Ray Optics and
Optical Instruments
Learn the concept. See the ray. Derive the formula. Solve the problem. Master the exam. A complete, interactive walk from "what is a ray?" to telescope magnification — built for boards, NEET, and JEE Main.
Pick how you want to move through this chapter
Every module works stand-alone, but here's how different students typically use it. You can switch paths any time — nothing is locked.
Starting from scratch
Do the Prerequisite Check first, then follow the sidebar top to bottom. Don't skip the Sign Convention Survival Guide — it's where most marks are lost later.
Board-exam revision
Jump to Formula Master Sheet → Conceptual Trap Gallery → Practice Question Bank (filter: CBSE). Use accordions to re-derive anything that feels shaky.
NEET / JEE sprint
Use the interactive ray-diagram labs to build speed on image location, then filter the Practice Question Bank to NEET or JEE Main tags for calculation-heavy problems.
Chapter roadmap
Ray Optics rests on two physical events — light bouncing off a surface (reflection) and light bending as it changes medium (refraction). Every instrument in this chapter is just a clever arrangement of mirrors and lenses built on these two ideas.
Prerequisite check
Before ray optics makes sense, three ideas from Class 10/11 need to be solid. Tick off what you already know — if any box is shaky, the linked module will rebuild it from zero.
Unsure about any of these? They're rebuilt from first principles in Module 02 below — just keep going.
Ray optics fundamentals
Ray optics (geometrical optics) is the branch of optics that ignores the wave nature of light and treats it as travelling in straight-line paths called rays. It works whenever the obstacles or apertures involved are much larger than the wavelength of light — which is true for mirrors, lenses and prisms, but not for tiny slits (that's where wave optics takes over, next chapter).
A ray is the path along which light energy travels, drawn as a straight line with an arrowhead showing the direction of travel. A beam is a bundle of many rays. A beam can be parallel (rays never meet — e.g. sunlight reaching Earth), convergent (rays meet at a point), or divergent (rays spread out from a point, like light from a bulb).
In a single uniform medium, light takes the path that requires the least time (Fermat's principle) — and in a uniform medium that path is a straight line, since the speed is the same everywhere. This is called rectilinear propagation, and it's why objects cast sharp shadows and why a pinhole camera works.
Reflection is light bouncing back into the same medium after hitting a surface. Refraction is light crossing into a different medium and changing direction because its speed changes. Both obey their own precise laws, covered in the next two tracks.
Refractive index — the number that describes a medium
When light moves from vacuum (or air, as a close approximation) into a medium, its speed drops. The absolute refractive index n of a medium tells you by what factor:
The relative refractive index when light goes from medium 1 to medium 2 is ₁n₂ = v₁/v₂ = n₂/n₁. A medium with higher n is called optically denser — this is about the bending power of light, and has nothing to do with mass density (water is optically denser than kerosene, but has lower mass density).
💡 Why this matters
Every refraction formula in this chapter — Snell's law, apparent depth, the lens maker's formula — is really just bookkeeping for how much the ray bends when v changes. Get comfortable with n = c/v now and the rest becomes mechanical.
| Medium | Approx. refractive index |
|---|---|
| Vacuum / air | 1.00 (defined / ≈1.0003) |
| Water | 1.33 |
| Glass (crown) | 1.5 |
| Diamond | 2.42 |
Reflection of light
Start with the flattest possible mirror — a plane mirror — before curving it. Everything here transfers directly to spherical mirrors.
Image in a plane mirror
A plane mirror forms an image that is: virtual, erect, laterally inverted, and the same size as the object — with the image appearing as far behind the mirror as the object is in front. Magnification m = +1.
A mirror doesn't actually swap left-right — it reverses front-to-back (the axis perpendicular to the mirror). What you perceive as "left-right flip" is a consequence of how you mentally rotate yourself to face your reflection. This is a favourite conceptual trap in CBSE viva/assertion-reason questions.
If a mirror is rotated by angle θ (keeping the incident ray fixed), the reflected ray rotates by 2θ. This is because both the angle of incidence and the angle of reflection change by θ each, and the reflected ray's direction depends on twice that angle. This result is used directly in problems on periscopes and rear-view mirror adjustment.
⚠ Common mistake
Students often measure i and r from the mirror surface instead of the normal. Always draw the normal first — it is perpendicular to the surface at the point of incidence — then measure both angles from it.
