# UPSC Physics Electric Current and Magnetism Electricity, Magnetism and Light

## Electricity, Magnetism and Light

Category : UPSC

ELECTRICITY, MAGNETISM AND LIGHT

ELECTRICITY, MAGNETISM

Electricity is the branch of physics in which we study electric charges, at rest (electrostatics or static electricity) and in motion (current electricity).

When we switch on the bulb of our rooms, it glows immediately. An electric signal in a conductor travels at a speed of light in vacuum. An electric current flowing in a conductor produces a magnetic field or magnetism around it.

ELECTRIC CHARGES

Charge is something associated with matter due to which it produces and experiences electric and magnetic effects.

Every atom contains two types of charged particles:

(i) Positive charge (Proton) and (ii) Negative charge (electron)

The magnitude of elementary positive or negative charge is same and is equal to$1.6\times {{10}^{-19}}C$.

Charge is a scalar quantity and its SI unit is ampere second or coulomb (C).

Basic Properties of Electric Charge

(i) Similar charges repel and opposite charges attract.

(ii) Charge is conserved i.e., the charge can neither be created nor be destroyed but it may simple be transferred from one body to other. Charge is transferable.

CONDUCTORS AND INSULATORS

The materials which allow electric charge (or electricity) to flow freely through them are called conductors.

The materials which do not allow electric charge to flow through them are called non-conductors or insulators.

Examples of good conductors are metals, impure water etc.

Examples of insulators are quartz, glass, air, rubber, etc.

Silver is the best conductors of electricity.

CLOUD FORMATION, THUNDERING AND LIGHTNING

Clouds are very small droplets of water in the form of vapour. Clouds roam about in the sky with the wind. Generally, a patch of cloud develops an electric charge on it by friction. As a result of friction the upper layers of cloud (which are away from earth) get positively charged and the lower layers of cloud (which are facing earth) get negatively charged.

Dry and pure water are bad conductors of electricity, hence clouds continue to carry the charge on them till the intensity of charge between the two gets too high.

When two patches of cloud bearing different charges cone face to face they get attracted to one another and the electrons from negatively charged cloud jump to the positively charged cloud. The jumping of electrons between the clouds results in a big spark. The heat from the spark results in sudden expansion of air setting the air in violent waves which are heard by us as thunder. The spark is seen as a flash of lightning first and then followed by a thunder, a little later.

To protect tall buildings from damage by lightning, a lightning conductor is fixed on them.

COULOMB’S LAW

The force exerted by one point charge (when separation between charged bodies is much larger than their linear sizes) on another, acts along the line joining the two charges and it varies inversely as the square of the distance separating the charges and is proportional to the product of the charges. The force is repulsive if the charges have the same sign and attractive if the charges have opposite signs.

i.e., $F=\frac{k/{{q}_{1}}{{q}_{2}}/}{{{r}^{2}}}$

Where k is an experimentally determined constant called the Coulomb constant, which has the value

$k=9\times {{10}^{9}}N{{m}^{2}}/{{C}^{2}}$

It is common practice to express k in terms of another constant ${{\varepsilon }_{0}}$, by writing $k=1/(4\pi {{\varepsilon }_{0}});{{\varepsilon }_{0}}$; is called the permittivity of free space or absolute electrical permittivity and has a value of ${{\varepsilon }_{0}}=1/(4\pi k)=8.85\times {{10}^{-12}}{{C}^{2}}/(N{{m}^{2}})$.

ELECTRIC POTENTIAL AND CURRENT

Electric Potential

Potential at a point can be physically interpreted as the work done by the field in displacing a unit + ve charge from some reference point to the given point.

i.e., $V=\frac{w}{{{q}_{0}}}$

$V=-$$\overrightarrow{ds}$ i.e. $E=-\frac{dv}{dr}$

It is a scalar quantity.

Its SI unit is volt or joule coulomb"1.

Electrostatic potential produced by a point charge,

$V=\frac{Kq}{r}$

Electric current

The time rate of flow of charge or electrons through any cross-section is called electric current.

Current through the conductor is, $I=\frac{q}{t}=\frac{ne}{t}$ where n is an integer.

Charge of one electron is$1.6\times {{10}^{-19}}C$.

Number of electrons flowing through a conductor in t second is $n=\frac{I\times t}{e}$

Electric current is measured in ampere (A). It is a scalar fundamental physical quantity.

