Optics is the branch of physics which deals with study behavior, effect and properties of light. Optics can be classified into three branches:

Ray Optics or Geometrical Optics
Wave Optics or Physical Optics
Quantum Optics

`text(Ray or geometrical optics)`
It concerns itself with the particle nature of light and is based on (i) the rectilinear propagation of light and (ii) the laws of reflection and refraction of light. It explains the formation of images in mirrors and lenses, the imperfection of optical images and the working and designing of optical instruments.

`text(Wave or physical optics)`
It concerns itself with the wave nature of light and is based on the phenomena like: (i) interference (ii) diffraction and (iii) polarization of light.

`text(Quantum optics)`
It deals with the interaction of light with the atomic entities of matter such as Photoelectric effect, Atomic excitation etc.

• Light is a form of energy which produces visual sensation in our eyes. Light is an electromagnetic waves which is transverse in nature. The speed of light in vacuum is `3 xx 10^8` m/s.
• When a light ray strikes on the surface of any object and gets reflected to reach our eyes, our eyes feel a sensation and we see the object. Our eyes are mostly sensitive for yellow color and least sensitive for violet and red color. Due to this reason commercial vehicles are painted with yellow color, sodium lamps are used in road lights.

`text(Properties of Light)`
(i) The particles of light emitted from the source carry energy from one point of the medium to another.
(ii) The source transmits energy in the medium and in this way energy propagates in the form of a wave.
(iii) It propagates in straight line.
(iv) It's velocity in vacuum is maximum whose value is `3 xx 10^8 m//sec (299,792,458 m//s)`
(v) Light does not need a material medium to travel that is it can travel through vacuum.
(vi) It exhibits the phenomena of reflection, refraction, interference, diffraction, polarization and photo-electric efFect.

Various theories about nature of light have been proposed from time to time. Some of the main theories are as follows:

`text(Corpuscular Theory of light)`
Newton, the greatest among the great, proposed in 1675 AD, According to this theory: Light is of particle nature.
(i) A source of light sends tiny, elastic massless, particles called corpuscles.
(ii) These corpuscles travel in all directions in straight lines with same speed.
(iii) The speed of corpuscles (light) is more in denser medium than in rarer medium.
(iv) Different colors of light are due to difference in the size of corpuscles.
(v) Vision is the result of stimulation of retina by corpuscles.
(vi) As corpuscles come out from the source, the mass of source decreases.

`text(Draw backs)`
(i) 'The corpuscular theory explained reflection and refraction (some extent), but it could not explain the other phenomena of light.
(ii) Decrease in mass of source of light, when it emits corpuscles is not observed.
(iii) Foucault's Rotating Mirror experiments proved that light travels with high speed in optically rarer medium and with low speed in optically denser medium and contradicts with Newton's assumption.

`text(Wave Theory of Light)`
In 1678, Dutch scientist Christian Huygens, suggested that light travels in the form of waves just as sound propagates through air. He proposed that light waves propagate through an hypothetical medium, called ether medium. Later on, the existence of such a medium was discarded due to its contradictory properties.
(i) Light propagates in the form of Transverse (Mechanical) Progressive Waves.
(ii) For the propagation of these light waves it is assumed that a hypothetical elastic, less dense, invisible medium called Ether medium is required.
(iii) Different colors of light arc due to difference in the frequency of waves.
(iv) Velocity of light is more in optically rarer medium and is less in optically denser medium.

`text(Drawbacks)`
(i) It explained most of the phenomena of light like Reflection, Refraction, Interference and Diffraction, but it could not explain Photo-electric effect etc.
(ii) The assumption of existence of Ether medium is proved wrong by Michelson-Morley experiments.

