CBSE Class 12 Physics Revision Notes Chapter 9

Class 12 Physics Chapter 9: Ray Optics and Optical Instruments

Class 12 Physics Chapter 9 Notes

Chapter 9 Physics Class 12 notes discuss light and essential phenomena related to light. This Chapter also explains different applications of optics in instruments like a microscope, telescope, etc. Several laws of reflection, Refraction and properties of light are described in detail. The notes include graphical representation and coloured illustrations to make learning engaging and interesting . These illustrations come handy in comprehension, problem solving and brainstorming 

The Class 12 Physics Chapter 9 notes are essential for students to attain good scores in the exams. Extramarks provides high-quality academic CBSE revision notes which are prepared strictly as per the latest guidelines for students to study efficiently and  improve their scores. 

 Class 12 Physics Chapter 9 Notes: Key Topics

REFLECTION OF LIGHT BY SPHERICAL MIRRORS

What is a Spherical Mirror?

It is a part of the reflective spherical surface and is spherical in shape. Spherical mirrors consist of a large number of extremely small plane mirrors.

They are of two types:

Concave Mirror: It is a mirror which is silvered on the inward part of the sphere and does not face the incident light. It is a converging mirror where the rays of light converge or meet at a single point. 

Convex Mirror: It is a mirror which is silvered on the outward part of the sphere. Here the rays of light do not meet at a particular point after reflection. Therefore, it is said to be a diverging mirror.

Basic Terminologies

Pole: The geometric centre of the reflecting surface of the mirror is said to be the Pole and is denoted by P. It serves as an origin and lies on the surface of the spherical mirror. 

Centre of curvature:

The mirror’s reflecting surface forms a part of an imaginary sphere. The sphere’s centre or midpoint of the aperture is called the centre of curvature and is denoted by C. For a concave mirror, C is in front, whereas for a convex mirror, it is behind it. 

NOTE: The centre of curvature does not lie on the mirror. It lies outside of the reflecting surface of the spherical mirror. 

The radius of curvature

The radius of an imaginary sphere from which the reflecting surface of a spherical mirror is cut is called the radius of curvature and is denoted by R.

Principal axis

A straight line which passes through the pole and the centre of curvature of the spherical mirror is the principal axis. The principal axis is normal or perpendicular to the mirror at the pole.

Focus

The rays which are parallel to the principal axis fall on a concave mirror that meets or intersects at the point on the principal axis. The point is known as the focus of the concave mirror.

The reflected rays appear to come from the point on a principal axis when the rays parallel to the principal axis fall on the convex mirror. This point is termed the principal focus of the convex mirror. It is denoted by F.

The distance between the pole and the focus of a mirror is known as the focal length and is represented by F. .

Aperture

Aperture is the diameter of the reflecting surface of the spherical mirror. 

If the aperture is smaller than the radius of curvature(R), we get R= 2f.

It is essential for students to gain a deeper understanding of these terms to understand complex concepts included in the Class 12 Physics Chapter 9 notes. 

Image formation by Spherical Mirrors

• The light rays passing through the centre of curvature trace the same path.
• The ray of light which passes parallel to the principal axis after reflection passes through the principal focus.
• The light rays passing through F get reflected back and travel parallel to the principal axis.
• There are two types of images formed: –

1. Real images of an object are formed where the reflected rays meet. It is inverted and formed on the same side of the object.
2. Virtual images of the object are formed where the reflected rays appear to meet. It is erect and cannot be obtained on the screen as it is formed beyond the spherical mirror.

Sign Conventions

1. The pole (P) is considered the origin. The principal axis of the mirror is considered to be the x-axis of the coordinate system.
2. The object is always placed on the left-hand side of the mirror. This means that the light will fall on the mirror from the left.
3. The distances that are parallel to the principal axis of the spherical mirror are measured from the pole of the mirror.
4. The distances measured from the right of the origin are taken as positive, and those to the left of the origin will be taken as negative.
5. The distances measured perpendicular to the principal axis, i.e., along + y-axis, will be taken as positive and along – y-axis are taken as negative.
6. The heights which are measured upwards for the x-axis are normal to the principal axis of the mirror or  lens and are positive, and the heights measured downwards will be negative.
7. The radius of curvature (R) and the focal length of a concave mirror is always negative, and for a convex  mirror are positive.