OHM’S LAW

According to Ohm’s law “The current passing through a conductor is directly proportional to the potential difference between its ends, provided the physical conditions such as temperature of conductor remain unchanged.”

i.e.,       $V\propto I$   or            $V=RI$

where R is a constant which is called resistance of the material.

Resistance of a material depends on its length, area of cross- section, and nature of material etc.

i.e., $R=r\frac{l}{A}$ where,  $\rho$ = resistivity of material.

The SI unit of resistance is ohm ($\Omega$).

The conductors, which obey the Ohm's law are called the ohmic conductors or linear resistances. All metallic conductors (such as silver, aluminium, copper, iron, etc.) are the ohmic conductors or linear resistances.

The conductors, which do not obey the Ohm’s law are called the non-ohmic conductors or non-linear resistances. Examples are, diode valve, triode valve, transistors, electrolyte, etc.

Electroplating

Electroplating is the process of depositing a thin film (coating a layer) of finer (non-corrosive and costly) metal over the objects made from corrosive and cheaper metal with the passing of electric current through an electrolyte.

The objective of electroplating is to

(i) protect the surface of the corrosive and cheaper metal.

For example chromium and nickel plating of bicycle handlebar made from iron. Tin plating of iron containers for storing food articles (oil and picles).

(ii) decoration by giving a shine to the objects. For example silver or gold coating on cutlery.

(iii) Making of artificial jewellery and zari for embroidery from copper or other cheaper metals electroplated with silver or gold.

COMBINATION OF RESISTORS - SERIES AND PARALLEL

Series Combination of Resistors

${{R}_{s}}={{R}_{1}}+{{R}_{2}}+{{R}_{3}}+.........+{{R}_{n}}$

The equivalent resistance is greater than largest of individual resistance.

Parallel Combination of Resistors

$\frac{1}{{{R}_{P}}}=\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}+\frac{1}{{{R}_{3}}}+....+\frac{1}{{{R}_{n}}}$

The equivalent resistance is smaller than smallest of individual resistance.

Science in Action

• Special resistors are commonly used as single-use fuse. The conductive material in the fuse gets completely destroyed when threshold current is reached. These are used to protect various electrical appliances.
• Resistors are also used as sensors for various applications like gas sensors, lie detectors etc.

MEASURING INSTRUMENT

Galvanometers

These are instruments used for detection and measurement of small currents.

Ammeter

An ammeter is a low resistance galvanometer used to measure strength of current in an electrical circuit.

(i) An ammeter is always connected in series in a circuit because, when an ammeter is connected in series it does not appreciably change the resistance of circuit and hence the main current flowing through the circuit.

(ii) An ideal ammeter has zero resistance.

Conversion of galvanometer into ammeter:

A galvanometer can be converted to an ammeter by connecting a low resistance or shunt in parallel to coil of galvanometer.

Voltmeter

A voltmeter is a high resistance galvanometer used to measure potential difference.

(i) A voltmeter is connected in parallel to a circuit element because, when connected in parallel it draws least current from the main current. So it measures nearly accurate potential difference.

(ii) An ideal voltmeter has infinite resistance.

Conversion of galvanometer into voltmeter:

A galvanometer is converted to a voltmeter by connecting a high resistance in series with the coil of galvanometer.

HEATING EFFECT OF ELECTRIC CURRENT

Joule’s Law of Heating: When a current I is made to flow through a conductor of resistance R for time t, heat Q is produced such that,

i.e., $Q={{I}^{2}}Rt=P\times t=VIt=\frac{{{V}^{2}}}{R}t$

SI unit of electric heat or energy is joule.

Electric Power: $P=VI=\frac{{{V}^{2}}}{R}={{I}^{2}}R$ SI unit: Watt

Science in Action

Bulbs fuse because when they are switched on, its temperature increases due to which the strength of its filament decreases. After long period of time the strength of the filament becomes very low, thus the filament burns off.

HOUSEHOLD CIRCUITS

Switches

A switch is a key in a circuit which is used to make or break the circuit. It is always connected in the live wire of the circuit so that when it is off, you can safety touch the exposed live wire.

Safety Fuse

A fuse is a device containing short length of thin wire which melts and breaks the circuit if the current exceeds a safe value. The fuse is ire is made up of a material which has high resistance and low melting point so that as soon as excessive current passes through, it gets melted. Generally, an alloy of tin and lead is used to make a fuse wire.

