Ray Optics and Optical Instruments Class 12 Physics Notes 2026-27 | Chapter 9
Ray Optics and Optical Instruments — Complete Notes
Ray Optics and Optical Instruments Class 12 Physics Notes for CBSE 2026–27, covering reflection, spherical mirrors, refraction, total internal reflection, optical fibres, spherical refracting surfaces, lenses, lens maker's formula, magnification, power, combinations of lenses, prisms, microscopes and astronomical telescopes.
Ray optics, or geometrical optics, treats light as rays that travel in straight lines in a homogeneous medium and change direction when reflected or refracted. In Class 12 Chapter 9, this model is used to analyse mirrors, lenses, prisms, optical fibres, microscopes and astronomical telescopes.
| Student question | Fast answer |
|---|---|
| Mirror formula? | 1/f = 1/v + 1/u |
| Thin-lens formula? | 1/f = 1/v − 1/u |
| Snell's law? | n1 sin i = n2 sin r |
| TIR conditions? | Higher refractive index → lower refractive index, and i > C. |
| Lens power? | P = 1/f, with f in metres; unit = dioptre. |
| Prism at minimum deviation? | i = e and r1 = r2 = A/2. |
| Refracting telescope in normal adjustment? | M = −fo/fe. |
1. CBSE 2026–27 Scope Map for Chapter 9
Official current scope:
- Reflection of light and spherical mirrors.
- Mirror formula.
- Refraction of light, total internal reflection and its applications, including optical fibres.
- Refraction at spherical surfaces.
- Lenses, thin-lens formula and lens-maker's formula.
- Magnification and power of a lens.
- Combination of thin lenses in contact.
- Refraction of light through a prism.
- Microscopes and astronomical telescopes, including reflecting and refracting telescopes and their magnifying powers.
The current CBSE 2026–27 curriculum does not list a separate detailed treatment of dispersion, the human eye and correction of eye defects, or scattering as Chapter 9 core topics. Those subjects may appear in older NCERT/syllabus resources; do not treat them as mandatory current Chapter 9 content unless CBSE updates the syllabus.
Unit VI — Optics: Chapter 9 is part of Unit VI along with Chapter 10, Wave Optics. The official curriculum gives 18 marks collectively to Units V and VI; CBSE does not publish a fixed Chapter 9-only mark allocation.
CBSE Class XII 2026–27 Sample Question Paper & Marking Scheme
2. The Core Idea of Geometrical Optics
In a homogeneous transparent medium, a light ray travels in a straight line. At a reflecting surface, its direction changes according to the laws of reflection. At the boundary between two transparent media, its direction may change because its speed changes; this is refraction.
Light returns into the original medium after striking a reflecting surface.
Light changes direction when it passes obliquely from one transparent medium to another because its speed changes.
Mirrors and lenses redirect rays so that they appear to meet at a real or virtual image position.
Microscopes and telescopes combine optical elements to produce useful magnification and viewing.
3. Cartesian Sign Convention — Foundation of Numericals
Use one sign convention consistently. In the Cartesian sign convention, distances are measured from the pole of a spherical mirror or optical centre of a thin lens. The positive direction is taken along the direction of incident light.
| Quantity | Typical sign rule | Practical reminder |
|---|---|---|
| Object distance u | Usually negative for a real object placed in front of the mirror/lens. | Do not insert an unsigned distance into a signed formula. |
| Image distance v | Sign depends on the image position relative to the reference point and positive direction. | Determine the actual side first. |
| Focal length f | Positive for a converging/convex lens; for mirrors, use the actual Cartesian sign based on focus position. | Never memorise a single sign without identifying the optical element. |
| Height | Positive above the principal axis; negative below it. | Image inversion is reflected in the sign of magnification. |
4. Reflection of Light and Spherical Mirrors
4.1 Laws of reflection
- The incident ray, reflected ray and normal at the point of incidence lie in the same plane.
- The angle of incidence equals the angle of reflection: i = r.
4.2 Spherical mirrors
A spherical mirror is a part of a spherical reflecting surface. The two common types are:
Reflecting surface faces inward toward the centre of curvature. It is a converging mirror for paraxial rays.
Reflecting surface bulges outward toward the object side. It is a diverging mirror for paraxial rays.
