The human eye contains a lens that helps us see by focusing light. The chapter explains the role of the eye lens, how the eye forms an image, and how spectacles using different lenses correct vision problems.

Central idea: The eye is a natural optical instrument. It focuses light on the retina, and the brain interprets the signals produced by light-sensitive cells.

2. How Our Eyes Work Like a Camera Lens

Light entry

Light rays from an object enter the eye. The eye lens focuses these rays, similar to a camera lens.

Image formation

The eye lens forms an inverted, real image on the retina.

Signal transmission

Light-sensitive cells in the retina produce electrical signals. These travel to the brain through the optic nerve.

Accommodation

The ability of the eye lens to change its focal length so that objects at different distances are seen clearly.

The brain interprets the electrical signals and enables us to see objects.

3. The Human Eye

The eyeball is roughly spherical and has a diameter of about 2.3 cm. Its lens system forms an image on the light-sensitive retina.

Structure and functions

Part	Function / Description
Cornea	Thin, transparent membrane at the front of the eye. Most refraction of incoming light occurs at its outer surface.
Iris	Dark muscular diaphragm behind the cornea; controls the size of the pupil.
Pupil	Central opening in the iris; regulates the amount of light entering the eye.
Crystalline lens	Provides fine adjustment of focal length to focus objects at different distances on the retina.
Retina	Light-sensitive screen containing cells that generate electrical signals when illuminated.
Optic nerve	Carries electrical signals from the retina to the brain.
Eye lens	A convex lens that forms an inverted, real image of the object on the retina.

Remember: Light enters through the cornea, passes through the pupil and lens, and is focused on the retina. The optic nerve carries signals to the brain.

4. Power of Accommodation

The eye lens is made of soft, jelly-like material. Its shape can be changed by the ciliary muscles.

Viewing condition	Ciliary muscles	Eye lens	Focal length
Distant objects	Relaxed	Becomes thinner	Increases
Nearby objects	Contract	Becomes thicker	Decreases

Accommodation: The ability of the eye lens to adjust its focal length with the help of the ciliary muscles.

Near point and far point

Near point / least distance of distinct vision: Minimum distance at which an object can be seen clearly without strain. For a normal adult eye, it is 25 cm.
Range of vision: From 25 cm to infinity (∞) for a normal eye.
Far point: Farthest point up to which the eye can see clearly. For a normal eye, it is at infinity (∞).

Cataract

Sometimes the crystalline lens of an elderly person becomes milky and cloudy. This condition is called cataract and may cause partial or complete loss of vision. Vision can be restored by surgically removing the cloudy lens and replacing it with an artificial intraocular lens.

5. Defects of Vision and Their Correction

Refractive defects make it difficult to see objects clearly and comfortably. The three common defects described in this chapter are myopia, hypermetropia and presbyopia. Spherical lenses are used to correct these defects.

5.1 Myopia (Near-sightedness)

A person can see nearby objects clearly but cannot see distant objects clearly.
For a distant object, the image is formed in front of the retina.
Causes: Excessive curvature of the eye lens or elongation of the eyeball.
Correction: A concave lens of suitable power.

MYOPIA → IMAGE IN FRONT OF RETINA → CONCAVE LENS

5.2 Hypermetropia (Far-sightedness)

A person can see distant objects clearly but cannot see nearby objects clearly.
The near point is farther away than the usual near point of 25 cm.
For a nearby object, the image is formed behind the retina.
The person may need to hold reading material beyond 25 cm for comfortable reading.
Causes: Focal length of the eye lens becomes too long, or the eyeball becomes too small.
Correction: A convex lens of suitable power.

HYPERMETROPIA → IMAGE BEHIND RETINA → CONVEX LENS

5.3 Presbyopia (Old-age Hypermetropia)

With age, the ability of the eye to adjust its focus generally decreases.
The near point gradually moves farther away, making nearby objects difficult to see clearly and comfortably.
Causes: Gradual weakening of ciliary muscles and decreasing flexibility of the eye lens.
Correction: A convex lens of suitable power.
If a person has both myopia and hypermetropia, bifocal lenses may be required. The upper part is concave for distant vision and the lower part is convex for near vision.