The signs and conventions are essential in solving problems included in the Class 12 Physics Chapter 9 notes. 

Mirror Formula

For a Concave Mirror

Let u be the distance of the object from the pole known as object distance, v is the distance of the image from the pole known as image distance, and f is the distance of principal focus from the pole, called the focal length. 

(1v) + (1u) = (1f) is the mirror equation for concave mirror and 

(1f) = (1v) – (-1u) is the mirror equation for convex mirrors. 

Students can practice a number of problems included in the Class 12 Physics Chapter 9 notes. 

Magnification of a Spherical Mirror:

Linear magnification of a spherical mirror, denoted by m, gives the proximate extent to which the image of the object can be magnified with respect to the object size.

Mathematically,

m= (height of the image h’height of the object h)

Or, m = (h’h)

If magnification is negative, then it implies that the image is real, and if it is positive, then the image is taken to be virtual.

For a concave mirror, m = (-vu) and for a convex mirror, m= -(vu)

REFRACTION OF LIGHT

Light travels in different directions in different media. When the light rays pass obliquely from a rarer medium to the denser medium, the direction of the propagation of light changes.

When a light ray passes from one medium to another, it bends. This is refraction.

This phenomenon takes place due to the change in the velocity of light from one medium to another.

Laws of Refraction (Snell’s law):

The incident light ray, refracted light ray and normal at the incidence point lie in the same plane.

The ratio of sin (i) to sin (r) is constant.

The angle of incidence (i) is described by the incident ray and is normal. Similarly, the angle of refraction (r) is the angle between refracted ray and the normal.

21 = (sin isin r)

Where 21= is the refractive index of the second medium with respect to the first.

NOTE: The refractive index (21) is dependent on the wavelength of light and the characteristic of mediums.

If 21 >1, r<i, this implies that the refracted light ray bends towards the normal. Therefore, the second medium will be optically denser than the first medium.

If 21<1, r>i this implies that the refracted light ray bends away from the normal. Therefore, the second medium will be optically rarer than the first medium.

Refraction through a Rectangular Glass Slab

For a parallel-side slab, refraction occurs at two interfaces, i.e., at the air-glass and glass-air interface. The emergent ray passes in the direction parallel to the incident ray. Therefore, there will be no deviation.

However, there is a lateral shift with respect to the incident ray.

The refractive index of medium 2 with medium 1 is given as 21=21, where 1, 2= refractive index of medium 1 and 2 ,respectively. 

To understand the refraction of light thoroughly, students  must  refer to the Class 12 Physics Chapter 9 notes. 

Natural phenomena of Refraction 

1. Advance Sunrise and Delay in Sunset:

We can see the sun a little before the actual sunrise occurs and a little after the actual sunset. This happens due to the phenomenon of the refraction of light in the atmosphere.

Actual sunrise means the crossing of the horizon by the sun.

The apparent shift of light towards the sun is by approximately half a degree and therefore this results in a corresponding time difference between the actual sunset and apparent sunset by a difference of 2 minutes.

The oval shape of the sun when it sets and rises is also due to the refraction.

1. Twinkling 

We know that stars have their own light. They appear to be twinkling because as the light reaches our eye, it passes through different layers of the atmosphere.

At one point in time the  star appears to be at one position, and in another minute, it is at another position. This means that the object is at two different places at a frequent time interval. 

Each concept is well explained in the Class 12 Physics Chapter 9 notes. 

TOTAL INTERNAL REFLECTION

When the ray of light travels from the optically denser medium to an optically rarer medium, it gets partly reflected into the first medium and partly refracted into the second. This reflection is known as internal reflection.

In total internal reflection, the refraction of light into the second medium does not take place. This means that the entire incident ray gets reflected.

Conditions for Total Internal Reflection(TIR)

• Light rays must pass from optically denser to an optically rarer medium.
• When a ray of light travels, it moves away from the normal. Refraction takes place at a point r (angle of refraction).
• If the angle of incidence increases, the light ray moves away from normal, and the angle of refraction reduces.
• On further increasing the angle of incidence(i), the angle of refraction becomes equal to 90.  If the angle of incidence increases more, then  no refraction will occur. In this case, the reflection will take place. This is  known as Total Internal Reflection.