4.3 Important terms
| Term | Meaning |
|---|---|
| Pole (P) | Geometrical centre of the reflecting surface. |
| Centre of curvature (C) | Centre of the sphere of which the mirror is a part. |
| Radius of curvature (R) | Distance PC. |
| Principal axis | Straight line joining P and C. |
| Principal focus (F) | Point on the principal axis where paraxial parallel rays converge, or from which they appear to diverge. |
| Focal length (f) | Distance PF. |
4.4 Ray rules for spherical mirrors
- A ray parallel to the principal axis reflects through the principal focus of a concave mirror or appears to come from the focus of a convex mirror.
- A ray passing through the principal focus of a concave mirror reflects parallel to the principal axis.
- A ray passing through the centre of curvature retraces its path after reflection.
- A ray striking the pole obeys the ordinary law of reflection with respect to the principal axis.
4.5 Mirror formula
Here u is object distance, v is image distance and f is focal length, all measured with the adopted sign convention.
4.6 Linear magnification by a mirror
A negative magnification indicates an inverted image; a positive magnification indicates an erect image under the standard convention.
4.7 Image formation — quick map
| Concave mirror object position | Image position / nature |
|---|---|
| Beyond C | Between C and F; real, inverted, diminished. |
| At C | At C; real, inverted, same size. |
| Between C and F | Beyond C; real, inverted, enlarged. |
| At F | At infinity; highly enlarged in the ideal paraxial picture. |
| Between F and P | Behind the mirror; virtual, erect, enlarged. |
| Convex mirror | Image is virtual, erect and diminished for a real object. |
5. Refraction of Light
Refraction is the change in direction of light when it crosses the boundary between two media with different optical properties. The frequency of light remains unchanged at the boundary, while its speed and wavelength change.
5.1 Refractive index
Here c is the speed of light in vacuum and v is its speed in the medium. A larger refractive index corresponds to a lower speed of light in that medium.
5.2 Snell's law
Equivalently, the refractive index of medium 2 relative to medium 1 is:
5.3 Optically denser and rarer media
When light enters a medium of higher refractive index, it bends towards the normal. When it enters a medium of lower refractive index, it bends away from the normal, provided the ray is incident obliquely.
6. Total Internal Reflection and Optical Fibre
Total internal reflection (TIR) occurs when light travelling from an optically denser medium to an optically rarer medium is incident at an angle greater than the critical angle.
6.1 Conditions for TIR
- Light must travel from a medium of higher refractive index to lower refractive index.
- The angle of incidence must be greater than the critical angle.
6.2 Critical angle
For light travelling from a medium of refractive index n1 to a medium of lower refractive index n2:
If the rarer medium is air, approximately:
6.3 Optical fibre
An optical fibre guides light through a transparent core surrounded by cladding of lower refractive index. Light can remain confined within the core through repeated total internal reflection when the fibre is designed for the required guiding conditions.
Central region through which most guided light travels.
Surrounding layer with lower refractive index than the core, supporting total internal reflection.
Total internal reflection at the core–cladding boundary.
High-bandwidth communication, medical endoscopy and sensing systems.
7. Refraction at a Spherical Surface
When light refracts at a spherical interface separating two transparent media, paraxial-ray geometry gives the spherical-surface refraction relation:
Here n1 and n2 are the refractive indices of the first and second media, u is the object distance, v is the image distance and R is the radius of curvature of the refracting surface.
8. Spherical Lenses
A lens is a transparent refracting medium bounded by two spherical surfaces, or by one spherical and one plane surface in common optical forms. The two principal types are:
Generally thicker at the centre and thinner at the edges. It is a converging lens in air.
Generally thinner at the centre and thicker at the edges. It is a diverging lens in air.
8.1 Important terms
| Term | Meaning |
|---|---|
| Optical centre | For a thin lens, a ray through the optical centre is treated as passing undeviated in the paraxial approximation. |
| Principal axis | Line passing through the optical centre and principal foci. |
| Principal focus | Point associated with convergence or apparent divergence of rays parallel to the principal axis. |
| Focal length | Distance between the optical centre and principal focus. |
8.2 Thin-lens formula
8.3 Linear magnification of a lens
8.4 Basic ray rules for a thin lens
- A ray parallel to the principal axis passes through the principal focus after a convex lens or appears to diverge from the focus after a concave lens.
