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NCERT Class 12 Physics Chapter 9 Notes Ray Optics and Optical Instruments - Download PDF

NCERT Class 12 Physics Chapter 9 Notes Ray Optics and Optical Instruments - Download PDF

Edited By Vishal kumar | Updated on Feb 02, 2024 05:18 PM IST

Class 12 Physics Revision Notes for Chapter 9: Ray Optics and Optical Instruments - Free PDF Download

Chapter 9 of NCERT Class 12 Physics explores Ray Optics and Optical Instruments. These class 12 physics chapter 9 notes provide a concise overview of key concepts required to understand light phenomena. Topics covered include light reflection by spherical mirrors, image formation by spherical mirrors, mirror formula, refraction of light, total internal reflection, lens maker's formula, lens power, and the operation of optical instruments such as the human eye, microscope, and telescope. The cbse class 12 physics ch 9 notes cover basic equations but do not include derivations.

Notably, this chapter is relevant not only for board exams but also for competitive exams such as JEE and NEET. Understanding these concepts is critical for aspiring engineers and physicians. Additionally, these Ray Optics and Optical Instruments class 12 notes are freely accessible as a PDF, providing students with a convenient resource to reinforce their understanding and excel in their academic pursuits.

See Also,

NCERT Class 12 Physics Chapter 9 Notes


  • In the chapter Ray Optics and Optical Instruments, we will learn about light and try to understand some important phenomena related to light and applications of optics in different optical instruments like microscopes, telescopes etc.

  • We will learn the phenomenon of laws of reflection and refraction play an important part in our day to day life.

  • With the help of light, we see all the objects around us.

  • Also, we will understand that certain objects enhance the properties of light more as compared to others.

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What is Light?

  • We know that light is a form of energy that enables us to see things around us.

  • Light is known to travel in a straight path.

  • The speed of light is given by c=3 ×108 m/s.

  • Light waves are considered to be the most common form of Electromagnetic waves.

  • Ray of light is the actual path of the light wave travelling from one point to another.

  • a beam of light is nothing but a bunch of rays of light.

Reflection of Light by Spherical Mirrors

  • The bouncing back off of a ray of light when it strikes a boundary between different media through which it cannot pass is the reflection of light.

  • With the help of reflection, we are able to see different objects in this world.

Laws of Reflection

There are two laws of reflection

  • The angle of reflection is equal to the angle of incidence (angle between incident ray and the normal). ∠i=∠r

  • In the same plane the incident ray, reflected ray and the normal to the reflecting surface at the point of incidence lie together.


Note: - These laws are valid at each point on any reflecting surface whether it is a plane or curved surface.

Spherical Mirrors

  • A spherical mirror is a part of a reflective spherical surface and they are spherical in shape.

  • It is a combination of a large number of extremely small plane mirrors.

Spherical Mirrors are of two types:-

  1. Concave Mirror: -

  • They are silvered on the inner side of the sphere.

  • It is a converging mirror.

  • In a Concave mirror, the reflected rays meet or converge at a point and are known as converging mirrors.

  1. Convex Mirror: -

  • They are silvered on the outer side of the sphere.

  • In Convex mirror the reflected rays don’t meet at a point after reflection and are known as diverging mirrors.


Some terminologies related to Spherical Mirrors:-


  • The centre of the reflective surface of a spherical mirror is known as the pole.

  • It generally lies on the surface of the mirror.

  • We usually represent the pole by the letter P.

Centre of curvature:

  • The surface of a spherical mirror that is reflecting is a part of a sphere. In other words, the centre of the sphere is only termed as the centre of curvature.

  • We represent it by the letter C.

  • The centre of curvature is not at all a part of the mirror. It generally lies outside its reflecting surface.

  • Generally, the position of the centre of curvature of a concave mirror is in front of it.

  • But it lies behind the mirror in case of a convex mirror.

Radius of curvature

  • The radius of curvature is nothing but the radius of the sphere.

  • It is represented by R.

Principal axis

  • The straight line that passes through the pole and the centre of curvature of a spherical mirror is known as the Principal axis.

  • Principal axis is perpendicular to the mirror at its pole.

Principal Focus

  • The rays that are parallel to the principal axis falling on a concave mirror meet or intersect at the point on the principal axis, are known as the principal focus of concave mirrors.