Spherical mirrors
A spherical mirror is a small cut-out piece of a hollow sphere, silvered on one side. Curve the reflecting surface inward and you get a concave mirror; curve it outward and you get a convex mirror.
| Term | Meaning |
|---|---|
| Pole (P) | The geometric centre of the mirror's reflecting surface. |
| Centre of curvature (C) | Centre of the sphere of which the mirror is a part. |
| Radius of curvature (R) | Distance PC — the sphere's radius. |
| Principal axis | The straight line through P and C. |
| Principal focus (F) | Point on the principal axis where paraxial rays parallel to the axis converge (concave) or appear to diverge from (convex) after reflection. |
| Focal length (f) | Distance PF. |
| Aperture | The effective diameter of the mirror that reflects light. |
| Paraxial rays | Rays that make small angles with the principal axis and stay close to it — the assumption under which all our formulas hold. |
Assumption used: the aperture of the mirror is small, so all rays are paraxial (make small angles with the axis) — this is what allows MF ≈ PF. For a wide-aperture mirror this approximation breaks down and causes spherical aberration (rays farther from the axis focus at slightly different points).
Sign convention — the New Cartesian Convention
Every mirror and lens formula in this chapter only works if distances are signed consistently. This is the single biggest source of silly mistakes in board exams — spend real time here.
📐 The rules, stated once, precisely
1. All distances are measured from the pole of the mirror/lens.
2. Distances measured in the direction of incident light (conventionally left→right) are positive; against it are negative.
3. Heights measured upward from the principal axis are positive; downward are negative.
4. The object is always placed to the left of the mirror/lens, so the object distance u is (almost) always negative.
| u | f | Typical v | Image nature | |
|---|---|---|---|---|
| Concave, object beyond F | − | − | −ve→real (+ by convention when using v positive for real... see note) | Real, inverted |
| Concave, object between P & F | − | − | + (behind mirror) | Virtual, erect, magnified |
| Convex, any real object | − | + | + (behind mirror) | Virtual, erect, diminished |
Note: for a concave mirror producing a real image, v comes out negative in the strict New Cartesian convention (since the real image also forms in front of the mirror, on the negative side) — many textbooks then just state "real image, in front of mirror" rather than worry about the sign once nature is identified. Always trust the calculation, then sanity-check the sign against the ray diagram.
⚠ Sign traps students fall into
Trap 1: Writing f = +R/2 for a concave mirror out of habit — it must be negative.
Trap 2: Forgetting that magnification's sign tells you orientation (negative m = inverted, positive m = erect) while its magnitude tells you size.
Trap 3: Mixing the mirror sign convention with the (different-looking but consistent) lens sign convention mid-problem in combination-of-mirror-and-lens questions.
Mirror formula & magnification
One equation connects object distance, image distance and focal length for any spherical mirror, in any situation — provided you plug in signed values.
| Symbol | Meaning |
|---|---|
| u | Object distance from pole |
| v | Image distance from pole |
| f | Focal length (= R/2) |
💡 Physical meaning, not just algebra
1/u and 1/v measure "how convergent/divergent" the incoming and outgoing wavefronts are (this is literally vergence in optics — the same idea used to define lens Power later). The mirror adds a fixed amount of convergence, 1/f, to whatever vergence the object rays already had. That's the whole formula in one sentence.
Magnification
Worked example CBSE style
An object 2 cm tall is placed 15 cm from a concave mirror of focal length 10 cm. Find the image position, size and nature.
Solution: u = −15 cm, f = −10 cm. From 1/f = 1/v + 1/u: 1/v = 1/f − 1/u = −1/10 − (−1/15) = −1/10 + 1/15 = (−3+2)/30 = −1/30. So v = −30 cm. Magnification m = −v/u = −(−30)/(−15) = −2. Image height = m × hₒ = −2 × 2 = −4 cm.
Nature: v is negative and real-image-side for a concave mirror here means the image forms 30 cm in front of the mirror — real, inverted, and magnified 2×.
Mirror ray diagram lab
Drag the object distance and watch the image form in real time. This single tool replaces the whole "six standard cases" table — the physics is identical, only u changes.
Try both mirror types across all six presets. Notice: a convex mirror never produces a real image for a real object, no matter where you place it — the readout will confirm this every time.