- A ray through the optical centre is treated as undeviated in the thin-lens approximation.
- A ray through the principal focus of a convex lens emerges parallel to the principal axis.
8.5 Convex-lens image cases
| Object position | Image position / nature |
|---|---|
| Beyond 2F | Between F and 2F; real, inverted, diminished. |
| At 2F | At 2F; real, inverted, same size. |
| Between F and 2F | Beyond 2F; real, inverted, enlarged. |
| At F | At infinity. |
| Between optical centre and F | Virtual, erect and enlarged on the object side. |
8.6 Concave-lens image
For a real object, a concave lens normally forms a virtual, erect and diminished image between the optical centre and the principal focus on the object side.
9. Lens Maker's Formula
The focal length of a thin lens depends on the refractive index of the lens material relative to its surrounding medium and the curvatures of its two surfaces.
For a lens in air, the surrounding-medium refractive index is approximately 1, so the familiar form becomes:
Here n is the refractive index of the lens material relative to the surrounding medium, while R1 and R2 are the signed radii of curvature of the two surfaces.
10. Power of a Lens
The power of a lens measures its ability to converge or diverge light.
The SI-derived practical unit is the dioptre (D), where 1 D = 1 m−1.
- Converging convex lens → positive power.
- Diverging concave lens → negative power.
- Shorter focal length → larger magnitude of power.
11. Combination of Thin Lenses in Contact
For thin lenses placed in contact along the same principal axis, the equivalent power is the algebraic sum of their powers:
Equivalently:
Here F is the equivalent focal length.
12. Refraction Through a Prism
A prism is a transparent refracting medium bounded by two plane refracting surfaces inclined to each other. A ray passing through a prism is deviated from its original direction.
12.1 Prism terminology
- Angle of prism (A): angle between the two refracting faces.
- Angle of deviation (δ): angle between the original direction of the incident ray and the emergent ray.
- Angles of incidence and emergence: i and e.
12.2 Minimum deviation
As the angle of incidence is varied, the deviation reaches a minimum value δm. At minimum deviation, the path through the prism is symmetric:
Using Snell's law, the refractive index of the prism material relative to the surrounding medium is:
13. Optical Instruments — Big Picture
Optical instruments use lenses and/or mirrors to form images that can be observed or measured. Chapter 9 focuses on microscopes and astronomical telescopes.
| Instrument | Main purpose | Optical idea |
|---|---|---|
| Simple microscope | Angular magnification of a small nearby object. | Single converging lens used as a magnifier. |
| Compound microscope | Large angular magnification of very small objects. | Objective forms an enlarged intermediate image; eyepiece magnifies it further. |
| Refracting astronomical telescope | Viewing distant astronomical objects. | Objective forms an image; eyepiece magnifies the angular size. |
| Reflecting astronomical telescope | Collecting and focusing light from distant objects. | Uses a reflecting mirror as the main objective. |
14. Simple Microscope
A simple microscope is essentially a converging lens of short focal length. It forms a magnified virtual image when the object is placed within its focal length.
14.1 Magnifying power
For the final image at the least distance of distinct vision D:
For the final image at infinity:
Here D is the least distance of distinct vision, commonly taken as 25 cm for the normal eye in school-level calculations.
15. Compound Microscope
A compound microscope uses two converging lenses: a short-focal-length objective and an eyepiece. The objective first forms a magnified real intermediate image; the eyepiece then acts as a magnifier.
15.1 Magnifying power — final image at infinity
Here L is the effective tube length, fo is the focal length of the objective and fe is the focal length of the eyepiece.
15.2 Final image at the least distance of distinct vision
16. Astronomical Telescope — Refracting Type
A refracting astronomical telescope uses a large-focal-length objective and a shorter-focal-length eyepiece to view distant objects under high angular magnification.
16.1 Normal adjustment
For normal adjustment, the final image is formed at infinity.
The negative sign indicates inversion in the standard sign convention for angular magnification.
16.2 Final image at the least distance of distinct vision
For the standard school-level treatment of a refracting telescope, when the final image is formed at the least distance of distinct vision D:
The negative sign represents inversion in the standard angular-magnification convention. In numerical problems, use the convention and approximation specified by the question.