  • The reflected rays come from a point on the principal axis where the rays parallel to the principal axis fall on a convex mirror. This point is known as the principal focus of convex mirrors.

  • The principal focus is represented by F.

  • When we measure the distance between the pole and the principal focus of a spherical mirror it is considered to be the focal length of the spherical mirror. It is represented by f.


  • In a spherical mirror, the diameter of the reflecting surface is known as the aperture.

  • For mirrors with a smaller aperture than their radius of curvature, we use R=2f

Image Formation By Spherical Mirror

  • When the light rays pass through the centre of curvature then it retraces its path.

  • The light rays parallel to the principal axis, pass through the focus after reflection.

  • The light rays passing through F are reflected back parallel to the principal axis.

Sign Convections:-

  • We take the pole (P) of the mirror as the origin. The principal axis of the mirror is considered to be the x-axis (X’X) of the coordinate system.

  • We consider the object to be placed to the left of the mirror. We assume that the light from the object always falls on the mirror from the left-hand side of the mirror.

  • We measure all the distances that are parallel to the principal axis from the pole of the mirror.

  • We measure all the distances to the right of the origin (along + x-axis) and take it as positive while those measured to the left of the origin (along – x-axis) are taken as negative.

  • Distances that are measured perpendicular to and above the principal axis (along + y-axis) are taken as positive whereas those which are measured along (-y-axis) are taken as negative.

  • The heights that are measured upwards with respect to the x-axis and normal to the principal axis (x-axis) of the mirror/ lens are considered to be positive. The heights that are measured downwards are taken to be negative.

  • We take the radius of curvature and the focal length of a concave mirror are negative and those for a convex mirror are positive.

Mirror Formula



u is the distance of the object measured from its pole

v is the distance of the image measured from the pole of the mirror

f is the distance of the principal focus measured from the pole

The mirror equation gives the relation between the image distance (v) with object distance (u) and focal (f) length of the mirror.

Magnification of a Spherical Mirror

Linear Magnification (m) of a spherical mirror tells us the extent to which the image of an object can be magnified with respect to the object size.


Or, m= h'/h

If the magnification is negative it means that the image is real and if it is positive then it means that the image is virtual.

Refraction of Light

  • Speed of light is not equal in all media. The direction of propagation changes, when a light ray passes obliquely from a rarer medium (air) to a denser medium (water, glass).

  • The bending of light at the boundary when it passes from one medium to another is known as refraction.

  • Refraction is due to change in the speed of light while entering from one transparent medium to another.


Laws of refraction given by Snell’s law

  1. In the same plane the incident ray, the refracted ray and the normal to the interface at the point of incidence, all lie together.

  2. We take the ratio of the sine of the angle of incidence to the sine of the angle of refraction to be constant.

The angles of incidence (i) and refraction (r) are the angles that the incident and its refracted ray make with the normal, respectively.

n21=sin i /sin r

Where n21is the refractive index of the second medium with respect to the first medium.

If n21>1, r<1 then the refracted ray bends towards the normal. Medium 2 will be optically denser compared to medium 1.

If n21<1,r>1 then the refracted ray bends away from the normal. Medium 2 will be optically rarer compared to medium 1.

Total Internal Reflection

When lightweight travels from an optically denser medium to a rarer medium at the interface, it is partly reflected into a similar medium and partly refracted to the second medium. This reflection is known as internal reflection.

In total internal reflection, there is no refraction and the entire incident ray will get reflected.


Total Internal Reflection

  • When a ray of light passes from a denser medium to a rarer medium it always bends away from the normal.

  • But if we increase the angle of incidence it will move from normal and the angle of refraction will become less.

  • Now, if we keep on increasing the angle of incidence, the angle of refraction will become equal to 90o and with a further increase in the angle of incidence there will be no refraction but reflection will take place. This is total internal reflection.

  • The conditions for total internal reflection are:-

  • The angle of incidence should be greater than the angle of incidence for which the angle of refraction is 90o. That is the angle of incidence should be greater than the critical angle.

Applications of Total Internal Reflection

  • Optical Fibres:-

  • They are used in telecommunication industries.

  • Optical fibres work on the phenomenon of total internal reflection.

Characteristics of Optical Fibres:-

  • They are small in size and light in weight. They can carry more information than metallic wires.