The limiting factor will be as follows: 

• The angle of incidence for which the angle of refraction is 90 must be smaller than the angle of incidence (i).
• The angle of incidence must be equal to the angle of refraction = 90. This is the Critical angle.
• The angle of incidence (i) has to be greater than the critical angle.

Refer to the Class 12 Physics Chapter 9 notes to solve unlimited problems, quickly and master the topic in no time.. 

APPLICATIONS OF TOTAL INTERNAL REFLECTION:

1. Optical Fibres:

They are used for telecommunication. The optical fibres work based on the total internal reflection.

Characteristics:

They are small in size 

They are light in weight.

They can carry greater information than metallic wires.

Working:

The optical fibres are fabricated with high-quality glass or  quartz fibres. Each fibre is made up of a core and cladding. 

The refractive index of the material used in the core is greater than the cladding material.

Because of the difference in the refractive index of core and cladding, the core becomes a denser medium, and cladding becomes the rarer medium.

The optical fibres are used in  fibre optic endoscopy and communication systems. They are also used as decorative items.  

The Class 12 Physics Chapter 9 Notes includes detailed information about optical fibres. 

2. Prism: 

• Prisms are based on the phenomena of total internal reflection in binoculars.
• They are designed to bend the light ray by 90º or 180º to invert images without changing the size.
• The critical angle in a prism, for the medium of the prism must be less than 45°.

3. Mirage: 

• On hot days, the air closer to the ground is hotter than the air at higher levels. 
• With respect to the refractive index,  hotter air is less dense than cooler air and has a smaller refractive index. If the air currents are small, then the optical density of air increases with height. Therefore, light from a tall tree passes through a medium where the refractive index of air decreases towards the ground. 
• Thus, the ray of light from tall objects bends away from the normal and total internal reflection occurs if and only if the angle of incidence (i) is greater than the critical angle. 
• To an observer at a distance, the light comes from somewhere below the ground, say, by a pool of water near the tree. The inverted images of trees cause an illusion to the observer. This phenomenon is known as a mirage. It commonly occurs in hot deserts. 

4. Diamond: 

• Diamonds are known for their spectacular brilliance due to multiple total internal reflections of light rays inside them. 

All important derivations and formulas are included in the Class 12 Physics Chapter 9 notes.

REFRACTION AT SPHERICAL SURFACES

Consider refraction at a spherical surface between two transparent mediums. A small part of a surface is regarded as planar, and the same laws of refraction are applied at every point.

The incident rays travel from the first medium of the refractive index 1, to the second of the refractive index 2.

(2v) – (1u) = (2 – 1R) gives the relation between object distance (u) and image distance (v) with refractive index and radius of curvature. 

 LENS  MAKER’S FORMULA

The refracting surface forms the image (I1) of object O.

The image is considered as a virtual object for the second surface and forms an image at point I. 

Applying equation, we get

(n1OB) + (n2BI1) = (n2–n1BC1) (Equation 1)

Similarly, for second interface ADC: (n2DI1) + (n1DI) =(n2–n1DC2) (Equation 2)

For thin lenses, BI1 = DI1.

Adding equation (1) and (2), we get

(n1OB) + (n1DI) = (n2–n1)(1BC1 + 1DC2) (Equation 3)

Suppose the object is at infinity and DI =f,

Therefore using Equation (3),

(n1f)=(n2–n1)(1BC1 + 1DC2) (Equation 4) 

The lens has two principal foci, F and F′, on either side of it.

Using sign convention,

BC1 = + R1, DC2 = –R2

Therefore, equation (4) becomes,

(1f)=(21-1)(1R1 – 1R2) Equation(5) is the Lens Maker’s Formula.

NOTE: The formula holds for a concave lens as well. In this case, R1 is negative, R2 positive and so, f will be negative.

From equation 3 and 4, (n1OB) + (n1DI) =(n1f)

For approximation, we take B and D very close to the optical centre of the thin lens.

Using sign conventions, BO=-u and DI=+ v

(1v)- (1u) = (1f) is the thin lens formula.