17. Reflecting Astronomical Telescope
A reflecting telescope uses a concave mirror as its primary light-collecting objective rather than a large objective lens. The reflected light is brought to focus and directed for viewing through the optical system.
A large mirror can collect substantial light without the chromatic-aberration issue associated with a large refracting objective lens.
The syllabus requires astronomical telescopes of both reflecting and refracting types and their magnifying powers; focus on the principle and standard textbook treatment.
18. Formula Map — Chapter 9 at a Glance
| Concept | Core relation |
|---|---|
| Spherical mirror | f = R/2 |
| Mirror formula | 1/f = 1/v + 1/u |
| Mirror magnification | m = −v/u = hi/ho |
| Refractive index | n = c/v |
| Snell's law | n1 sin i = n2 sin r |
| Critical angle | sin C = n2/n1, n1 > n2 |
| Spherical surface refraction | n2/v − n1/u = (n2 − n1)/R |
| Thin lens | 1/f = 1/v − 1/u |
| Lens magnification | m = v/u = hi/ho |
| Lens maker | 1/f = (n21 − 1)(1/R1 − 1/R2) |
| Power | P = 1/f (f in m) |
| Lenses in contact | P = P1 + P2 + … |
| Prism | δ = i + e − A |
| Minimum-deviation prism | n = sin[(A + δm)/2] / sin(A/2) |
| Simple microscope, final image at infinity | M = D/f |
| Simple microscope, final image at D | M = 1 + D/f |
| Compound microscope, final image at infinity | M ≈ (L/fo)(D/fe) |
| Compound microscope, final image at D | M ≈ (L/fo)(1 + D/fe) |
| Refracting telescope, normal adjustment | M = −fo/fe |
19. How to Choose the Correct Formula
Identify u, v, f and sign convention → use 1/f = 1/v + 1/u.
Identify u, v, f → use 1/f = 1/v − 1/u.
Use Snell's law for a plane interface or the spherical-surface formula for a curved interface.
Check denser → rarer and i > C. Then use sin C = n2/n1.
If radii and refractive index are given, think lens-maker's formula.
For thin lenses in contact, add powers algebraically.
Look for A, δ, i, e or minimum deviation δm.
Identify objective/eyepiece and whether final image is at infinity or D.
Identify refracting/reflecting type and whether the final image is at infinity.
20. High-Yield Concept Traps
Do not write the lens equation using the mirror equation's plus sign.
Incidence and refraction angles are measured from the normal.
Total internal reflection requires travel from higher refractive index to lower refractive index.
At i = C, the refracted ray grazes the interface; complete TIR occurs for i > C.
Use focal length in metres when calculating power in dioptres.
Convex and concave lens powers are added algebraically.
At minimum deviation, the path is symmetric: i = e and r1 = r2.
The negative sign in the normal-adjustment angular magnification indicates inversion in the standard convention.
21. Worked Quick Examples
Example 1 — Mirror formula
A concave mirror has focal length −20 cm and an object is placed at −30 cm. Find the image distance.
Therefore v = −60 cm. The negative sign indicates a real image on the object side under the adopted convention.
Example 2 — Critical angle
A medium has refractive index 1.5 relative to air. For light going from this medium to air:
Hence C ≈ 41.8°.
Example 3 — Lens power
A converging lens has focal length 20 cm = 0.20 m.
Example 4 — Two lenses in contact
Two thin lenses of powers +4 D and −1.5 D are in contact.
Therefore the equivalent focal length is F = 1/2.5 = 0.40 m.
22. Direct Questions Students Search
What is the mirror formula for Class 12 Physics?
The spherical-mirror formula is 1/f = 1/v + 1/u using the Cartesian sign convention.
What is Snell's law?
Snell's law is n1 sin i = n2 sin r. It relates the angles of incidence and refraction to the refractive indices of the two media.
What are the conditions for total internal reflection?
Light must travel from a higher-index medium to a lower-index medium, and the angle of incidence must exceed the critical angle.
What is lens maker's formula?
For a thin lens, 1/f = (n21 − 1)(1/R1 − 1/R2). For a lens in air, n21 is commonly written as the refractive index n of the lens material relative to air.
What is the power of a lens?
Power is P = 1/f when f is measured in metres. Its unit is the dioptre.