Earthing

Earthing is a safety process which is used to prevent the shocks due to leakage, short circuiting, etc. The cable coming from an appliance has three wires. One is live, the other neutral and the third one is earth. The earth wire is connected to the outer part of body metallic framework of the appliance.

Short circuit is a condition in which live wire comes in direct contact with a neutral wire and excessive current flows in the circuit.

When a large current (as compared to normal current) flows in a circuit which causes overheating, the circuit is said to be overloading of the electrical circuit.

PERMANENT MAGNETS AND ELECTROMAGNETS

The permanent artificial magnets are made of some metals and alloys like Carbon-steel, Alnico, Platinum-cobalt, AIcomax, Ticonal etc. The permanent magnets are made of ferromagnetic substances with large coercivity and retentivity and can have desired shape like bar-magnet, U shaped or horse-shoe magnet and magnetic needle etc. These magnets retain its attracting power for a long time.

The temporary artificial magnets like electromagnets are prepared by passing current through coil wound on soft iron core. These cannot retain its strength for a long time. Electromagnets are stronger than permanent magnet.

The strength of an electromagnet depends on

(i) the number of turns in the coil (n)

(ii) the strength of current (I)

(iii) the nature of the core material.

Properties of magnet

(i) A freely suspended magnet always points in the north-south direction (directive property)

(ii) Like magnetic poles repel each other and unlike magnetic poles attract each other.

(iii) Magnetic poles always exist in pairs. It is not possible to have either S-pole alone or N-pole alone.

Uses of Magnets

Magnets have their lot of applications in daily life.

(i) In the refrigerators to keep the door close.

(ii) In the Electric bells, speakers which can convert the electrical energy into sound energy.

(iii) In telephones and in tape recorders.

(iv) Electromagnets are used for removing pieces of iron and steel from the non-magnetic heap of metal scrap.

(v) Doctors use the magnets to cure arthritis, gout, and to stimulate the nerves in human body.

MAGNETIC EFFECT OF CURRENT

Magnetic effect of electric current means-an electric current flowing in a conductor produces a magnetic field in the space around it. In 1820, Hans Christian Oersted Showed that electricity and magnetism are related phenomena.

Oersted discovered a magnetic field around a conductor carrying electric current.

(a)  A magnet at rest produces a magnetic field around it while an electric charge at rest produces an electric field around it.

(b) A current carrying conductor has a magnetic field and not an electric field around it. On the other hand, a charge moving with a uniform velocity has an electric as well as a magnetic field around it.

Burglar Alarms, Microphones, loud speakers, car horns and electric bells, A.C. generator, D.C. motor, transformer, etc. are based on magnetic effect of electric current.

A.C. Generator or Dynamo

An A.C. generator or dynamo is a device which converts mechanical energy into electrical energy, an electric generator is based on the principle of electromagnetic induction, according to which if a closed coil is rotated about an axis perpendicular to a uniform magnetic field, an induced e.m.f. is set up across the coil whose direction is governed by Fleming's right hand rule.

DC Motor

A D. C. motor converts direct current energy from a battery into mechanical energy of rotation.

It is based on the fact that when a coil carrying current is held in a magnetic field, it experiences a torque, which rotates the coil.

Uses of D.C Motor:

1. The D.C. motors are used in D.C. fans (exhaust, ceiling or table) for cooling and ventilation.
2. They are used for pumping water.
3. Big D.C. motors are used for running tram-cars and even trains.

Transformer

It is a device used for transforming a low alternating voltage of high current into a high alternating voltage of low current and vice versa, without increasing power or changing frequency.

Principle: It works on the phenomenon of mutual induction. If a low voltage is to be transformed into a high voltage, then the number of turns in secondary is more than those in primary. The transformer is called a step-up transformer.

If a high voltage is to be transformed into a low voltage, then the number of turns in secondary is less than those in primary. The transformer is called a step-down transformer.

Transformation ratio of the transformer,

$K=\frac{Number\,\,of\,\,turns\,\,in\,\,\sec ondary\,\,({{N}_{s}})}{Number\,\,of\,\,turns\,\,in\,\,primary\,\,({{N}_{p}})}$

THE EARTH’S MAGNETISM

The branch of Physics which deals with the study of earth’s magnetic fields is called terrestrial magnetism.