The 3-ray rulebook
You only ever need two of these three rays to locate an image — the third is a check. Memorise all three; use whichever two are geometrically easiest for the given object position.
Rule 1 — Parallel ray
A ray parallel to the principal axis reflects (or, for a lens, refracts) through the focus F.
Rule 2 — Focal ray
A ray passing through F reflects/refracts parallel to the principal axis (the reverse of Rule 1).
Rule 3 — Centre ray
For a mirror: a ray through C retraces its own path (it hits the surface normally). For a lens: a ray through the optical centre passes straight through, undeviated.
Rule 1 and Rule 2 are the same law of reflection applied in two directions — light paths are reversible, so if parallel-in gives focus-out, then focus-in must give parallel-out. Rule 3 works because CM (the radius) is always normal to a spherical mirror's surface, so a ray along that radius hits "head-on" and reflects straight back. For a thin lens, the optical centre is defined as the point where the two refracting surfaces are effectively parallel to each other, so a ray through it suffers no net deviation.
Exam tip
In JEE Main/NEET numericals, Rule 1 + Rule 3 are usually the fastest pair to sketch because they don't require locating F on both sides. For an object exactly at F, Rule 2 becomes useless (the ray never "arrives" from F in a normal sense) — use Rules 1 and 3 instead, and note the image forms at infinity.
Refraction of light
When light crosses from one medium into another obliquely, it bends. Before the maths, get the physical picture right.
💡 Why does light bend at all?
Light slows down (or speeds up) when it enters a new medium, because it's interacting with the medium's atoms. Picture a wide beam like a marching band crossing at an angle from a paved road onto sand — the end that hits the sand first slows down while the other end is still moving fast on the road, so the whole line pivots. That pivot is refraction. Frequency never changes (it's set by the source), but speed and hence wavelength do.
| Going from | Speed change | Bending |
|---|---|---|
| Rarer → denser (e.g. air → glass) | Decreases | Bends towards the normal |
| Denser → rarer (e.g. glass → air) | Increases | Bends away from the normal |
Snell's law
This single equation is the complete law of refraction. Combined with n = c/v, it directly explains the bending direction table above: if n₂ > n₁ (denser), then sin r < sin i, so r < i — the ray bends toward the normal.
What changes when light enters another medium?
| Quantity | Changes? | Why |
|---|---|---|
| Speed | Yes | Depends on the medium's optical density |
| Frequency | No | Set by the source; must stay continuous across the boundary |
| Wavelength | Yes | λ = v/f, and v changes while f doesn't |
| Direction | Yes (unless i = 0) | Governed by Snell's law |
⚠ Common mistake
Students often think frequency changes with medium because "everything about the wave changes." It doesn't — frequency is the one refraction-invariant quantity, and it's a favourite one-mark conceptual question in both CBSE and NEET.
Refraction through a glass slab
A parallel-sided slab bends the ray twice — once entering, once leaving — and the two bends exactly cancel in direction, so the emergent ray is parallel to the incident ray, just shifted sideways.
Depends on: increases with thickness t, increases with angle of incidence i, and increases with refractive index n (since higher n means smaller r for the same i, widening (i − r)).
Worked example
A ray hits a 6 cm thick glass slab (n = 1.5) at i = 45°. Find the lateral shift. Using Snell's law: sin r = sin 45°/1.5 = 0.4714, so r ≈ 28.1°. Shift = 6 × sin(45° − 28.1°)/cos 28.1° = 6 × sin16.9°/cos28.1° ≈ 6 × 0.2907/0.8827 ≈ 1.98 cm.
Apparent depth
A coin at the bottom of a pool looks closer to the surface than it really is. This is refraction happening at a flat, horizontal interface as you look down from above.
💡 Why it looks raised
Rays from the coin bend away from the normal as they leave water and enter air (denser → rarer). Your eye extends these diverging rays straight back and perceives a virtual image higher up than the actual coin.
Everyday examples: a coin at the bottom of a glass of water appears closer to the surface; a swimming pool always looks shallower than it is (a genuine safety concern); a fish looking up sees the outside world compressed into a cone (related to total internal reflection, next module).
Worked example NEET style
A tank is filled with water (n = 4/3) to a depth of 12 cm. What is the apparent depth when viewed from directly above? Apparent depth = Real depth / n = 12/(4/3) = 9 cm.
