors with signs.
  • Concave can magnify (inside f) or invert (beyond f); convex always diminishes.
  • m = −v/u — size and often orientation.

🪜 Where this lesson leads

Mirrors open ray optics. Master them and you are already climbing toward:
Law of reflection
Plane mirrors
Concave & convex
Mirror formula & magnification
Lenses & lens formula
Refraction & Snell's law
The eye & camera
Optical instruments

Keep exploring

A mirror never invents light — it only keeps the promise that whatever angle arrives, the same angle leaves.

Copyright © Pawan Nayar · LLOS.ai · 2026 — Original pedagogy, voice, and design — all rights reserved.
▶ Move the light