`text(Electromagnetic Theory of Light)`
In 1873, Maxwell suggested that light propagates as electric and magnetic field oscillations. "These are called electromagnetic waves which requires no medium for their propagation. Also, these waves are transverse in nature.
(i) Light is a form of energy which is propagated as electromagnetic waves with a speed `3 xx 10^8 ms(-1)` through vacuum.
(ii) An electromagnetic wave consisting of oscillating electric E and magnetic B fields which are perpendicular to each other and perpendicular to the direction of wave propagation. It is non mechanical wave, so that it does not require any material medium for its propagation.

`text(Color Wavelenth (nm))`
`text(VIOLET 400-450)`
`text(BLUE 450-520)`
`text(GREEN 520-560)`
`text(YELLOW 560-600)`
`text(ORANGE 600-625)`
`text(RED 625-700)`

(V) Electromagnetic waves exhibit all the phenomena of light. They carry momentum and energy along with them.

`text(Draw Backs)`
It could not explain Photo-electric effect, Compton Effect, Raman Effect etc.

`text(Note)`
Frequency of visible light is of the order of `10^(14) Hz`, while the maximum frequency that we can get with modern electronic circuits is of the order of `10^11 Hz.`

`text(Quantum Theory of Light)`
• According to Quantum theory, light is discrete in nature, it is not continuous. When light falls on the surface of metals like cesium, potassium etc., electrons are given out. These electrons are called 'photoelectrons' and phenomenon is called 'photo-electric effect.'

• This was explained by Einstein. According to Max Planck light consisted of packets or quanta's of energy called photons. The rest mass of photon is zero. Each quanta carries energy `E= h nu`

`h-> "Planck's constant"= 6.6 xx 10^(-34) J-s, nu-> "frequency of light"`

• Every electromagnetic wave is associated with a discrete energy packet called Quanta or Photon. Photon has no charge, it travels with a speed `c = 3 xx 10^8 s ms^-1`

• Einstein's photo-electric equation `h(v- v_0) = (l/2)mv^2_(max)`
`hv_0` = amount of energy spent in ejecting and electron out of metal surface.
`v_(max)` = maximum velocity of the ejected electron

• So we see that in phenomena like interference, diffraction and polarization, light behaves as a wave. While in Photoelectric effect, Raman Effect, Compton Effect etc. it behaves as a particle.

• Later on, De-Broglie suggested that light has a dual nature. i.e., it can behave as particles as well as waves.

`text(Draw Backs of Quantum Theory)`
It explained only the phenomena like Photo-electric effect, Raman Effect, Compton Effect etc. but not the phenomena connected with Wave nature of light.

`text(Note)`
From the observed facts, experiments and various theories of nature of light, it is concluded that light has Dual Nature, when it is propagating it takes electromagnetic wave nature while interacting with matter it exhibits particle behavior (photon).

`(i) "Luminous Bodies:"` The bodies which give out light energy by themselves are called luminous bodies. Example: The sun, the stars, burning candle, glowing electric bulb etc.

`(ii) "Non-Luminous Bodies:"` The bodies which do not give light energy on their own, but reflect light energy falling on them are called non-luminous bodies. Example: Planets, Moon, Rocks, Mirror, etc.

`(iii) "Optical Medium:"` Anything (material or non-material), through which light energy passes wholly or partially, is called optical medium. Example: Vacuum, air, most of the gases, water, glass, plastics, etc.

`(iv) "Homogeneous Medium:"` An optical medium which has uniform composition throughout is called homogeneous medium. Example: Vacuum, distilled water, pure alcohol, glass, plastics, diamond etc.

`(v) "Heterogeneous Medium:"` An optical medium, which has different composition at different points is called heterogeneous medium. Example: Air, muddy water, fog, mist etc.

`(vi) "Transparent Medium:"` A medium which allows most of the light energy to pass through it, is called transparent medium. Example: glass

`(vi) "Translucent Medium:"` A medium which partially allows the light energy to pass through it is called translucent medium. In such a medium, we cannot see through clearly. Example: Butter Paper, oiled paper, tissue paper, ground glass.