Some Definitions

Geographic axis: It is straight line passing through the geographic poles of the earth. It is the axis of rotation of the earth. It is known as polar axis.

Geographic meridian: It is a vertical plane passing through geographic north and south pole of the earth.

Geographic equator: A great circle on the surface of the earth in a plane perpendicular to geographical axis is called geographic equator. All places on geographic equator are at equal distances from geographical poles.

Magnetic axis: It is a straight line passing through the magnetic poles of the earth. It is inclined to geographic axis at nearly $17{}^\circ$.

Magnetic meridian: It is a vertical plane passing through the magnetic north and south pole of the earth.

Magnetic equator: A great circle on the surface of the earth in a plane perpendicular to magnetic axis is called magnetic equator. All places on magnetic equator are at equal distance from magnetic poles.

Elements of Earth’s Magnetic Field

Angle of declination ($\phi$): The angle between the magnetic meridian and geographical meridian at a place is called angle of declination.

(a) Isogonic lines: Lines drawn on a map through places that have same declination are called isogonic lines.

(b) Agonic lines: The lines drawn on a map through places that have zero declination is known as an agonic lines.

Angle of dip or inclination ($\theta$): The angle through which the N pole dips down with reference to horizontal is called the angle of dip. At magnetic north and South Pole, angle of dip is$90{}^\circ$. At magnetic equator, the angle of dip is$0{}^\circ$.

Horizontal component of earth’s magnetic field: The total intensity of the earth’s magnetic field makes an angle $\theta$ with horizontal. It has

(a) Component in horizontal plane called horizontal component${{B}_{H}}$.

(b) Component in vertical plane called vertical component B${{B}_{V}}$.

DIA, PARA AND FERROMAGNETIC SUBSTANCES

Diamagnetic Substances

The substances which when placed in a magnetic field are feebly magnetised in a direction opposite to that of the magnetising field are called diamagnetic substances, e.g., Cu, Zn, Bi, Ag, Au, Pb, He, Ar, $NaCl$, ${{H}_{2}}O$, marble, glass etc.

Paramagnetic Substances

The substances which when placed in a magnetic field are feebly magnetised in the direction of magnetising field are called paramagnetic substances. e.g., -

Al, Na, Sb, Pt, $CuC{{l}_{2}}$, Mn, Cr, liquid oxygen etc.

Ferromagnetic Substances

The substances which when placed in a magnetic field are strongly magnetised in the direction of the magnetising field are called ferromagnetic substances. Iron, cobalt, nickel etc. are some examples of ferromagnetic substance.

LIGHT

The branch of physics which deals with nature, source, properties and the effects of light is called optics. It is mainly through light and the sense of vision that we know and interpret the world around us.

LIGHT AND ITS CHARACTERISTICS

Light is a form of energy that produces the sensation of vision on our eyes. It is an electromagnetic radiation, such as that emitted by the Sun, which acts like a wave in a wavelength range from 400 nm to 750 nm that the human eye can perceive. It is a combination of electric and magnetic oscillations in mutually perpendicular directions, but the light wave itself propagates in a direction perpendicular to both the oscillations.

Characteristics of Light

(i) Light travels along a straight line in a medium or vacuum. The path of light changes only when the medium changes. This is also called the rectilinear propagation of light. The path is called a ray of light, and bundle of such rays constitutes a beam of light.

(ii) Light travels with a speed nearly equal to $3\times {{10}^{8}}$ m/s in vacuum. According to current theories, no material particle can travel at a speed greater than the speed of light.

(iii) The speed of light depends on the medium through which they pass.

(iv) Light shows different behaviour such as reflection, refraction, interference, diffraction, polarisation etc.

Science in Action

The casting of shadows and eclipses are due to the rectilinear propagation of light.

REFLECTION OF LIGHT

The turning back of light in the same medium is called reflection of light.

Laws of Reflection

• The angle of incidence (i) is always equal to the angle of reflection (r). i.e., $\angle i=\angle r$
• The incident ray, the normal, and the reflected ray all lie in the same plane.

Characteristics of Image Formed by Plane Mirror

(i)  A plane mirror always forms virtual and erect image of the object.

(ii) Distance of object from mirror = distance of image from mirror.

(iii) The image is laterally inverted (better word perversion).  i.e., the left of the object becomes the right of the image and vice versa.