Comparison of refractive defects

Defect	Vision problem	Image location	Causes	Correction
Myopia	Nearby clear; distant blurry	In front of retina	Excessive lens curvature; elongated eyeball	Concave lens
Hypermetropia	Distant clear; nearby blurry	Behind retina	Focal length too long; eyeball too small	Convex lens
Presbyopia	Nearby vision becomes difficult in elderly people	Near point recedes beyond 25 cm	Weakening ciliary muscles; less flexible eye lens	Convex lens or bifocal lens

Exam tip: Myopia is corrected using a concave lens. Hypermetropia is corrected using a convex lens. In the bifocal lens described in the notes, the upper part is concave and the lower part is convex.

6. Refraction of Light Through a Prism

Structure: A triangular glass prism has two triangular bases and three rectangular lateral surfaces.
Angle of a prism: The angle between two adjoining lateral surfaces.
At the first surface (AB): A ray entering the prism from air bends towards the normal.
At the second surface (AC): A ray emerging from glass into air bends away from the normal.
Angle of deviation (D): The angle between the direction of the incident ray and the emergent ray.

Key definitions

Prism: A transparent piece of glass with two triangular bases and three rectangular lateral surfaces.

Angle of deviation: The angle between the directions of the incident ray and the emergent ray.

7. Dispersion of White Light by a Glass Prism

When a ray of white light is incident on a glass prism, it splits into a band of seven colours: Violet, Indigo, Blue, Green, Yellow, Orange and Red (VIBGYOR).

VIBGYOR = Violet • Indigo • Blue • Green • Yellow • Orange • Red

Spectrum: The band of coloured components of a light beam.
Dispersion: The splitting of white light into its component colours.
Different colours are deviated through different angles and emerge along separate paths.
Red is deviated the least because it has the longest wavelength among the visible colours.
Violet is deviated the most because it has the shortest wavelength among the visible colours.

8. Recombination of White Light

Isaac Newton was the first person to prove that sunlight is made up of seven colours.

He passed sunlight through a glass prism and obtained a band of seven colours.
He tried to split the colours further by placing another prism in the path of the spectrum, but no additional colours were obtained.
He formed a spectrum from sunlight and placed an identical but inverted prism in front of the first prism. The seven colours combined through the inverted prism and emerged as white light.

Key point: The seven colours of the spectrum can recombine to produce white light.

9. Rainbow Formation

A rainbow is a natural spectrum that appears in the sky after a rain shower.
It forms when sunlight is dispersed by tiny water droplets in the atmosphere.
A rainbow always appears in the direction opposite to the Sun.
Water droplets act as small prisms: they refract and disperse sunlight, reflect it internally, and refract it again as it emerges.
This dispersion and internal reflection produce the different colours visible to an observer.

10. Atmospheric Refraction

Atmospheric refraction is the refraction of light by the different layers of the atmosphere.

Apparent flickering behind a hot surface

Air above a hot surface becomes hot and rises; cooler air takes its place.
The refractive index of hot air is less than that of cool air.
Changing air conditions cause the refractive index to keep changing, so light appears to come from different directions.
This fluctuates the apparent position of the object, making it appear to flicker.

Stars near the horizon

The refractive index of Earth's atmosphere generally increases from the upper layers to the lower layers.
Light from a star near the horizon passes through layers of increasing optical density and bends towards the normal.
As a result, the star appears slightly higher than its actual position.

Advanced sunrise and delayed sunset

The Sun appears about two minutes earlier than the actual sunrise and remains visible for about two minutes after the actual sunset.
When the Sun is below the horizon, its rays pass through layers of air of increasing optical density and bend towards the normal.
Consequently, the Sun appears higher than its actual position.