`(viii) "Opaque Bodies:"` Those bodies which do not allow the light energy to pass through them are called opaque bodies. We cannot see through opaque bodies. "These bodies can either absorb light energy or reflect it. Example: Bricks, wood, stones, metals etc.

`(ix) "Point Source of Light:"` A source of light which is of the size of pin head is called point source of light.

`(x) "Extended Source of Light:"` Any source of light, which is bigger than point source of light is called extended source of light. Example: A bulb, a tube light, a burning candle, etc.

`(xi) "Ray of Light:"` The path along which light energy travels in a given direction is called ray of light. A ray of light is represented as a straight line. The arrowhead on it gives the direction of light.

`(xii) "Beam of Light:"` A collection of number of rays of light is called beam of light. Sometimes, if the number of rays are too small then such a collection of rays is called pencil of light.

`(xiii) "Parallel Rays:"` When the rays of light travel parallel to each other, then the collection of such rays is called parallel rays. E.g. Sun rays entering into a room through a ventilator constitute a parallel beam of light.

`(xiv) "Divergent Beam:"` When the rays of light originating from a point, travel in various directions, then the collection of such rays is called divergent beam. E.g. rays originating from a point source of light constitute divergent beam.

`"(xv) Convergent Beam:"` When the rays of light coming from different directions, meet at a point, then the collection of such rays is called convergent beam.

• The phenomenon due to which, when a ray of light travels from one optical medium to another optical medium, a part of the incident light is thrown back into the original medium is called reflection of light.

Or

• Reflection of light is the phenomenon of bouncing back of light in the same medium on striking the surface of any object.

`"Reflection is of Two Types"`
Regular Reflection
Irregular Reflection or diffused reflection

`(i) "Regular Reflection"`
When the reflecting surface is smooth and well-polished, the parallel rays falling on it are reflected parallel to one another, as shown in figure 2.7, i.e., the reflected light goes in one particular direction. This is regular reflection. The smooth and well-polished surface is called a mirror. Silver metal is one of the best reflectors of light

`(ii) "Irregular reflection"`
When the reflecting surface is rough, the parallel rays falling on it are reflected in different directions, as shown in figure 2.8. Such a reflection is known as diffused reflection or irregular reflection.

`(i) "Mirror:"` Any smooth polished surface which can turn rays of light into the same medium is called the mirror. When a glass plate is polished on one side with reflecting material such as silver or nickel then it becomes a mirror.

`(ii) "Incident Ray:"` A ray of light which travels from an optical medium towards the mirror is called the incident rays.

`(iii) "Reflected Ray:"` A ray of light which bounces off the mirror surface, into the same optical medium in which incident ray was travelling, is called the reflected ray.

`(iv) "Normal:"` A light perpendicular to the surface of mirror.

`(v) "Point of incidence:"` The point on the mirror surface, where the incident ray strikes the mirror is called point of incidence.

`(vi) "Angle of incidence:"` The angle which the incident ray makes with the normal is called the angle of incidence.

`(vii) "Angle of Reflection:"` The angle which the reflected ray makes with normal is called angle of reflection.

`(viii) "Rectilinear Propagation of Light:"` Light travels in straight line. It is called Rectilinear Propagation of Light. The formation of shadows (eclipses) is due to Rectilinear Propagation of Light.

`text(Note)`
Principle of Reversibility: If a light ray is reversed, it always retraces its path. It is called the Principle of Reversibility. So that the object and image positions are interchangeable. So they are conjugate points.

When light travelling in one medium falls on the surface of a second medium, the following three effects may occur.

(i) A part of the incident light is turned back into the first medium. This is called reflection of light.

(ii) A part of the incident light is transmitted into the second medium along a changed direction. This is called refraction of light.

(iii) The remaining third part of light energy is absorbed by the second medium. This is called absorption of light.

Consider a reflecting surface (say a plane mirror) `M_1 M_2` ,. Let a ray of light AB falls on the surface at B which comes back along BC. The ray of light AB is known as incident ray and the ray BC is known as reflected ray.

