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

Have you ever looked into a mirror or through a microscope and wondered how it works? Chapter 9 of class 12 physics helps you to understand this things! These easy notes cover how light reflects and bends, how lenses and mirrors form images, and how instruments like telescopes and the human eye work. It’s a simple way to revise all the important ideas about light in one go!

This chapter is useful not just for your board exams, but also for big entrance exams like JEE and NEET. If you dream of becoming an engineer or doctor, understanding ray optics really helps. These notes are easy to follow and free to download—perfect for quick and clear revision!

See Also,

• NCERT Notes Class 12 Physics
• NCERT Solutions for Class 12 Physics Chapter 9 Ray Optics and Optical Instruments
• NCERT Exemplar Class 12 Physics Chapter 9 Ray Optics and Optical Instruments

NCERT Class 12 Physics Chapter 9 Notes

Introduction

• 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.

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.

PROPERTIES OF LIGHT
(i) Speed of light in vacuum, denoted by c , is equal to $3\times {10}^5\mathrm{m}/\mathrm{s}$ approximately.
(ii) Light is electromagnetic wave (proposed by Maxwell). It consists of varying electric field and magnetic field.

(iii) Light carries energy and momentum.
(iv) The formula $\mathrm{v}=\mathrm{f}\lambda$ is applicable to light.

REFLECTION OF LIGHT
When light rays strike the boundary of two media such as air and glass, a part of light is turned back into the same medium. This is called Reflection of Light.

(a) Regular Reflection:

When the reflection takes place from a perfect plane surface it is called Regular Reflection. In this case the reflected light has large intensity in one direction and negligibly small intensity in other directions.

(b) Diffused Reflection

When the surface is rough, we do not get a regular behaviour of light. Although at each point light ray gets reflected irrespective of the overall nature of surface, difference is observed because even in a narrow beam of light there are many rays which are reflected from different points of surface and it is quite possible that these rays may move in different directions due to irregularity of the surface. This process enables us to see an object from any position.
Such a reflection is called as diffused reflection.
For example reflection from a wall, from a news paper etc. This is why you can not see your face in news paper and in the wall.

Laws of Reflection

(i) The incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane.
(ii) The angle of incidence is equal to the angle of reflection. That is $\mathrm{\angle }i=\mathrm{\angle }r$.

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.

2. 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:-

Pole:

• 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.

Aperture

• 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

Reflection at Spherical Mirror (Laws of Image Formation):

1. A ray initially parallel to principal axis and close to it, after reflection, passes or appears to pass through the principal focus.
(from law of reflection i.e., $\mathrm{\angle }i=\mathrm{\angle }$ rand by definition of focus)

2. A ray initially passing or appearing to pass through the principal focus, after reflection, becomes parallel to the principal axis (by the principle of reversibility i.e., after any number of reflections if the direction of light ray is reversed, it retraces its whole path).


3. A ray initially passing or appearing to pass through the centre of curvature, after reflection, retraces its path.

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.

Image Formation by a Concave Mirror:

Image Formation by a Convex Mirror :

Mirror Formula

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Where:-

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

Magnification $(m)$ of a spherical mirror is defined as the ratio of the height of the image to the height of the object. Its magnitude indicates how many times the size of the image is as compared to that of the object and its sign indicates whether it is erect or inverted. Positive sign indicates an erect image and negative sign indicates an inverted image.

$m=\frac{\text{ height of the image }}{\text{ height of the object }}=\left[\frac{h^{\prime }}{h}\right]=-\frac{v}{u}$

Important points about Spherical Mirrors
You should remember the following important points while dealing with the spherical mirrors.
(i) As an object is held in front of a spherical mirror, the distance of the object $(u)$ is always negative.
(ii) The real image is formed in front of the mirror. So its distance $(v)$ is taken as negative.
(iii) The virtual image is formed at the back of the mirror. So its distance $(v)$ is taken as positive.
(iv) Focal length of concave mirror is considered as negative.
(v) Focal length of convex mirror is considered as positive.
(vi) When image formed is virtual and erect, magnification is positive.
(vii) When image formed is real and inverted, magnification is negative.
(viii) The height of the object is taken to be positive as the object is usually placed above the principal axis.
(ix) The height of the image should be taken as positive for virtual images while, it is taken as negative for real images.

Uses of Spherical Mirrors

Concave mirror is used :
(i) As a reflector in search lights, head lights of motor vehicles to get powerful parallel beams of light. It is also used in telescope, solar cookers etc.
(ii) In ophthalmoscope for reflecting light on to the retina of the eye.
(iii) As a shaving mirror, make-up mirror as it can form erect and magnified image.
(iv) By dentists to see large images of the teeth of patients.

Convex mirror is used :
As rear-view mirror in automobiles (like cars, trucks and buses) to see the traffic at the back side. Such a mirror is preferred because it has a much wider field of view as compared to plane mirror or a concave mirror and always produces an erect image.

Refraction of Light

Refraction is the phenomenon in which direction of propagation of light changes (as shown in the figure) when it passes from one transparent medium to another. This is because, the speed of light is different in different media.