Working of Optical fibres:

  • Optical fibres are fabricated with high-quality composite glass/quartz fibres.

  • Each fibre consists of a core and cladding due to which the refractive index of the material of the core is higher.


  • The signal has repeated total internal reflections along the length of the fibre. It finally comes out at the other end, when a signal is in the form of light. It is directed at one end of the fibre at a suitable angle.

  • The light undergoes total internal reflection at each stage. There is no loss in the intensity of the light signal.

  • Optical fibres are fabricated in such a way that the light reflected at one side of the inner surface strikes the other at an angle larger than the critical angle.

  • Light can easily travel along its length if the fibre is bent. An optical fibre can be used to act as an optical pipe and is made up of plastic.

Glass vs. Plastic Optical Fibres

Plastic Optical fibres

Glass Optical fibres

1. Cheaper

They are not so cheap.

2. Flexible

They are not so flexible.

3. They can withstand more stress.

They cannot withstand more stress.

4. Less efficient transmission.

More efficient transmission over large distances.

Applications of Optical Fibers

  1. Fibre optic endoscopy

  2. Decorative items

  3. In communication system

  4. Prism

Refraction at Spherical Surfaces

  • Let us consider refraction at a spherical interface between two transparent media. An infinitesimal part of a spherical surface can be regarded as planar. The same laws of refraction are applicable at every point on the surface.

  • The rays are incident from a medium of refractive index n1, to another medium of refractive index n2.


Lens Maker’s Formula


Here, f is focal length, n is the refractive index, R1 and R2 are radii of curvature of two refracting surfaces of the lens.

Power of a Lens

  • We define the power of a lens as the tangent of the angle by which it converges or diverges a beam of light falling at a unit distant from the optical centre.

tanδ=h/f if h =1


Or δ= 1/f for a small value of δ.

Therefore, P=1/f

Where P = power of the lens and f = focal length of the lens in meters.

In other words power of a lens is defined as a measure of the convergence or divergence produced by a lens.

A lens of a shorter focal length bends the incident light more. The light is converging in the case of convex and diverging in the case of concave.

The SI unit of power of a lens is given as dioptre (D)

1D = 1m–1.

It means that the power of a lens of a focal length of 1 metre is one dioptre.

We have the positive power of a lens for a converging lens and the negative for a diverging lens.

Combination of Thin Lenses in Contact

The effective focal length of combination of several thin lenses of focal length f1, f2, f3... that are in contact is given by:


In terms of power, P=P1+P2+…

A combination of lenses helps

(a) To meet desired magnification

(b) To enhance the sharpness of the image.

(c) To make the erect image.

(d) To remove certain defects of the lens.

This system of combination of lenses is used in cameras, microscopes, telescopes and other optical instruments.

Refraction by Lens: Convex & Concave

  1. A ray of light incident on the lens parallel to the principal axis after refraction passes through the second principal axis.

  2. A ray of light passing through the first principal focus after refraction should move parallel to the principal axis.

  3. A ray of light passing through the optical centre goes undeviated after refraction.

Magnification of a Lens

  • It is defined as the ratio of the size of the image to the size of the object.

  • It is denoted as m= h'/h=v/u

Refraction Through Prism

Prism is a transparent optical material with flat polished surfaces that refracts light.


Incident Ray: - The ray entering the prism.

Refracted Ray: - The ray coming out of the prism inside the prism.

Emergent Ray: - The ray coming out of the prism.

The angle of deviation δ:-The angle showing the deviation of emergent ray from the original incident ray.

The angle of Prism: - The angle of prism ∠A is known as the angle of prism.

  • With the increase in the angle of incidence, the angle of deviation decreases. When it reaches a point where the angle of incidence is equal to the angle of emergence, the angle of deviation is minimum, and again it will start decreasing.

Optical Instruments

  • Optical instruments are the instruments that use the reflecting and refracting properties of mirrors, lenses and prisms.

  • A number of optical devices and instruments use reflecting and refracting properties of mirrors, lenses and prisms.

  • Some examples of optical devices and instruments are periscope, kaleidoscope, binoculars, telescopes; microscopes

Some examples of optical instruments consisting of lenses and prisms are mentioned below:-





Human Eye

Our eyes are organs that have the capability to interpret incoming electromagnetic waves in the form of images through a complex process. These are our greatest assets and we must take proper care to protect them.

