CBSE Class 12 Physics Revision Notes Chapter 9: Ray Optics and Optical Instruments

Ray optics treats light as rays travelling in straight lines and explains reflection, refraction and image formation.
The chapter connects mirrors, lenses and prisms with optical instruments such as microscopes and telescopes.

Ray Optics and Optical Instruments explains how light behaves at reflecting and refracting surfaces. It covers image formation by spherical mirrors and lenses, total internal reflection, prisms and the working of optical instruments.

Use these CBSE Class 12 Physics Revision Notes Chapter 9 for the 2026–27 session. Start with sign conventions and image formulas. Then revise refraction, total internal reflection, lenses, prisms, microscopes and telescopes.

Key Takeaways

• Mirror formula: 1/v + 1/u = 1/f relates object, image and focal distances.
• Snell’s law: n21 = sin i/sin r gives the relative refractive index.
• Lens formula: 1/v − 1/u = 1/f applies to thin convex and concave lenses.
• Telescope magnification: m = fo/fe for final image formed at infinity.

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Reflection by Spherical Mirrors in Class 12 Physics Chapter 9 Notes

Reflection occurs when light returns to the same medium after striking a surface.

Laws of Reflection

The laws of reflection are:

• The angle of reflection equals the angle of incidence.
• The incident ray, reflected ray and normal lie in the same plane.

These laws apply to plane and curved reflecting surfaces.

Important Terms for Spherical Mirrors

For a spherical mirror:

f = R/2

For a concave mirror, the focus is real.

For a convex mirror, the focus is virtual.

Paraxial Rays

Paraxial rays travel close to the principal axis and make small angles with it.

Most mirror and lens formulas are derived using paraxial rays and the small-angle approximation.

Cartesian Sign Convention in CBSE Class 12 Physics Chapter 9 Notes

The Cartesian sign convention is used for mirrors and lenses.

Its main rules are:

• All distances are measured from the pole of a mirror or optical centre of a lens.
• Distances measured in the direction of incident light are positive.
• Distances measured opposite to incident light are negative.
• Heights above the principal axis are positive.
• Heights below the principal axis are negative.

Mirror Sign Convention

For the usual case where light travels from left to right:

Correct signs must be substituted before solving the formula.

Mirror Formula and Magnification in Ray Optics Revision Notes

The mirror formula is:

1/v + 1/u = 1/f

Here:

• u is object distance.
• v is image distance.
• f is focal length.

The formula applies to concave and convex mirrors and to real and virtual images.

Magnification by Spherical Mirrors

Linear magnification is:

m = h′/h

For a spherical mirror:

m = −v/u

Here:

• h is object height.
• h′ is image height.

Meaning of Magnification Sign

Image Formation by a Concave Mirror

Image Formation by a Convex Mirror

A convex mirror always forms an image that is:

• Virtual
• Erect
• Diminished
• Located between P and F behind the mirror

Refraction of Light in Class 12 Physics Ray Optics Notes

Refraction of light is the change in direction of light when it travels from one transparent medium to another.

The change occurs because the speed of light changes from one medium to another.

Laws of Refraction

The laws are:

• The incident ray, refracted ray and normal lie in the same plane.
• The ratio sin i/sin r is constant for a given pair of media and wavelength.

Snell’s Law

According to Snell’s law:

sin i/sin r = n21

Therefore:

n1 sin i = n2 sin r

Here:

• i is the angle of incidence.
• r is the angle of refraction.
• n21 is the refractive index of medium 2 with respect to medium 1.

Refractive Index

The absolute refractive index of a medium is:

n = c/v

Here:

• c is the speed of light in vacuum.
• v is the speed of light in the medium.

For two media:

n21 = n2/n1

Also:

n12 = 1/n21

Direction of Bending

When light travels:

• From a rarer to a denser medium, it bends towards the normal.
• From a denser to a rarer medium, it bends away from the normal.
• Normally along the interface, it does not bend.

Optical density should not be confused with mass density.

Apparent Depth

For viewing nearly normally:

Refractive index = Real depth/Apparent depth

Therefore:

Apparent depth = Real depth/n

The apparent shift is:

Shift = Real depth − Apparent depth

Refraction Through a Glass Slab

For a parallel-sided slab:

• The ray bends at both surfaces.
• The emergent ray is parallel to the incident ray.
• It undergoes a lateral shift.