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.

$\frac{\sin i}{\sin r}=$ constant $=n_{21}$

This constant value $n_{21}$ is the optical property of the two media and is called refractive index of medium 2 with respect to medium 1. If the first medium is air, then $n_{21}$ is called absolute refractive index or simply refractive index of medium 2. It is then simply denoted as $n$.

Conditions for no refraction
1. If light is incident normally on a boundary $(\mathrm{\angle }i=0)$.

From Snell's law

$\begin{array}{rl}& \frac{\sin i}{\sin r}=n_{21}\Rightarrow \frac{\sin 0^{\circ }}{\sin r}=\frac{n_2}{n_1}\\ & \Rightarrow n_1\sin 0^{\circ }=n_2\sin r\\ & \text{ or }\sin r=0\text{ or }\mathrm{\angle }r=0^{\circ }\end{array}$

So, light ray in the second medium will pass undeviated at the boundary.

2. If the refractive indices of two media are equal $(n_1=n_2)$,

From Snell's law,

$\begin{array}{ll}& n_1\sin i=n_2\sin r\\ \text{ or }& n\sin i=n\sin r\\ \text{ or }& \mathrm{\angle }i=\mathrm{\angle }r\end{array}$

So, light ray in the second medium will pass undeviated at the boundary.

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 90^o 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 90^o. That is the angle of incidence should be greater than the critical angle.

Applications of Total Internal Reflection

• Optical Fibres:-

• They are used in the telecommunications industry.

• 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

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.

n=n₁/n_{2
Refraction through a parallel slab
When light passes through a parallel slab, having same medium on both sides, then
(a) Emergent ray is parallel to the incident ray.
(b) Light is shifted laterally, given by (students should be able to derive it)}

$d=\frac{t\sin (i-r)}{\cos r};t=$ thickness of slab

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.

Lens Formula

As we have a formula for spherical mirrors, we also have a formula for spherical lenses. This formula gives the relationship between object-distance ( $u$ ), image distance $(v)$ and the focal length $(f)$. The lens formula is expressed as

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

Lens Maker’s Formula

$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$

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

Power $(P)$ of a lens characterises the converging or diverging properties of a lens and is defined as the reciprocal of its focal length.

$P=\frac{1}{(f\text{ in }\mathrm{m})}=\frac{100}{(f\text{ in }\mathrm{cm})}$

The SI unit of power of a lens is 'dioptre' and is denoted by the letter D.

Combination of Thin Lenses in Contact

Power and Focal Length of the Combination of Lenses
If a number of lenses are combined (or placed adjacent and touching each other) to increase the magnification, then the net power of the combination $(P)$ is given as

$P=P_1+P_2+P_3+\dots \dots \dots$
As $P=\frac{1}{F}$ so for effective focal length $(F)$,

$\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}+\dots \dots \dots \dots$

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.

Dispersion : It is the separation of light into its constituent colours.
Spectrum : When light undergoes dispersion the band of colours obtained is called spectrum.
The band of colours obtained with the white light is violet, indigo, blue, green, yellow, orange and red (VIBGYOR).

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.

ANGLE OF DEVIATION

$\delta =(i+e)-A$

where $i=$ Angle of incidence
$e=$ Angle of emergence
$A=$ Angle of prism

CONDITION FOR MINIMUM DEVIATION

For minimum deviation
(i) Refracted ray becomes parallel to the base of the prism.
(ii) Angle of incidence becomes equal to the angle of emergence. i.e., $\mathrm{\angle }i=\mathrm{\angle }e$

Hence minimum angle of deviation $\delta ={\delta }_m$

$\begin{array}{c}{\delta }_m=i+i-A\\ {\delta }_m=2i-A\end{array}$

Critical Angle

It is the angle of incidence in denser medium corresponding to which the angle of refraction in rarer medium is ${90}^{\circ }$. It is represented by $C$ and depends upon nature of media in contact. Mathematically, it is given by the relation.

$\sin C=\frac{1}{n}\Rightarrow C={\sin }^{-1}\left(\frac{1}{n}\right)$

where, $n\to$ Refractive Index of the denser medium with respect to rarer medium.
$C\to$ Critical angle in degree
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:-

Binoculars

Telescope

Microscopes

Eye

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.

Microscope

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:-

m=v/u=v(1/v-1/f)

= 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:-

tanθ₀=h/D≈θ₀

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).

θ_i= h/f

The angular magnification is m=θ_i/θ₀=D/f

m =(θ_i/θ₀) =(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 (m_o) due to objective =h'/h=L/f₀

Where

h’ = size of the first image

h = size of the object

f₀ = focal length of the objective lens

f_e= 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:-

m_e=1+D/f_e

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

m_e=D/f_e

Total magnification will be given as:-

m=m₀m_e=(L/f₀)(D/f_e)

Telescope

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.

Magnification

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/f_e)(f₀/h)=f₀/f_e

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

We use refracting telescopes for both terrestrial and astronomical observations.

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