Components of Eye:-

  1. Cornea

  2. Aqueous Humour

  3. Pupil

  4. Iris

  5. Lens

  6. Ciliary Muscles

  7. Vitreous humour

  8. The retina contains Rods and Cones.


  • Light enters the eye through a curved front surface, known as the cornea. After that, it passes through the pupil which is the central hole in the iris. Under the control of muscles, the size of the pupil can change

  • On the retina, the light is focused by the eye lens. The retina contains a film of nerve fibres that covers the curved back surface of the eye.

  • The retina has rods and cones which senses light intensity and colour respectively and transmit electrical signals through the optic nerve to the brain. It finally processes this information.

  • In order to maintain the same image-lens distance (≅5 cm), the focal length of the eye lens becomes shorter by the action of the ciliary muscles, when the object is brought closer to the eye.

  • This is called accommodation. If the object is very close to the eye, then the lens cannot curve enough to focus the image onto the retina, and as a result, the image is blurred.

  • The shortest distance for which the lens can focus light on the retina is called the least distance of distinct vision, or the near point.

  • The standard value for normal vision is 25 cm.

  • The near point may be as close as about 7 to 8 cm in a child of ten years of age. It may increase to 200 cm at 60 years of age.

  • The image appears to be blurred if an elderly person tries to read a book at about 25 cm from the eye. This defect of the eye is called presbyopia.

Some Optical Defects of Eye

Myopia: - When the light from a distant object arriving at the eye-lens gets converged at a point in front of the retina. This defect is called near-sightedness or myopia.

It means that the eye is producing too much convergence in the incident beam. We interpose a concave lens between the eye and the object, with the diverging effect desired to get the image focused on the retina, in order to correct this defect.


Hypermetropia: - If the eye-lens focuses the incoming light at a point behind the retina, a converging lens is needed to compensate for the defect in vision. The defect is called farsightedness or hypermetropia.


Astigmatism:- It occurs when the cornea is not spherical in shape.

Due to astigmatism, we see perpendicular lines in one direction that are focused and appear to be distorted.

Astigmatism is basically corrected by using a cylindrical lens of the desired radius of curvature. This defect can also occur along with myopia or hypermetropia.



The microscope is an instrument that gives an enlarged image of a minute object.

There are 2 types of the microscope:-

  • Simple

  • Compound

Simple Microscope

It is an instrument that gives an enlarged image of a minute object.

  • The lens is held near the object and the eye is positioned close to the lens on the other side.

  • The image that we get is erect, magnified and virtual at a distance so that it can be viewed comfortably, i.e., at 25 cm or more.

To Increase Magnifying Power of Simple Microscope

  • If the object is at a distance ‘f’ the image will be formed at infinity. If the object is at a distance slightly less than the focal length of the lens in that case the image is virtual and closer than infinity.

  • The closest comfortable distance for viewing the image is when it is at the near point at a distance D≅25cm. But it causes some strain on the eye.

  • Therefore, we consider the image formed at infinity to be the most suitable for viewing by the eye.


We can acquire linear magnification ‘m’, for the image shaped at the close to purpose D, by an easy magnifier by the relation:-


= 1-(v/f)

Using the sign conventions, v = (-) ive and same as D.

Therefore, magnification will be m=1+(D/f)

D is 25 cm, so in order to have a magnification of six, one needs a convex lens of focal length, f = 5 cm.

Magnification When The Image is at Infinity-

Suppose the object has a height h. The maximum angle subtended and clearly visible without a lens is at a distance D.

The angle subtended is then given by:-


Therefore, h/'h=m=v/u

The angle subtended by the image will be:-

tanθ1=h'/(-v)= [h/(-v)][v/u]

= h/(-u)≈θ

When the object is at u, the angle subtended by it is (-f).

θi= h/f

The angular magnification is m=θi0=D/f

m =(θi0) =(D/f)

Compound Microscope

In order to have large magnifications, a compound microscope is used.


The lens that is nearest to the object is known as the objective. It forms a real, inverted, magnified image of the object. This act as the object for the second lens known as the eyepiece. It acts like a simple microscope or magnifier, produces the final image, which is enlarged and virtual.