(iv) The size of the image is the same as that of the object

SPHERICAL MIRROR, ITS TYPES AND USES

A highly polished curved surface whose reflecting surface is a cur part of a hollow sphere of a glass or any polished metal is called spherical mirror. Spherical mirrors are of two types:

Concave or Convergent Mirrors

Imagine a sphere of hollow glass. If we cut out a spherical cap and polished it with silver on the outside, we have a concave mirror

Convex or Divergent Mirrors

If we polished the inner surface of a concave mirror with silver and look at the outward bulge, we have a convex mirror.

Image Formed by Convex Mirror

The image is always virtual, erect, smaller than the object and is located between the pole and the focus no matter where in front of the mirror the object is placed.

Terms Related to Spherical Mirror

Centre of curvature (C): It is the centre of sphere of which the mirror is apart.

Radius of curvature (R): It is the radius of the sphere of which the mirror is a part.

Pole (P): It is the geometrical centre of the spherical reflecting surface. All distances are measured from the pole.

Principal axis: It is the straight line joining the centre of curvature to the pole.

Focus (F): When a narrow beam of rays of light, parallel to the principal axis and close to it (known as paraxial rays), is incident on the surface of a mirror, the reflected beam is found to converge (concave mirror) or appear to diverge (convex mirror) from a point on principal axis. This point is called focus.

Focal length (f): It is the distance between the pole and the principal focus. For spherical mirrors,$f=R/2$.

Uses of Concave Mirror

Makeup and shaving mirrors are concave mirrors. Concave mirrors are also used in a new method for displaying the speed of a car, as a dentist mirror, in floodlight, in solar cooker etc.

Uses of Convex Mirror

C on vex mirrors, give a wider field of view than do other types of mirrors. Therefore, they are often used for security purposes and rear view mirror in vehicles.

MIRROR FORMULA AND MAGNIFICATION

Mirror Formula

A relationship among the object distance (u), the image distance (v) and the focal length (f) of a mirror

i.e.,       $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

Magnification

If the mirror is plane, the size of the image is always equal to the size of the object i.e., magnification is unity. But the case is different for a curved mirror. The size of the image is different from the size of the object in such a ‘mirror’. Image may be greater or smaller in size than the object depending upon the nature of the mirror or the location of the object.

Let I and O be the size of the image and the object respectively then

Magnification,  $m=\frac{1}{O}=-\frac{v}{u}$

This is also called linear magnification.

REFRACTION OF LIGHT

The bending of the light ray from its path in passing from one medium to the other medium is called refraction of light.

If the refracted ray bends towards the normal relative to the incident ray (Passing obliquely), then the second medium is said to be denser than the first medium. But if the refracted ray bends away from the normal, then the second medium is said to be rarer than the first medium.

If a ray of light passing normally i.e., at right angles from one medium to another optical medium then it does not bend or deviate from its path.

Cause of refraction of light: Refraction of light takes place due to change in the speed of light as it enters from one medium to another medium.

Laws of Refraction

There is two laws of refraction

• The incident ray, the refracted ray, and the normal to the refracting surface at the point of incidence are in the same lane.
• The ratio of sine of angle of incidence to the sine of angle of refraction is constant for a pair of media

i.e.  $\frac{\sin \,i}{\sin \,r}=cons\tan t\,{{(}^{1}}{{\mu }_{2}})$

where $^{1}{{\mu }_{2}}$ is the refractive index of medium 2 w.r.t medium 1. This law is also known as snell’s law.

REFRACTIVE INDEX

Light travels through a vacuum at a speed c = $3.00\times {{10}^{8}}$ m/s. It can also travel through many materials, such as air, water and glass. Atoms in the material absorb, remit and scatter the light, however. Therefore, light travels through the material at a speed that is less than c, the actual speed depending on the nature of the material.

To describe the extent to which the speed of light in a material medium differs from that in a vacuum, we use a parameter called the index of refraction (or refractive index).

The ratio of speed of light in free space c to that in a given medium v is called absolute refractive index

i.e.,         $\mu \,\,or\,\,n=\frac{c}{v}$

Relative refractive index: When light passes from one medium to the other, the refractive index of medium 2 relative to 1 is written as $^{1}{{\mu }_{2}}$ and is defined as $_{1}{{\mu }_{2}}=\frac{{{\mu }_{2}}}{{{\mu }_{1}}}=\frac{(c/{{v}_{2}})}{(c/{{v}_{1}})}=\frac{{{v}_{1}}}{{{v}_{2}}}$

Real and Apparent Depths

When an object is seen from other medium, we don’t see

Its actual or real depth or height. The depth we see is called apparent depth.