There is no angular deviation between the incident and emergent rays.

Total Internal Reflection in Class 12 Ray Optics Revision Notes

Total internal reflection occurs when light travelling from a denser medium to a rarer medium is completely reflected back into the denser medium.

Conditions for Total Internal Reflection

Both conditions must be satisfied:

• Light must travel from an optically denser medium to a rarer medium.
• The angle of incidence must be greater than the critical angle.

Critical Angle

The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°.

For a denser medium of refractive index n with air outside:

sin ic = 1/n

Therefore:

n = 1/sin ic

For two media:

sin ic = nrarer/ndenser

Cases at the Interface

Applications of Total Internal Reflection

Prisms

Right-angled prisms can use total internal reflection to:

• Turn light through 90°
• Turn light through 180°
• Invert an image without changing its size

Optical Fibres

Optical fibres consist of:

• A high-refractive-index core
• A lower-refractive-index cladding

Light undergoes repeated total internal reflection inside the core.

Optical fibres are used in:

• Communication systems
• Medical endoscopy
• Transmission of audio and video signals
• Decorative lighting

Refraction at Spherical Surfaces in Physics Chapter 9 Revision Notes

Consider refraction at a spherical surface separating media of refractive indices n1 and n2.

The formula is:

n2/v − n1/u = (n2 − n1)/R

Here:

• u is object distance.
• v is image distance.
• R is radius of curvature.
• n1 is the refractive index of the first medium.
• n2 is the refractive index of the second medium.

The Cartesian sign convention must be used.

This relation is applied separately to the two surfaces of a lens to derive lens formulas.

Lens Maker’s Formula in CBSE Class 12 Ray Optics Notes

The lens maker’s formula relates focal length to the lens material and curvatures.

For a thin lens in air:

1/f = (n − 1)(1/R1 − 1/R2)

Here:

• n is the refractive index of the lens material.
• R1 is the radius of the first surface.
• R2 is the radius of the second surface.

For a lens placed in a medium:

1/f = (nlens/nmedium − 1)(1/R1 − 1/R2)

Sign of Focal Length

• A converging lens has positive focal length.
• A diverging lens has negative focal length.

A convex lens may stop behaving as a converging lens if placed in a medium with a higher refractive index than the lens.

Thin Lens Formula in Ray Optics and Optical Instruments Class 12 Notes

The thin lens formula is:

1/v − 1/u = 1/f

It applies to:

• Convex lenses
• Concave lenses
• Real images
• Virtual images

Magnification by a Lens

Linear magnification is:

m = h′/h

For a lens:

m = v/u

Meaning of Magnification

• Positive magnification means an erect image.
• Negative magnification means an inverted image.
• Magnitude greater than 1 means an enlarged image.
• Magnitude less than 1 means a diminished image.

Ray Rules for Convex and Concave Lenses

Convex Lens

• A ray parallel to the axis passes through the second focus.
• A ray through the optical centre passes undeviated.
• A ray through the first focus emerges parallel to the axis.

Concave Lens

• A parallel ray appears to diverge from the first focus.
• A ray through the optical centre passes undeviated.
• A ray directed towards the second focus emerges parallel to the axis.

Image Formation by a Convex Lens

Image Formation by a Concave Lens

A concave lens always forms an image that is:

• Virtual
• Erect
• Diminished
• Between the optical centre and first focus

Power of a Lens in Chapter 9 Physics Notes

The power of a lens measures its ability to converge or diverge light.

P = 1/f

Here, f must be in metres.

The SI unit is dioptre.

1 D = 1 m⁻¹

Sign of Power

• Convex lens: Positive power
• Concave lens: Negative power

A lens with a shorter focal length has a greater magnitude of power.

Combination of Thin Lenses in Ray Optics Revision Notes

For thin lenses placed in contact:

1/f = 1/f1 + 1/f2 + 1/f3 + ...

In terms of power:

P = P1 + P2 + P3 + ...

The powers are added algebraically.

Magnification of a Lens Combination

The total magnification is:

m = m1 × m2 × m3 × ...

The image formed by one lens acts as the object for the next lens.

Lens combinations are used in:

• Cameras
• Microscopes
• Telescopes
• Binoculars

Refraction Through a Prism in Class 12 Physics Chapter 9 Notes

A prism is a transparent refracting medium bounded by two inclined plane surfaces.