Total internal reflection
Push the angle of incidence far enough while going from a denser to a rarer medium, and the refracted ray disappears entirely — all the light reflects back. This is TIR.
Conditions for TIR
1. Light must travel from a denser to a rarer medium.
2. The angle of incidence must exceed the critical angle C for that pair of media.
Worked example
Find the critical angle for glass-air interface if n(glass) = 1.5. sin C = 1/1.5 = 0.667, so C = sin⁻¹(0.667) ≈ 41.8°.
Applications of total internal reflection
Optical fibres
A thin core of high-refractive-index glass surrounded by lower-index cladding. Light entering at a suitable angle hits the core-cladding boundary beyond the critical angle every time, so it's guided along the fibre by repeated TIR with almost no loss — used in telecom and medical endoscopy.
Totally reflecting prisms
A right-angled prism (45°-45°-90°) can turn light through 90° or 180° using TIR at its hypotenuse, used in periscopes and binoculars — cleaner than a silvered mirror, since TIR reflects ~100% of light with no absorption losses.
Mirage & sparkle of diamond
A mirage is TIR at layers of hot air near the ground (a "denser-to-rarer" gradient formed by temperature). A diamond's brilliance comes from its very high refractive index (2.42) giving a small critical angle (~24°), so light entering it undergoes multiple internal reflections before escaping.
Prism & angle of deviation
A prism refracts light at two non-parallel surfaces, so — unlike a slab — the emergent ray is not parallel to the incident ray. The net bend is called the angle of deviation, δ.
As i₁ is varied, δ first decreases, reaches a minimum value δₘ, then increases. At minimum deviation, the ray passes symmetrically through the prism: i₁ = i₂ and r₁ = r₂ = A/2. This symmetry gives the prism formula:
Dispersion of light
Refractive index actually depends slightly on wavelength — a fact called dispersion — with violet bending more than red in ordinary (glass) prisms, since n(violet) > n(red).
Atmospheric refraction
Earth's atmosphere gets progressively less dense with altitude, so it acts like a medium with continuously decreasing refractive index. Two classic everyday effects follow directly.
Twinkling of stars
Light from a star bends gradually as it passes through air layers of fluctuating density and temperature, so the apparent position and brightness fluctuate rapidly — perceived as twinkling. Planets don't twinkle (much) because they're extended sources — many points average the fluctuation out.
Advance sunrise / delayed sunset
Atmospheric refraction bends sunlight so that the Sun is visible for about 2 minutes before it geometrically crosses the horizon at sunrise, and for about 2 minutes after at sunset.
Refraction at a spherical surface
Before combining two curved surfaces into a lens, look at what a single curved refracting surface does — this formula is the building block for the lens maker's formula.
Notice the mirror formula's shape hiding inside this — swap n₁ = n₂ = −1 (reflection convention) and it reduces to the familiar mirror formula. This is not a coincidence: reflection is refraction's limiting case with the "second medium" being a return into the first.
Lenses & ray diagrams
A lens is a transparent medium bound by two (usually spherical) surfaces. A convex (converging) lens is thicker in the middle; a concave (diverging) lens is thinner in the middle.
A concave lens always gives a virtual, erect, diminished image for a real object, exactly like a convex mirror — try every preset above and confirm it.
Lens formula, magnification & power
⚠ The #1 lens-vs-mirror mix-up
Students frequently import the mirror's "1/f = 1/v + 1/u" and "m = −v/u" into lens problems, or vice-versa. They are genuinely different formulas because the sign convention direction is applied differently to reflected vs. refracted light. Write down which device you're dealing with before writing any formula.
Power of a lens
Combination of lenses
For thin lenses placed in contact, the net power (and hence 1/f) simply adds:
Lens maker's formula
This connects a lens's focal length to the physical properties an optician actually controls: the material and the curvature of the two surfaces.
Apply the single-spherical-surface refraction formula (Module 18) twice in succession — once at the first surface (air → lens material), once at the second (lens material → air) — treating the image formed by the first surface as the object for the second. For a thin lens (negligible thickness), adding the two equations and simplifying gives exactly the lens maker's formula above.
Worked example JEE Main style
A convex lens is made of glass (n = 1.5) with R₁ = +20 cm and R₂ = −20 cm (equi-convex). Find f. 1/f = (1.5−1)(1/20 − 1/(−20)) = 0.5 × (1/20+1/20) = 0.5 × 0.1 = 0.05, so f = 20 cm.