The first inverted image is near the focal plane of the eyepiece. The final image is inverted.

Using tanβ=h/f0=h'/L

Magnification (mo) due to objective =h'/h=L/f0


h’ = size of the first image

h = size of the object

f0 = focal length of the objective lens

fe= focal length of the eye-piece

L = Distance between the focal length of the second objective lens and the first focal length of the eye-piece.

  • If the final image is formed at the near point, then in that case the angular magnification will be:-


  • If the final image is formed at infinity, then, in that case, angular magnification due to the eyepiece is:-


Total magnification will be given as:-



An instrument is used to view distant objects clearly.

It consists of

(a) Objective lens

(b) Eyepiece

Working of Telescope

We use the telescope for angular magnification of distant objects. The objective lens has a large focal length and a much larger aperture than the eyepiece as the object is very far away.

Light from a distant object enters the objective and a real and inverted image is formed at its second focal point.

This image acts as an object for the eyepiece and it magnifies this image producing a final inverted image.


The magnifying power ‘m’ is nothing but the ratio of the angle β subtended at the eye by the final image to the angle α that is subtended by the object at the lens or the eye.

Therefore, m≈β/α=(h/fe)(f0/h)=f0/fe

In this case, the length of the telescope tube is f0+ fe.

We use refracting telescopes for both terrestrial and astronomical observations.


Significance of NCERT class 12 physics chapter 9 notes

Comprehensive Revision: The NCERT Ray Optics and Optical Instruments class 12 notes provide a concise summary of the chapter, allowing students to effectively review key concepts.

Main Topic Coverage: These class 12 physics chapter 9 notes provide a clear outline of the main topics covered in the Ray Optics and Optical Instruments chapter, allowing students to focus on the most important areas.

Syllabus Coverage: Effective for covering the main topics in the Class 12 CBSE Physics Syllabus while ensuring alignment with curriculum requirements.

Preparation for Competitive Exams: These Ray Optics and Optical Instruments notes class 12 are valuable resources for competitive exams such as VITEEE, BITSAT, JEE Main, NEET and others, allowing students to prepare thoroughly for such assessments.

Versatile Use: The availability of physics class 12 chapter 9 notes pdf format allows students to use them for preparation both online and offline, improving

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Frequently Asked Question (FAQs)

1. What are the main derivations covered in the Ray Optics and Optical Instruments Class 12 notes?

No derivations are covered in the NCERT notes for Class 12 Physics chapter 9. This NCERT note is a brief of the main topics and equations covered in the chapter and can be used for revising the Ray Optics and Optical Instruments.

2. According to Ray Optics and Optical Instruments, will the focal length of a lens for red light be more, same or less than that for blue light?

The focal length of a lens for red light will be larger than that for blue light.

3. What are optical fibres? Give their one use

Optical fibres consist of thin and long strands of fine quality glass or quartz coated with a thin layer of material of refractive index less than the refractive index of strands. They work on the principle of total internal reflection so they do not suffer any loss.


The optical fibres are used in medical investigations i.e. one can examine the inside view of the stomach and intestine by a method called endoscopy.

4. Is Ray Optics and Optical Instruments class 12 notes important for NEET?

Yes, understanding Ray Optics and Optical Instruments Class 12 notes is crucial for NEET as it covers topics relevant to optics, which are frequently tested in the physics section of the exam

5. ou are given prisms made of crown glass and flint glass with a wide variety of angles. Suggest a combination of prisms according to the notes for class 12 physics chapter 9 which will (a) deviate a pencil of white light without much dispersion, (b) disper

(a) Place the two prisms beside each other. Make sure that their bases are on the opposite sides of the incident white light, with their faces touching each other. When the white light is incident on the first prism, it will get dispersed. When this dispersed light is incident on the second prism, it will recombine and the white light will emerge from the combination of the two prisms.

(b) Take the system of the two prisms as suggested in answer (a). Adjust (increase) the angle of the flint-glass-prism so that the deviations due to the combination of the prisms become equal. This combination will disperse the pencil of white light without much deviation.

These topics can also be downloaded from Ray Optics and Optical Instruments class 12 notes pdf download.


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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg


An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)


Option 2)

\; K\;

Option 3)


Option 4)


In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)


Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)


Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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