• When object in denser medium and observer in rarer medium, then

$\mu =\frac{real\,\,depth}{apparent\,\,depth}$

And in this case,

real depth > apparent depth

• When object in rarer medium and observer in denser medium, then

$\mu =\frac{apparent\,\,depth}{real\,\,depth}$

And in this case,

apparent depth > real depth

Science in Action

Refraction causes many illusions. One of them is the apparent bending of a stick that is partially submerged in water.

The submerged part appears closer to the surface than it actually is. The same is true when you look at a fish in water. The fish appears nearer to the surface and closer than it really is. If we look straight down into water, an object submerged 4 meters beneath the surface appears to be only 3 meters deep. Because of refraction, submerged objects appear to be magnified.

TOTAL INTERNAL REFLECTION

When a light ray, travelling from a denser medium to a rarer medium is incident at the interface at an angle of incidence greater than critical angle (c) i.e., the angle of incidence in a denser medium for which the angle of refraction in rarer medium becomes$90{}^\circ$, then light rays reflected back into the denser medium. This phenomenon is called total internal reflection (TIR).

Sparkling of diamond, optical fibres etc. are the applications of total internal reflection.

Critical angle: The angle of incidence in a denser medium for which the angle of refraction in rarer medium becomes $90{}^\circ$ is called critical angle.

Refractive index of denser medium $\mu =\frac{1}{\sin \,\,c}$

Science in Action

• Optical fibre-based on total internal reflection, is used in telecommunication, and to send laser light rays inside the human body.
• Brilliance of diamond is based on total internal reflection. Critical angle for diamond and air interface = ${{24}^{o}}$is very small. Thus by cutting diamond suitably, multiple total internal reflection are made to occur.
• Mirage is an optical illusion of water which appears in the desert in hot summer. This is due to total internal reflection.

LENS

A lens is a piece of transparent material with two refracting surfaces such that at least one is curved and refractive index of used material is different from that of the surroundings.

Convex lens: A thin spherical lens with refractive index greater than that of surrounding behaves as a convergent or convex lens i.e. converges parallel rays. Its central (i.e. paraxial) portion is thicker than marginal one.

Concave lens: If the central portion of a lens (with${{\mu }_{L}}>{{\mu }_{M}}$) is thinner than marginal, it diverges parallel rays and behaves as a divergent or a concave lens.

Uses of Convex Lens and Concave Lens

Uses of convex lens: As a magnifying glass, search lights, spotlights in the theatres, in microscope, telescope, photographic camera etc.

Uses of concave lens: In spectacles for the correction of myopia, Gallilean telescope etc.

TERMS RELATED TO THIN SPHERICAL LENS

Optical centre (O) - It is the geometrical centre of the lens or a point for a given lens through which any ray passes un deviated.

Principal axis (${{C}_{1}}{{C}_{2}}$) - It is a line passing through optical centre and perpendicular to the lens. The centre of curvature of curved surface always lie on the principal axis.

Principal focus (F) - A lens has two surfaces and hence two focal points, first focal point is an object point on the principal axis for which image is at infinity while second focal point is an image point on the principal axis for which object is at infinity.

Focal length (f) - The distance between optical centre of a lens and the principal focus.

Aperture - In reference to lens, aperture means to effective diameter of its light transmitting area so that brightness i.e. intensity of image formed by a lens which depends on the light passing through the lens will depend on the square of aperture. i.e. $I\propto {{(aperture)}^{2}}$

For Divergent or Concave lens

(i) If object is at infinity image will be formed at focus on the same side of the lens as the object, virtual, erect and point sized.

(ii) If object is in front of lens, anywhere between the optical centre and infinity image will be formed between focus and the optical centre, on the same side of the lens, highly diminished, virtual and erect.

LENS FORMULA

If an object is placed at a distance u from the optical centre ‘O’ of a lens and its image is formed at a distance v (from the optical centre) and focal length of this lens is f then

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

MAGNIFICATION

If a thin object of linear size 0 situated vertically on the axis of a lens at a distance u from the optical centre and its image of size I is formed at a distance v (from the optical centre) then

Magnification, $m=\frac{I}{O}=\frac{v}{u}$.