Twinkling of stars

Starlight is continuously refracted by Earth's atmosphere, whose refractive index changes from layer to layer and with atmospheric conditions.
Stars are very far away and appear as point sources of light.
Small changes in the path of light cause noticeable changes in apparent brightness. The star appears to brighten and dim, producing twinkling.

Why do planets not twinkle?

Planets are extended sources of light and can be considered collections of numerous tiny point sources. Fluctuations from their different parts tend to average out, so the overall intensity entering our eyes remains relatively stable. Therefore, planets do not appear to twinkle.

Phenomenon	Cause / mechanism	Observation
Twinkling of stars	Continuous refraction through changing atmospheric layers	Apparent brightness fluctuates
Planets do not twinkle	Light fluctuations from different parts average out	Overall intensity remains relatively stable
Advanced sunrise / delayed sunset	Atmospheric refraction bends sunlight	Sun appears about 2 minutes early and remains visible about 2 minutes after actual sunset

11. Scattering of Light

Light interacts with particles and objects to produce natural phenomena such as the blue sky, the colour of deep-sea water and the red hues of sunrise and sunset.

Tyndall Effect

The path of light through a true solution is not visible, but it becomes visible in a colloidal solution because colloidal particles are large enough to scatter light.
Tyndall effect: Scattering of light by colloidal particles.
Examples: A sunbeam entering a smoke-filled room, and sunlight passing through a misty forest canopy where tiny water droplets scatter light.
The colour of scattered light depends on the size of the scattering particles. Very fine particles mainly scatter blue light, while larger particles scatter longer wavelengths. If particles are sufficiently large, scattered light may appear white.

Why is the clear sky blue?

Molecules of air and very fine particles in the atmosphere are smaller than the wavelength of visible light.
These particles scatter shorter wavelengths, such as blue light, more effectively than longer wavelengths, such as red light.
The wavelength of red light is approximately 1.8 times that of blue light.
As sunlight passes through the atmosphere, blue light is scattered more strongly than red light. The scattered blue light makes the sky appear blue.
Without an atmosphere, there would be no scattering of sunlight and the sky would appear dark.
At very high altitudes, the atmosphere is thinner, so there is less scattering and the sky appears darker.

Remember: Fine atmospheric particles scatter shorter wavelengths (blue) more effectively. This is why the clear sky appears blue.

Quick Revision • Important Facts

Human eye

Image on retina is inverted and real. Normal near point = 25 cm. Normal far point = infinity.

Accommodation

Near object: lens thicker, focal length decreases. Distant object: lens thinner, focal length increases.

Vision correction

Myopia → concave lens. Hypermetropia → convex lens. Presbyopia → convex or bifocal lens.

Prism

Red deviates least; violet deviates most. White light disperses into VIBGYOR.

Rainbow

Water droplets refract, disperse and internally reflect sunlight; rainbow appears opposite the Sun.

Atmospheric refraction

Explains twinkling of stars, apparent higher position of stars near horizon, and advanced sunrise/delayed sunset.

Planets

They do not appear to twinkle because fluctuations from different parts average out.

Scattering

Tyndall effect is scattering by colloidal particles. Fine particles scatter blue light strongly.

Light - Reflection And Refraction Notes

MG SCHOOL SCIENCE • CLASS 10

Light: Reflection and Refraction

Complete chapter notes with definitions, laws, ray rules, image-formation tables, sign conventions and important formulae.

Class 10 ScienceChapter NotesStudy • Revise • Practise

1. Introduction to Light

Light is a form of electromagnetic energy that causes the sensation of vision and makes things visible to our eyes. It acts like a messenger carrying information about the world around us.

Common phenomena associated with light

Image formation by mirrors
The twinkling of stars in the night sky
The beautiful colours of a rainbow
Bending of light rays when passing through different media

Properties of light

Medium independentElectromagnetic waves do not require any physical medium to travel.

Rectilinear propagationLight tends to travel in straight lines.

Dual natureLight exhibits both wave and particle characteristics.

Shadow formationLight casts distinct shadows when obstructed by opaque objects.