`"According to law of reflection:"`
(i) Angle of incidence is equal to angle of reflection i.e. `angle i = angle r`
(ii) The incidence ray, reflected ray and normal to the reflecting surface at the point of incidence are coplanar.

`text(Note)`
• Non luminous bodies are visible only when the light reflected from them reaches our eye.
• Laws of reflection are same whether the reflecting surface is plane or curved. Reflection of light from the curved surfaces is shown in

`(i) "Plane Mirror:"` A highly polished plane surface is called a plane mirror or if a flat (totally plane) surface of a glass plate is polished on one side with reflecting material, it becomes a plane mirror.

`(ii) "Spherical Mirror:"` A mirror whose polished, reflecting surface is part of a hollow sphere of glass, is called a spherical mirror. For a spherical mirror, one of the two curved surfaces is coated with a thin layer of silver followed by a coating of red lead oxide paint. Thus one side of the spherical mirror is made opaque and the other side acts as a reflecting surface. For the polishing side there are two type of spherical mirror. (a) Convex mirror (b) Concave mirror

`(a) "Concave (Converging) Mirror:"` A spherical mirror whose inner hollow surface is the reflecting surface.

`"(b) Convex (diverging) Mirror:"` A spherical mirror whose outer bulging out surface is the reflecting

• Object is a point of intersection of the incident rays.
• Image is a point at which all the reflected rays or refracted rays intersect after passing through an optical system.
• An object is said to be real if the incident rays are diverging in natural's.
• An object is said to be virtual if the incident rays are converging in nature.
• If the light rays after reflection or refraction are converging in nature, then the image is a real image.
• An image is said to be virtual when the light rays after reflection or refraction are diverging in nature.

(i) The image formed by a plane mirror is virtual.

(ii) The image formed by a plane mirror is erect.

(iii) The image formed by a plane mirror is of the same size as that of an object.

(iv) The image formed by a plane mirror is at the same distance behind the mirror as the object is in front of it.

(v) the image is laterally inverted i.e. the right side of the object appears as the left side of the image and vice versa.

(vi) The reflected ray deviates from the direction of incident ray by an `angle delta = pi - 2i`
`text(Derivation:)`
`i +i + delta = pi` ........ angles in linear pair
`delta = pi - 2i`

(vii) For a given incident ray, if the mirror is rotated through an angle `theta`, then the reflected ray turns through an angle of `2theta`
The new angle of incidence `i' =i + theta`
`angleROR' = angleSOR' - angleSOR`
`i^'=r^'` and ` i=r`
So `"ROR"' (i'+r') - (i+r) = 2i- 2i = 2(i+theta)-2i+2 theta`

(vii) The length of the plane mirror to have the full length image of a person standing in front of it, is equal to half the height of the person.

(ix) When two plane mirrors are placed at an angle 8 to each other, the object is kept between them, then the number of images observed is `n = 360° // theta`
If n is even then it is `(n- 1).` 'n' should be always odd number.

(x) When two plane mirrors are held facing each other and parallel to each other `(theta = 0^o)` and the object is kept between them, then the number of images observed is infinite.

`(i) "Pole:"` Geometric Centre of the spherical mirror is called pole. It is denoted by the letter P.

`(ii) "Centre of Curvature:"` The Centre of the imaginary sphere to which the mirror belongs is called the Centre of curvature. The Centre of curvature of a concave mirror is in front of it but the Centre of curvature of a convex mirror is behind it.

`(iii) "Radius of Curvature:"` It is radius of the imaginary sphere of which the mirror is a part.

`(iv) "Principal Axis:"` The straight line passing through the pole and Centre of curvature is called the
principal axis.

`(v) "Principal Focus:"` The principal focus of a spherical mirror is a point on the principal axis of the mirror, where all the rays travelling parallel to the principal axis and close to it after reflection from the mirror converge to for concave mirror or appear diverge from for convex mirror. Thus, a concave mirror has a virtual focus but a convex mirror has a virtual focus because the rays appear to come from focus.