What is the prism formula at minimum deviation?
n = sin[(A + δm)/2] / sin(A/2).
What is the magnifying power of a simple microscope?
For final image at infinity, M = D/f. For final image at the least distance of distinct vision, M = 1 + D/f.
What is the magnifying power of a refracting astronomical telescope in normal adjustment?
M = −fo/fe, where the negative sign represents inversion in the standard angular-magnification convention.
23. Direct Questions Students Search
What is the difference between a real and virtual image?
A real image is formed where light rays actually converge and can generally be obtained on a screen. A virtual image is formed where rays only appear to meet when extended backward and cannot be obtained on a screen in the usual way.
Why does light bend during refraction?
Its speed changes when it enters a medium with a different refractive index. For oblique incidence, the change in speed causes a change in direction.
Why does frequency not change during refraction?
The frequency is fixed by the source and remains unchanged at the boundary; the speed and wavelength change according to the new medium.
Why is an optical fibre able to guide light?
The core has a higher refractive index than the cladding, allowing guided rays to undergo total internal reflection under the required conditions.
What is the difference between focal length and power?
Focal length is a length measured in metres or other length units; power is the reciprocal of focal length in metres and is measured in dioptres.
What is magnifying power?
Magnifying power is the ratio of the angle subtended by the final image at the eye to the angle subtended by the object when viewed directly at the reference distance.
23. Chapter 8 → Chapter 9 Concept Bridge
Chapter 8 established electromagnetic radiation and visible light as part of the electromagnetic spectrum. Chapter 9 now studies how light travels, reflects, refracts and forms images using the ray model.
Revise Chapter 8 — Electromagnetic Waves Notes
24. Official Reference Points
- CBSE Physics Curriculum 2026–27 — official Chapter 9 scope and assessment framework.
- CBSE Class XII 2026–27 Sample Question Paper & Marking Scheme — official examination resources.
- NCERT Physics Part-II textbook portal — official NCERT textbook access.
This page is original study material. The official CBSE curriculum and current examination documents remain the final authority if syllabus or assessment guidance changes.
25. One-Minute Revision
- Mirror formula: 1/f = 1/v + 1/u.
- Mirror magnification: m = −v/u.
- Refractive index: n = c/v.
- Snell's law: n1 sin i = n2 sin r.
- TIR: denser → rarer and i > C.
- Critical angle: sin C = n2/n1.
- Spherical surface: n2/v − n1/u = (n2 − n1)/R.
- Lens formula: 1/f = 1/v − 1/u.
- Lens magnification: m = v/u.
- Lens maker: 1/f = (n − 1)(1/R1 − 1/R2) for a lens in air.
- Power: P = 1/f, with f in metres.
- Lenses in contact: P = P1 + P2 + ….
- Prism: δ = i + e − A.
- At minimum deviation: i = e and r1 = r2 = A/2.
- Simple microscope: M = D/f at infinity.
- Compound microscope: objective first magnifies, eyepiece magnifies again.
- Refracting telescope: objective has long focal length; eyepiece has short focal length.
- Reflecting telescope: primary mirror collects and focuses light.
26. Final Chapter 9 Checklist
- ☐ Cartesian sign convention is clear.
- ☐ Spherical mirror terms, ray rules and image cases are understood.
- ☐ Mirror formula and magnification are practised.
- ☐ Refractive index and Snell's law are understood.
- ☐ TIR conditions and critical angle are clear.
- ☐ Optical-fibre principle is understood.
- ☐ Refraction at a spherical surface is revised.
- ☐ Thin-lens formula and magnification are practised.
- ☐ Lens-maker's formula and power are understood.
- ☐ Combination of thin lenses in contact is practised.
- ☐ Prism relations and minimum-deviation formula are revised.
- ☐ Simple and compound microscope magnifying power is understood.
- ☐ Refracting and reflecting astronomical telescopes are understood.
- ☐ Formula selection and sign conventions have been practised in numericals.
- ☐ Current CBSE 2026–27 scope has been checked against the official curriculum.
Learn Revise Hub note: These notes are designed for CBSE Class 12 Physics 2026–27. The current official CBSE curriculum, sample paper and marking scheme remain the final authority if the syllabus or assessment guidance is updated.
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