It is valid for convex and concave lenses.

Students must regularly practice the sums included in the Class 12 Physics Chapter 9 notes based on each concept.

Power of a lens:

The power (P) is defined as the tangent of the angle by which it converges or  diverges a beam of light which falls at a unit distance from the optical centre.

P =(1f) where f = focal length measured in  metres.

The power of a lens measures the convergence or divergence of a lens.

A lens with a short focal length bends the incident light more, converging for convex and diverging for concave.

The SI unit for power is dioptre (D):

The Power is positive for a converging lens and negative for a diverging lens.

Combination of thin lenses in contact

Consider lenses A and B having focal lengths f1 and f2 to be placed in contact with each other.

(1f) = (1f1) + (1f2) + (1f3) + … 

In terms of power, P = P1 + P2+ P3+ … where P is the total (net) power of the combination of thin lenses.

This helps to meet particular magnification, enhances the sharpness of the image and also eliminates the defects in the lens. 

It is commonly used in designing lenses for cameras and other optical instruments like microscopes and telescopes.

REFRACTION THROUGH PRISM

A Prism is a transparent optical material made up of flat polished surfaces which can refract light.

The angle of deviation δ tells how much the emergent ray has deviated from the incident ray.

The angles of incidence and refraction at AB are i and r1. The angle of incidence is r2 and the angle of emergence is e.

The angle made by the emergent ray and incident ray is the angle of deviation (δ) = (i + e – A) 

It depends on the angle of incidence (i).

As (i) increases, the angle of deviation decreases, and when the angle of incidence is equal to the angle of emergence, then the angle of deviation is minimum and starts decreasing.

This implies min when ∠i = ∠e.

Angle of Deviation

When the angle of deviation is minimum, the refracted ray inside the prism is parallel to the base.

Therefore, the refractive index is given as 21 = ((A + min )/ 2A/2)

Angles A and min are experimentally measured. Therefore we can say that min =(21-1). A

To gain in-depth knowledge about this concept, refer to the Class 12 Physics Chapter 9 notes. 

DISPERSION OF LIGHT
Splitting white light into different colours is dispersion. The pattern of colours obtained on the screen is said to be the spectrum. The red light bends the least, whereas the violet light bends the most. 

Causes of Dispersion:

• Newton proved the prism has a property due to which white light is split into its constituent seven colours with each colour having a different wavelength.
• The colours get deviated with different angles of deviation.

NATURAL PHENOMENA DUE TO LIGHT

Rainbow

A rainbow occurs due to the combined effect of dispersion, refraction and reflection of sunlight by droplets of water.

It appears when the sun is shining in  one half of the sky  and rain falls on the other. .

Refraction occurs first when sunlight enters a raindrop. It causes the different wavelengths of light to separate.

Next, total Internal reflection takes place when light rays strike the inner part of the droplet. Here, the angle of refraction is greater than the critical angle. 

Now, the reflected light gets refracted again while coming out of the drop.

Thus, the different colours of light emerge at different angles and form a rainbow.

Scattering of light 

As sunlight travels, it gets scattered by the particles present in the atmosphere. 

Light of shorter wavelengths scatter more.

The sky appears to be blue because  blue has a shorter wavelength and spreads more widely. . 

At sunset or sunrise, the sunlight passes through a larger distance in the atmosphere. Most of the shorter wavelengths are removed by scattering. The least scattered light reaching our eyes is red. Therefore, the sun looks reddish in  appearance near the horizon.

Several objective questions are included in the Class 12 Physics Chapter 9 notes based on the natural phenomena due to light. 

OPTICAL INSTRUMENTS

Optical instruments use the properties of reflection and refraction of mirrors, lenses and prisms.

Some optical instruments are:

Human Eye

The light enters the human eye through the cornea. It passes through the pupil in the iris. Muscles can control the size of the pupil.

The light is focussed by the eye lens on the retina, which is a  layer  of nerve fibres  on the rear surface of the human eye.

The retina then transmits electrical signals to the brain through the optic nerve. The curvature and focal length are modified by the ciliary muscles.

This property is termed as accommodation. 

The least distance of distinct vision is the closest distance for which the lens can focus light on the retina.