`(vi) "Focal Length:"` It is the distance of the principal focus from the pole of the mirror If R is radius of curvature of the mirror of focal length, f, then `R = 2f.`

`text(Lateral Inversion)`
The phenomenon due to which the image of an object turns through an angle of 180° through vertical axis rather than horizontal axis, such that the right side of the image appears as left or vice versa is called lateral inversion.

`text(Inversion)`
During inversion image tums around horizontal axis through an angle of 180°.

To construct the image of an extended object the image of two end points is only drawn. To construct the image of a point object two of the following four rays are drawn passing through the object.

(i) The ray moving parallel to principal axis-will pass through principal focus F or appear to diverge from it after reflection.

(ii) The ray passing through principal focus F or a ray which appears to converge at F will become parallel to principal axis after reflection.

(iii) A ray passing through centre of curvature C will retrace its path as it is incidental normally .

(iv) A ray falling at pole making some angle with the principle axis will make the same angle with the principal axis after reflection.

Let us start with the object at infinity and gradually bring it nearer to the mirror. The following cases arise:

`(i) "When the object lies at infinity:"` We have real, inverted & diminished image formed at focus.

Use: E.N.T. specialist use a concave mirror as a 'head mirror' to concentrate light on the body parts like eye, ear, nose, throat etc. to be examined. The mage is real, inverted, very much diminished and on the focus.

`(ii) "When the object lies beyond the Centre of curvature:"` Let AB be an object, placed beyond C, the Centre of curvature of the mirror. A'B' is the image of AB formed by the mirror and as is clear from the figure 2.23, it is between the focus and the Centre curvature, and it is real, inverted and diminished.

Use: Reflecting telescope

`(iii) "When the object lies at the Centre of curvature:"` Let the object AB, lie at C; the Centre of curvature of the mirror. We get the image A'B', of the object AB. Which also lie at the Centre of curvature. Image is real, inverted and of the same size as the object.

`(iv) "When the object lies in between the Centre of curvature and the focus:"` Let the object AB be now placed between C and Fin figure 2.25. We have its real inverted and magnified image A'B', formed beyond C, the Centre of the curvature of the mirror.

Use: Floodlight have the light source between the center and the focus of a concave mirror in order to spread the rays.

`(v) "When the object lies at the focus:"` Here, we consider a point object (0) at the focus F, rays from it, incident on the mirror are rendered parallel and will meet at infinity. And thus the image is formed at infinity, and is real, inverted and highly magnified.

Use: Search light, car head lights, and flush lights have the light source near the focus of a concave mirror to use this property.

`(vi) "When the object lies in between the focus and the pole of the mirror:"`
Let an object above placed on the axis of the mirror, between F and P (pole of the mirror). Then proceeding exactly as in case (v) above, we find that the two reflected rays DF and OC appear to meet at A', when produced backwards, and thus we get a virtual magnified and erect image A'B' of the object AB, behind the mirror.

Use: Shaving mirrors, dental mirrors, make up mirrors for ladies use this arrangement to get
virtual, magnified image.

`(vii) "When the object lies very near to the pole of mirror:"`
If we have a small or a point object placed right on the pole of the concave mirror, then since a small portion of it would just behave like a plane mirror, we shall have an image of the object, in accordance with the ordinary laws of reflection at plane surfaces. Image will also lie at the pole of the mirror and will be virtual, erect and of the same size, but laterally inverted.

`text(Note)`
For a concave mirror when an object is moved from `-infty` to F, the image (real) moves from F to `-infty` and then when the object is further moved from F to P, the image (now virtual) moves from `+infty` to P.

• In the case of a convex mirror only two positions of the object, are possible (i) at infinity and (ii) between infinity and the pole of the mirror.

• In either case, the image lies behind the mirror and is virtual erect and extremely diminished.