Speed of lightMaximum in vacuum; its value is 3 × 10⁸ m/s.

2. Reflection of Light

When light encounters a surface, it bounces back into the same medium. Reflection of light is the phenomenon in which light rays strike a surface and change direction.

Laws of reflection

Angle equality: The angle of incidence (∠i) is always equal to the angle of reflection (∠r).
Planar coincidence: The incident ray, reflected ray and normal to the reflecting surface at the point of incidence all lie in the same plane.

∠i = ∠r First law of reflection

Real and virtual images

Real imageFormed when light rays actually meet after reflection or refraction. It can be obtained on a screen.

Virtual imageFormed when light rays only appear to meet when produced backwards. It cannot be obtained on a screen.

Image formed by a plane mirror

Virtual and erect.
Image size is exactly equal to object size.
Image is formed as far behind the mirror as the object is in front of it.
Laterally inverted.

Lateral inversion: The right side of an object appears as the left side in its image and vice versa. The word “AMBULANCE” is written in reverse on emergency vehicles so drivers ahead can read it correctly in their rear-view mirrors.

3. Spherical Mirrors

Spherical mirrors are mirrors whose reflecting surface forms part of a hollow glass sphere.

Concave mirrorReflecting surface is curved inwards (towards the centre of the sphere). It is a converging mirror.

Convex mirrorReflecting surface is curved outwards. It is a diverging mirror.

Common terms for spherical mirrors

Principal axis: Straight line passing through the pole and centre of curvature.
Pole (P): Centre of the reflecting surface of the spherical mirror.
Aperture (MN): Effective diameter of the reflecting surface.
Centre of curvature (C): Centre of the hollow sphere of glass of which the mirror forms a part.
Radius of curvature (R): Radius of that sphere; distance PC.
Principal focus (F): Point on the principal axis where rays parallel to the principal axis actually converge (concave) or appear to diverge from (convex) after reflection.
Focal length (f): Distance between pole (P) and principal focus (F).

f = R / 2 Focal length of a spherical mirror is half its radius of curvature.

Rules for ray diagrams in spherical mirrors

A ray parallel to the principal axis passes through the principal focus (concave mirror) or appears to diverge from the focus (convex mirror) after reflection.
A ray passing through or directed towards the principal focus emerges parallel to the principal axis after reflection.
A ray passing through or directed towards the centre of curvature (C) is reflected back along the same path.
A ray incident obliquely at the pole (P) reflects obliquely, making equal angles with the principal axis (∠i = ∠r).

Image formation by a concave mirror

Object position	Image position	Nature of image	Size of image
At infinity	At focus (F)	Real and inverted	Point-sized / highly diminished
Beyond C	Between F and C	Real and inverted	Diminished
At C	At C	Real and inverted	Same size as object
Between F and C	Beyond C	Real and inverted	Enlarged
At F	At infinity	Real and inverted	Highly enlarged
Between P and F	Behind the mirror	Virtual and erect	Enlarged

Uses of concave mirrors

Torches, searchlights and vehicle headlights to produce powerful parallel beams of light.
Dentists use them to see enlarged images of teeth (teeth placed between P and F).
Shaving mirrors to view a larger image of the face.
Large concave mirrors concentrate sunlight to generate heat in solar furnaces.

Image formation by a convex mirror

Object position	Image position	Nature of image	Size of image
At infinity	At focus (F) behind mirror	Virtual and erect	Point-sized
Between pole (P) and infinity	Between P and F behind mirror	Virtual and erect	Diminished

Uses of convex mirrors

Rear-view mirrors in vehicles because they provide an erect, diminished image and a wider field of view.
At blind turns and traffic merging points to facilitate viewing incoming traffic.
Security mirrors in shops and stores.