POWER OF A LENS

If focal length of a lens is measured in metre (m) then its reciprocal gives the power (P) of the lens.

i.e., Power of a lens, $P=\frac{1}{f(in\,\,m)}$

The S.I. unit of power is diopter (D).

Power of a combination of lenses:

$P={{P}_{1}}+{{P}_{2}}+......{{P}_{n}}$

INTERFERENCE OF LIGHT

When two light waves of exactly same frequency travels in li medium, in the same direction simultaneously then due to their superposition, the intensity of light is maximum at some points while the intensity is minimum at some other points. This phenomenon is called interference of light. The colours in soap hubbies and oil slicks are due to this property of light.

DIFFRACTION OF LIGHT

The wavelength of light is of the order of angstroms. So, when light waves encounter obstacles of very small sizes, the light waves bend around the edges of the obstacle and travel. This is known as diffraction of light.

POLARISATION OF LIGHT

An ordinary source of light such as bulb consists of a large it umber of waves emitted by atoms or molecules in all directions symmetrically. Such light is called unpolarized light

Science in Action

• In order to avoid glare in observing very minute particles, the objectives of microscopes are fitted with Polaroids.
• Polaroids are used in holography (three dimensional motion pictures).
• In polar regions where magnetic compass cannot be operated, polarization of scattered sunlight is used for navigation.

THE HUMAN EYE

The eye allows us to see and interpret the shapes, colors, and dimensions of objects by processing the light they reflect or emit. The eye is able to see in bright light or in dim light, but it cannot see objects when light is absent.

Eye lens: It is a convex lens made of transparent and flexible jelly like material. Its curvature can be adjusted with the help of ciliary muscles.

Power of Accommodation

The ability of the eye lens to change its shape to focus near and distant objects clearly is called power of accommodation.

The minimum distance, at which objects can be seen most distinctly without strain, is called the least distance of distinct vision. It is also called the near point (N.R) of the eye. For a young adult with normal vision, the near point is about 25 cm.

DEFECTS OF VISION AND THEIR CORRECTION

Myopia or Short-Sightedness

A person with myopic eye can see nearby objects clearly but cannot see off objects distinctly.

Remedy: This defect can be corrected by using a concave lens of suitable focal length. A concave lens diverges the rays coming from the object so that they get focused at the retina.

Hypermetropia or Far-sightedness

A person with hypermetropic eye can see far off objects clearly but cannot see nearby objects clearly.

Remedy: Eyeglass with convex lens is used to rectify this problem.

Presbyopia

Presbyopia is due to a lessening of flexibility of the crystalline lens, as well as to a weakening of the ciliary muscles which control lens focusing, both attributable to the ageing process.

Remedy: Person suffering from presbyopia require bifocal lenses. A common type of bi-focal lenses consists of both concave and convex lenses. The upper portion consists of a concave lens. It facilitates distant vision. The lower part is a convex lens. It facilitates near vision.

Astigmatism

Astigmatism is the most common problem responsible for blurry vision.

Remedy: cylindrical lens is use to correct astigmatism.

Cataract

A cataract is a clouding of the lens in the eye.

DISPERSION OF WHITE LIGHT BY A GLASS PRISM

The phenomenon of decomposition of the white light into seven component colours when passing through a prism or through a transparent object delimited by non parallel surfaces is called dispersion of light. A beam of light containing all the visible spectrum of the light is white, because the sum of all the colors generates the white color. Normally the light we use is white. It’s the light containing all the colors mixed together. The light is decomposed in all the component colours, i.e., Violet, Indigo, Blue, Green, Yellow, Orange and Red, called as VIBGYOR.

RAINBOW

A rainbow is a natural spectrum of sunlight in the form of bows appearing in the sky when the sun shines on raindrops after the rain. Rainbows are generated through refraction and total internal reflection of light in small rain drops. The sun is always behind you when you face a rainbow, and that the centre of the circular arc of the rainbow is in the direction opposite to that of the sun.

After rain, there are still some tiny water droplets remained in the air. If there is sunshine, a white sunbeam will be reflected and refracted by these tiny droplets. Different colors of light have different refractivity. They will be reflected in slightly different directions inside a water droplet. Since, water is more dense than air, light is refracted as it enters the drop-red is bent less, blue more. Some of the light will reflect off the back of the drop if the angle is larger than the critical angle (48${}^\circ$ for water)

The light is then refracted again as it leaves the drop (act like a small prism), the colours of white light have been dispersed.