`(i) "When object is at infinity:"` Image position will be at focus F. Nature of image is virtual and point sized.

`(ii) "When object is between infinity and the pole:"` Image position will be between the focus and the pole. Nature of image is virtual, smaller and erect.

Number of sign conventions are in use. New Cartesian sign conventions used herein, are explained as
under:

•All the distances are measured from the pole of the spherical mirror.

• Distances measured in the direction of incident light are taken as positive whereas the distances measured in the direction opposite to that of the incident light are taken as negative.

• The upward distances perpendicular to the principal axis are taken as positive, while the downward distances perpendicular to the principal axis are taken as negative.

`text(Note)`
As per the new sign convention, Focal length 'f' and radius of curvature 'R' are negative for a mirror and positive for a convex mirror.

If an object is placed at a distance u from the pole of a mirror and its image is formed at a distance v (from the pole), then as shown, if angle is very small:

`alpha = (MP)/(u), beta = (MP)/(R), gamma =(MP)/(v)`

from `DeltaCMO, beta=alpha +theta`.......(i)
from `DeltaCMI,gamma = beta+theta`........(ii)

Subtracting (ii) from (i) we get
`2beta = gamma + alpha`

Therefore putting the above values of alpha, beta, and gamma in this equation we get,
`2/R= 1/u+1/v`.......(iii)

`text(Relation between f and R for the Spherical Mirror:)`
If Q is near to pole P then from `DeltaQCP tan theta approx theta = (QP)/(R)` and
from `DeltaQFP` `tan 2theta aproxx theta = (QP)/(f)`
so `(2QP)/(2) = (QP)/f => f = R/2`.....(iv)

Form (iii) and (iv) we have the relation, known as the Mirror Formula,
`1/f= 1/u+1/v`

Caution: Always use the formula with proper sign convention.

`text(Linear Magnification)`
It is defined as the ratio of the height of the image to the height of the object, it is denoted by m.
if `h_2=` height of the image and `h_1` = height of the object

`DeltaABP` and `DeltaA'B'P` are similar, so `(-h_2)/(h_2) = (-v)/(-u)`
So liner magnification of a spherical mirror is `m = (h_2)/(h_1)=(-v)/(u)`

• If `|m| > 1,` i.e., linear magnification is greater than one, then image is magnified or enlarged, size of image is greater than the size of the object.

• If `|m| = 1,` i.e., linear magnification is equal to one, then image is of the same size as that of the object.

• If `|m| < 1,` i.e., linear magnification is less than one, then image is smaller than the object.

`text(Power of a Mirror)`
The power of a mirror is defined as `p = - 1/f(m) = - 100/(f(m)`

`text(Note)`
Radius of Curvature of a plane mirror is infinite and so is its focal length.

`text(Concave Mirror)`

(i) Concave parabolic mirrors are used in search light, motor head light, torch etc.

(ii) Concave parabolic mirrors are used as dish antennas to receive and send radio signals.

(iii) Concave mirrors are preferred over plane mirror for shaving and make up. When a man keeps his face between the pole and the focus of the concave mirror, virtual, erect and highly magnified image of his face is formed. It helps him to have a better shave, similarly, a lady can see her face better with the help of a concave mirror while doing make up.

(iv) Concave mirrors are used as reflectors in cinema projectors.

(v) Concave mirrors are used by dentists and ENT specialists to focus light on teeth, an eye or in the ear or a nose to examine these organs.

(vi) It is preferred in solar cookers to focus the sun light.

`text(Convex Mirror)`

(i) Convex mirror is used as a rear view mirror because it produces erect and diminished images, since the image is small in size, so the field view is increased, this mirror is also known as driver's mirror.

(ii) It is used as a reflector for street lighting purpose.


`text(Note)`
If an object is placed with its length along the principal axis, then so called longitudinal magnification is given as,

`m_L = text(Length of Image)/text(Length of Object)= -(v_2-v_1)/(u_2-u_2) = - (Deltav)/(Deltau)`