Important Prism Angles

Let:

• A be the prism angle.
• i be the angle of incidence.
• e be the angle of emergence.
• r1 and r2 be internal refraction angles.
• δ be the angle of deviation.

The prism relations are:

A = r1 + r2

δ = i + e − A

Minimum Deviation

The deviation becomes minimum for a symmetrical ray path.

At minimum deviation:

i = e

r1 = r2

Therefore:

r1 = r2 = A/2

Also:

i = (A + Dm)/2

The refractive index of the prism is:

n = sin[(A + Dm)/2]/sin(A/2)

Here, Dm is the angle of minimum deviation.

Thin Prism Formula

For a small-angle prism:

Dm = (n − 1)A

A prism deviates light towards its base.

Dispersion of Light in Class 12 Physics Ray Optics Notes

Dispersion is the splitting of white light into its constituent colours.

The sequence is:

Violet, Indigo, Blue, Green, Yellow, Orange, Red

Cause of Dispersion

The refractive index of a material depends on wavelength.

Therefore, different colours travel at different speeds and suffer different deviations.

• Violet light deviates the most.
• Red light deviates the least.

The prism produces a spectrum because each colour emerges in a different direction.

Simple Microscope in Optical Instruments Revision Notes

A simple microscope is a convex lens of short focal length.

It forms a:

• Virtual image
• Erect image
• Magnified image

The object is placed between the optical centre and principal focus.

Let D be the least distance of distinct vision.

D ≈ 25 cm

Image at the Near Point

Magnifying power is:

m = 1 + D/f

This gives greater magnification but may cause eye strain.

Image at Infinity

For a relaxed eye:

m = D/f

The object is placed near the focus of the lens.

A smaller focal length gives greater magnification.

Compound Microscope in CBSE Class 12 Physics Chapter 9 Notes

A compound microscope uses two convex lenses:

• Objective
• Eyepiece

Working of a Compound Microscope

The objective:

• Has a short focal length.
• Is placed close to the object.
• Forms a real, inverted and enlarged intermediate image.

The eyepiece:

• Acts like a simple microscope.
• Magnifies the intermediate image.
• Produces a virtual final image.

The final image is inverted relative to the original object.

Magnification by the Objective

Approximately:

mo = L/fo

Here:

• L is tube length.
• fo is objective focal length.

Eyepiece Magnification

For the final image at infinity:

me = D/fe

For the final image at the near point:

me = 1 + D/fe

Total Magnifying Power

For the final image at infinity:

m = mo × me

m = (L/fo)(D/fe)

For the final image at the near point:

m = (L/fo)(1 + D/fe)

A compound microscope requires:

• A small objective focal length
• A small eyepiece focal length
• A suitable tube length

Astronomical Telescope in Ray Optics and Optical Instruments Notes

An astronomical telescope is used to observe distant objects.

It contains:

• An objective lens of large focal length and large aperture
• An eyepiece of short focal length

Working of a Refracting Telescope

The objective:

• Receives light from a distant object.
• Forms a real, inverted image near its focal plane.

The eyepiece:

• Magnifies this intermediate image.
• Produces the final virtual image.

For normal adjustment, the final image is at infinity.

Magnifying Power

The magnitude of angular magnification is:

m = fo/fe

The negative sign is sometimes used to show that the final image is inverted:

m = −fo/fe

Length of Telescope

For normal adjustment:

L = fo + fe

Objective Aperture

A large objective aperture:

• Collects more light.
• Helps observe faint objects.
• Improves resolving power.

Refracting and Reflecting Telescopes

A Cassegrain telescope uses a large concave primary mirror and a convex secondary mirror.

Ray Optics and Optical Instruments Formula Notes

Important Terms in Class 12 Physics Chapter 9

Access Class 12 Physics Chapter 9 Ray Optics Notes in 30 Minutes

Divide the chapter into three revision blocks:

• First 10 minutes: Spherical mirrors, sign convention, mirror formula and magnification
• Next 10 minutes: Refraction, total internal reflection, spherical surfaces and lenses
• Final 10 minutes: Prism formulas, microscope and astronomical telescope

While solving numericals, write the sign of every distance before using a formula. Also check whether an angle is measured from the normal or from the optical surface.

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