• Violet light will leave the drop at an angle of $40{}^\circ$ from the beam of sunlight
• Red light will leave the drop at an angle of $42{}^\circ$ from the beam of sunlight.

ATMOSPHERIC REFRACTION

The density of air in the atmosphere is not the same everywhere. It is greatest at the earth's surface and goes on decreasing as we move higher. The refractive index of air depends on its density-higher the density of air, greater its refractive index. The changes in refractive index of earth's atmosphere or air give rise to many phenomena like twinkling of stars, advance sunrise and delayed sunset etc.

Twinkling of Stars

The scientific name for the twinkling of stars is stellar scintillation (or astronomical scintillation). Stars twinkle when we see them from the Earth’s surface because we are viewing them through thick layers of turbulent (moving) air in the Earth’s atmosphere. Stars (except the Sun) appear as tiny dots in the sky; as their light travels through the many layers of the Earth’s atmosphere, the light of the star is bent (refracted) many times in random directions (light is bent when it hits a change in density-like a pocket of cold air or hot air). This random refraction results in the twinkling of stars.

Advance Sunrise and Delayed Sunset (Approximately 2 minutes)

The actual sunrise takes place when the sun is just above the horizon. When the sun is just below the horizon, the light rays coming from it, on entering the earth's atmosphere suffer atmospheric refraction from a rarer medium to a denser medium. So, they bend towards the normal at each refraction. Due to the continuous refraction of light rays at each layer of the atmosphere, it follows a curved path as shown in Figure and reaches the eyes of the observer at O.

SCATTERING OF LIGHT

The interplay of light with objects around us gives rise to several spectacular phenomena in nature like the blue colour of the sky, colour of water in deep sea, the reddening of the sun at sunrise and the sunset etc. When sunlight enters the earth atmosphere, air and water vapour molecules absorb part of the light and reradiate it to all directions. This is called scattering of light.

Tyndall Effect

When a beam of sunlight enters a dusty (or smoke filled) room through a window then path becomes visible due to scattering of light by dust or smoke particles this phenomenon is called Tyndall effect.

The reddening of the Sun at Sunrise and Sunset

At noon, the light of sun travels relatively shorter distance through earth’s atmosphere thus appears white as only a little of blue and violet colours are scattered. Near the horizon, most of the blue and green light and shorter wavelengths are scattered and hence the sun appears reddish at sunrise and sunset.

OPTICAL INSTRUMENTS

Simple Microscope (Magnifying Glass or Reading Lens)

It consists of a convergent lens with object between its focus and optical centre and eye close to it. The image formed by it is erect, virtual, enlarged and on same side of lens between object and infinity.

Magnification by a simple microscope

The magnifying power (MP) of a simple microscope

$MP=\frac{Visual\,\,angle\,\,with\,\,instrument}{Max.\,\,visual\,\,angle\,\,for\,\,unaided\,\,eye}=\frac{\theta }{{{\theta }_{0}}}$

Compound Microscope

It consists of two convergent lenses ${{f}_{eye\,\,lens}}>{{f}_{objective}}$and${{(diameter)}_{eyelens}}>{{(diameter)}_{objective}}$arranged co-axially. The separation between objective and eye-piece can be varied.

Magnification produced by a compound microscope:

$M={{m}_{objective}}\times {{m}_{eye\,\,piece}}$

Telescope

It is used to provide angular magnification of distant objects. i.e., to see far off objects.

Astronomical Telescope (Refracting Type)

It consists of objective, i.e., a converging lens, of larger focal length ${{f}_{0}}$ and larger aperture, and an eyepiece, also a converging lens, of smaller focal length ${{f}_{e}}$ and smaller aperture, placed coaxially.

Magnifying Power (M)

Magnifying power (M), a so called angular magnification of a telescope is defined as the ratio of the visual angle subtended by the final image at the eye and the visual angle subtended by the object when the object lies in the actual position.

Astronomical telescope is used to see heavenly bodies and terrestrial telescope to see far off objects on earth.

PRIMARY AND SECONDARY COLOURS OF LIGHT

Primary colours

The group of colours which can be used to form all other colours by mixing.

Examples: red, green, blue. White = Blue + Green + Red

Secondary colours

These are created by combining two or more primary colours.

Examples: Red + Blue = Magenta,

Red + Green = Yellow, Blue + Green = Cyan

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