The standard value for normal vision is about 25 cm. It increases with age. It may be about 7 to 8 cm in a child and may increase to 200 cm at 60 years of age.

If an elderly person tries to read at a distance of about 25 cm from the eye, then the image appears blurred. This condition is called Presbyopia.

Optical Defects of the Eye:

• Myopia: The light from an object kept at a distance arrives at the eye lens and converges at a point in front of the retina. This defect is called near-sightedness or myopia. To correct this, a concave lens is interposed between the eye and the object.
• Hypermetropia: – When the light from an object kept at a distance arrives at the eye lens and converges at a point behind the retina, it is called farsightedness or hypermetropia. A  converging lens is interposed between the eye and the object.
• Astigmatism: It occurs when the shape of the cornea is not spherical. Astigmatism results in lines only in one direction being well focussed. However, it can be corrected by using a cylindrical lens of the desired radius of curvature.

The Human Eye is an important concept in the Class 12 Physics Chapter 9 notes.

Microscope: 

The microscope is an instrument that gives an enlarged image of a small object. It includes a converging lens of a small focal length.

1. Simple Microscope

• The lens is kept near the object, and the eye is positioned closer to the lens from the other side.
• The image will be erect, magnified and virtual.

Increase Magnifying Power of a Simple Microscope

• If the object is kept at a distance f, then the image is obtained at infinity. But, if the object is at a distance less than f, then the image is virtual but slightly closer than infinity.

Linear magnification (m) =(1 +(Df)), where D is distance and F  is focal length.

Questions based on the magnifying power of  the microscope are included in the Class 12 Physics Chapter 9 Notes. 

1. Compound Microscope

To get large magnifications, a compound microscope is used.

The lens near the object (objective) forms a real, inverted, magnified image of the object. It serves as the object for the second lens(eyepiece), functions as a simple microscope and produces an enlarged and virtual image.

Let h’ = size of the first image, h= size of the object, fo = focal length of the objective lens, fe= focal length of the eye-piece and L = Distance between the focal length of the objective lens and the focal length of the eye-piece.

Total magnification will (m) = (mome) =(Lfo)(Dfe)

Students must learn the difference between simple and compound microscopes using Class 12 Physics Chapter 9 notes. 

Telescope:

• A telescope is used to view objects which are very far from us clearly.
• It consists of an Objective lens and an Eyepiece

Working:

• The telescope provides angular magnification of faraway objects. The objective has a greater focal length and aperture than the eyepiece as the object is very far away.
• The light coming from a distant object enters the objective, and an image is formed at its second focal point. The image is real and inverted and acts as an object for the eyepiece, which magnifies and produces a final inverted image.

The magnifying power (m) ≈ () = (fofe), where β is the angle subtended by the final image at the eye, and α is the angle subtended at the lens or the eye.

Extramarks provide solutions to all questions in the Class 12 Physics Chapter 9 notes. 

Class 12 Physics Chapter 9 Notes: Exercise &  Solutions

The Class 12 Physics Chapter 9 notes are very important for board exams and competitive exam preparation. Students can gain practice with many CBSE extra questions and objective and subjective questions. It provides logical solutions to all exercise questions. Each solution in the Class 12 Physics Chapter 9 notes is well explained in a step by step manner. It strictly follows the latest CBSE syllabus and NCERT books. The CBSE Class 12 Physics Chapter 9 Notes provided by Extramarks strengthen the student’s foundation in Physics. 

Refer to the links below to access the in text and end text exercises and answer solutions for Class 12 Physics Chapter 9: 

Class 12 Physics Chapter 9 notes: Key Features

• Class 12 Physics Chapter 9 notes are a complete guide and will help students ace their exams. 
• Extramarks CBSE Class 12 Physics Chapter 9 notes are prepared by  subject matter experts  in Physics.
• The explanations provide conceptual clarity and solve all doubts of the students. The students obtain a basic understanding of all fundamental concepts.
• The Class 12 Physics Chapter 9 notes provide  step by step solutions for all the topics for thorough knowledge and conceptual clarity .
• The notes of Class 12 Physics Chapter 9 are prepared by analysing several CBSE  past years question papers and CBSE sample papers.