4. Sign Convention and Mirror Formula

New Cartesian sign convention for reflection

The object is always placed to the left of the mirror.
All distances parallel to the principal axis are measured from the pole (P).
Distances measured in the direction of incident light (along +X axis) are positive.
Distances measured against the direction of incident light (along −X axis) are negative.
Distances measured perpendicular to and above the principal axis (along +Y axis) are positive.
Distances measured perpendicular to and below the principal axis (along −Y axis) are negative.
Object distance (u) is always negative.
Focal length of a concave mirror is negative; focal length of a convex mirror is positive.

Mirror formula and magnification

1/v + 1/u = 1/f Mirror formula

m = hᵢ / hₒ = −v/u Magnification produced by a spherical mirror

Key rules for magnification (m)

Negative magnification: If m is negative, the image is real and inverted (concave mirror).
Positive magnification: If m is positive, the image is virtual and erect.
Unit magnification: If hᵢ = hₒ (m = 1), image size equals object size.
Magnitude: If |m| > 1, the image is enlarged; if |m| < 1, it is diminished.
Plane mirror: Magnification is always +1.
Convex mirror identification: If m is positive and less than 1 (0 < m < 1), the mirror is convex.
Concave mirror identification: If m is positive and greater than 1 (m > 1), the mirror is concave.

5. Refraction of Light

Refraction is the bending of a light ray as it passes obliquely from one transparent medium to another. It occurs due to a change in the speed (velocity) of light across different media.

Speed of light and media density

Maximum speed of light occurs in vacuum or air: c = 3 × 10⁸ m/s.
Light travels slower in optically denser media compared to optically rarer media.

Laws of refraction

The incident ray, refracted ray and normal to the interface of two transparent media at the point of incidence all lie in the same plane.
Snell’s law: The ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is constant for a given pair of media and colour of light.

sin i / sin r = constant (n₂₁) Snell’s law as given in the notes

Bending behaviour of light

Rarer → denserLight bends towards the normal (∠i > ∠r).

Denser → rarerLight bends away from the normal (∠i < ∠r).

Refractive index depends on the nature of the medium and the wavelength of light. It is maximum for violet light and minimum for red light.

Refractive index (n)

Refractive index measures how fast light propagates through a material. It is a dimensionless quantity.

n = c / v Absolute refractive index: speed of light in vacuum (c) divided by speed in the medium (v).

n₂₁ = v₁ / v₂ = n₂ / n₁ Relative refractive index of medium 2 with respect to medium 1.

n₁₂ = v₂ / v₁ = n₁ / n₂ Relative refractive index of medium 1 with respect to medium 2.

n₂₁ × n₁₂ = 1; therefore n₂₁ = 1 / n₁₂ Reciprocal relation.

6. Lenses

A lens is a transparent optical material bounded by two curved surfaces or one curved and one flat surface.

Convex (converging) lensThicker at the centre than at the edges; converging lens.

Concave (diverging) lensThinner at the centre than at the edges; diverging lens.

Key terminologies for lenses

Optical centre (O): Central point of a lens through which an incident light ray passes without deviation.
Principal axis: Line C₁C₂ passing through the optical centre and perpendicular to both surfaces of the lens.
Principal focus: A lens has two principal foci (F₁, F₂). Rays parallel to the principal axis converge at or appear to diverge from F₂.
Focal length (f): Distance between optical centre (O) and principal focus (F).
Aperture: Effective diameter of the circular outline of a spherical lens.

Rules for ray diagrams in lenses

A ray passing through the optical centre (O) proceeds completely undeviated through the lens.
A ray passing through or directed towards the first focus (F₁) emerges parallel to the principal axis after refraction.
A ray parallel to the principal axis passes through (convex lens) or appears to diverge from (concave lens) the second focus (F₂).

Image formation for a convex lens

Object position	Image position	Nature of image	Magnification (m)
At infinity	At focus (F₂)	Real, inverted, very small	m < 0, approaches 0
Between infinity and 2F₁	Between F₂ and 2F₂	Real, inverted, diminished	−1 < m < 0
At 2F₁	At 2F₂	Real, inverted, same size	m = −1
Between 2F₁ and F₁	Beyond 2F₂	Real, inverted, enlarged	m < −1
At F₁	At infinity	Real, inverted, highly enlarged	m < 0, very large magnitude
Between F₁ and optical centre O	On same side as object	Virtual, erect, enlarged	m > +1

Image formation for a concave lens

A concave lens always forms a virtual, erect and diminished image on the same side as the object (m > 0).