The human eye
The eye is a natural optical instrument: a convex-lens system that forms a real, inverted image on the retina, with the brain flipping it back mentally.
| Term | Meaning |
|---|---|
| Accommodation | The eye's ability to change the focal length of its lens (by ciliary muscles) to focus on objects at different distances. |
| Near point | Closest distance at which the eye can focus comfortably — about 25 cm for a normal (young adult) eye. Also called the least distance of distinct vision, D. |
| Far point | Farthest distance the relaxed eye can focus on — infinity, for a normal eye. |
The near point, D = 25 cm, is the reference distance used throughout the magnification formulas for the simple and compound microscope below — it is not an arbitrary constant, it's literally "as close as a normal eye can comfortably focus."
Simple microscope (magnifying glass)
A single convex lens, used to view a small object closer than the eye normally could, forming a magnified, virtual, erect image.
Compound microscope
Two converging lenses in series: a short-focal-length objective forms a real, magnified image close to the eyepiece, which then acts as a simple magnifier on that intermediate image.
💡 Why two stages beat one
A single lens can't give huge magnification without introducing severe aberration and requiring impossibly short focal lengths. Splitting the job — one lens forms a large real image, a second lens then further magnifies that image — lets each lens do a modest, manageable amount of work while the total effect multiplies.
Astronomical telescope
Unlike a microscope, a telescope makes a distant object subtend a larger angle at the eye — it doesn't make the object bigger, it makes it appear closer.
| Compound microscope | Astronomical telescope | |
|---|---|---|
| Object | Small, very close | Large, very far (effectively at infinity) |
| Objective focal length | Very short | Very long |
| Eyepiece focal length | Short | Very short (shorter than objective) |
| Job of the instrument | Increase visual angle of a small nearby object | Increase visual angle of a large distant object |
Formula master sheet
Every formula in this chapter, in one scroll. Use this for last-minute revision, not first-time learning.
Conceptual trap gallery
Every trap below has cost real students real marks. Read each one once, slowly.
⚠ Trap
Writing m = −v/u for a lens (that's the mirror formula). For lenses, m = +v/u.
⚠ Trap
Assuming frequency changes when light enters a new medium. It never does — only speed and wavelength change.
⚠ Trap
Forgetting that a convex mirror and a concave lens both always give virtual, erect, diminished images for real objects — no exceptions, so there's no "case analysis" needed for these two.
⚠ Trap
Using sin C = 1/n with n being the wrong medium's index. C is defined for light going from denser to rarer, and n in the formula is the denser medium's index relative to the rarer one.
⚠ Trap
Treating "twinkling" and "advance sunrise" as the same phenomenon in explanation — one is about rapid random fluctuation (turbulence), the other is about a steady, predictable bending near the horizon.
⚠ Trap
Forgetting the negative sign convention for u — plugging in u = +15 instead of u = −15 flips every subsequent sign in the calculation.
Practice question bank
All questions below are original, exam-style practice questions written for this guide — not reproductions of actual CBSE, NEET or JEE papers. They're tagged by the exam style they most resemble.
Rapid recall flashcards
Click the card to flip. Use the arrows to move through the deck.
Ray Optics mastery checklist
Tick each box honestly. Anything unchecked is your revision list — click the linked module name above it if you need to revisit.
Frequently asked questions
They actually use the same New Cartesian convention for measuring distances — the difference in the magnification formula (−v/u for mirrors, +v/u for lenses) comes from how a real image's v works out with opposite signs relative to u for each device given the geometry of reflection versus transmission. Rather than memorising "why," memorise which formula belongs to which device.
Yes — the derivation in Module 04 works identically for a convex mirror; only the sign of R (and hence f) differs, since both C and F now sit behind the mirror.
A slab's two surfaces are parallel, so the wavelength-dependent bending at the first surface is exactly undone by the second — every colour emerges parallel to the incident ray (just laterally shifted by very slightly different amounts, invisible in practice). A prism's surfaces are not parallel, so the two bends add up instead of cancelling, spreading the colours into a visible spectrum.
Check your specific board's latest syllabus document for whether the derivation is examinable that year — NCERT presents it, and CBSE has historically asked for it as a 3-5 mark derivation, but always confirm against the current year's official syllabus rather than assuming.