Object position	Image position	Nature of image	Magnification (m)
At infinity	At focus (F₁)	Virtual, erect, point-sized	m ≪ +1
In front of lens (any distance)	Between F₁ and optical centre O	Virtual, erect, diminished	0 < m < +1

Sign convention for lenses

Parameter / quantity	Real image	Virtual image
Object distance (u)	Negative (−)	Negative (−)
Image distance (v)	Positive (+)	Negative (−)
Object height (hₒ)	Positive (+)	Positive (+)
Image height (hᵢ)	Negative (−)	Positive (+)
Magnification (m)	Negative (−)	Positive (+)

7. Lens Formula, Power and Combination

Lens formula

The lens formula relates object distance (u), image distance (v) and focal length (f) of a lens.

1/f = 1/v − 1/u Lens formula

Rules for applying lens formula

Substitute known values with their proper algebraic sign conventions.
Do not assign a sign to the unknown variable; its sign will emerge automatically from the calculation.
A positive calculated image distance (v > 0) indicates an image on the opposite side of the lens (real image). A negative image distance (v < 0) indicates an image on the same side as the object (virtual image).

Magnification of lens

Magnification (M) of a lens is the ratio of image height (hᵢ) to object height (hₒ).

M = hᵢ / hₒ = v / u Lens magnification

Power of a lens

The power (P) of a lens is defined as the reciprocal of its focal length (f) expressed in metres.

P = 1 / f (in metres) Power formula

SI unit: Dioptre (D) or m⁻¹.
Power of a convex lens is positive (+D).
Power of a concave lens is negative (−D).

Combination of thin lenses

When two or more thin lenses are placed in contact with each other:

P = P₁ + P₂ + P₃ + … Total power

1/F = 1/f₁ + 1/f₂ + 1/f₃ + … Equivalent focal length

⚡ Quick Formula Revision

Spherical mirrorf = R/21/v + 1/u = 1/fm = −v/u

Refractionsin i / sin r = n₂₁n = c/vn₂₁ × n₁₂ = 1

Lens1/f = 1/v − 1/uM = v/uP = 1/f (metres)

Lenses in contactP = P₁ + P₂ + …1/F = 1/f₁ + 1/f₂ + …

Remember: Use the correct sign convention before substituting values in mirror and lens numericals. For lens power, focal length must be expressed in metres.

Magnetic Effect Of Electric Current Notes

MG SCHOOL SCIENCE • CLASS 10

Magnetic Effects of Electric Current

Chapter Notes • Important Concepts • Rules • Quick Revision • Self-Test

1. Introduction to Magnetism

What is a magnet?

A magnet is a material that generates a magnetic field and can attract or repel materials with magnetic properties. Examples of magnetic materials include iron, nickel and cobalt. Lodestone is a natural magnet.

Every magnet has two poles: north and south.
Magnetic poles always occur in pairs and cannot be separated.
A freely suspended magnet aligns approximately in the north–south direction.

Electric current and magnetism

An electric current-carrying wire behaves like a magnet. A compass needle gets deflected when electric current passes through a metallic conductor.

Electromagnets and electric motors involve the magnetic effect of electric current. Electric generators involve the generation of electric current by moving magnets.

Bar magnet

A bar magnet is a solid, typically rectangular object made from a magnetic material such as iron or steel. It has two distinct poles: north and south. Its north pole points approximately towards the Earth's geographic north when freely suspended. This property is useful in magnetic compasses.

NORTH (N)← attraction / repulsion →SOUTH (S)

2. Properties of Magnets

Every magnet has two poles: North and South.
Like poles repel each other.
Unlike poles attract each other.
A freely suspended bar magnet aligns itself approximately in the north–south direction, with its north pole towards the north.

N↔NLike poles repel

N→←SUnlike poles attract

3. Magnetic Field and Field Lines

Magnetic field: A magnetic field is a vector quantity; it has both magnitude and direction. Its direction at a point is indicated by the direction in which the north pole of a compass needle points at that point.

Characteristics of magnetic field lines

Outside a magnet, field lines emerge from the north pole and enter the south pole.
Inside the magnet, field lines go from south to north, forming continuous closed loops.
The closeness of field lines indicates field strength. Closer lines represent a stronger magnetic field.
Magnetic field lines never intersect. If they intersected, a compass needle at the intersection would have to point in two directions at once.

Remember the direction:
Outside the magnet: North → South
Inside the magnet: South → North

Oersted's discovery

H. C. Oersted was the first person to demonstrate that an electric current produces a magnetic field.

A magnetic field can be thought of as an invisible region around a magnet or current-carrying conductor where magnetic force can be experienced.

4. Magnetic Field Due to Current Through a Straight Conductor

The magnetic field around a straight current-carrying conductor forms concentric circles centred on the wire.
The direction of the field can be found using the Right-Hand Thumb Rule or a magnetic compass.
The circles are closer together near the conductor, showing that the field is stronger near the wire.
Increasing the current increases the magnetic field strength and the compass needle's deflection.
Moving the compass farther from the wire decreases the needle's deflection when current is constant.

Magnetic field strength ∝ Current

Magnetic field strength ∝ 1 / Distance from conductor

Right-Hand Thumb Rule

Imagine holding a current-carrying straight conductor in your right hand so that your thumb points in the direction of current. The curled fingers give the direction of the magnetic field lines around the conductor.

Thumb
Direction of current

➜

Curled fingers
Direction of magnetic field

5. Magnetic Field Due to Current Through a Circular Loop

The magnetic field around a circular loop varies with distance.
Near the centre of the loop, the magnetic field lines appear as straight lines.
At the centre, the magnetic field contributions from each part of the wire are in the same direction and add together.
If a coil has multiple turns, the magnetic field becomes stronger because the field due to each turn adds up.

Factors affecting the magnetic field of a circular current-carrying coil

Factor	Relationship stated in the notes
Current through the conductor	Magnetic field ∝ Current
Radius of the coil	Magnetic field ∝ 1 / Radius
Number of turns	Magnetic field ∝ Number of turns
Multiple loops	Fields due to the loops add together when current flows in the same direction in each turn.

6. Magnetic Field Due to Current in a Solenoid

Solenoid: A solenoid is a coil made of many circular loops of insulated copper wire wrapped tightly in a cylindrical shape.

One end of a current-carrying solenoid acts like a north pole and the other like a south pole.
The magnetic field pattern of a solenoid resembles that of a bar magnet.
Inside the solenoid, magnetic field lines are straight and parallel, indicating a uniform magnetic field.
A solenoid can magnetise a soft iron material placed inside it, forming an electromagnet.

Direction of field:
Outside the solenoid: North → South
Inside the solenoid: South → North

7. Force on a Current-Carrying Conductor in a Magnetic Field

André-Marie Ampère (1775–1836) proposed that if a current-carrying conductor produces a magnetic field and exerts a force on a magnet, the magnet must also exert an equal and opposite force on the conductor.
When an aluminium rod carrying electric current is placed in a magnetic field, it experiences a mechanical force and gets displaced.
Reversing the current reverses the direction of force.
Reversing the magnet's poles also reverses the direction of force.
The force is greatest when the current direction is perpendicular (90°) to the magnetic field.

Fleming's Left-Hand Rule

Stretch the thumb, forefinger and middle finger of your left hand so that they are mutually perpendicular to one another.

Finger	Indicates
Forefinger	Direction of magnetic field
Middle finger	Direction of electric current
Thumb	Direction of motion or force on the conductor

Memory tip: Forefinger = Field; Middle finger = Current; Thumb = Thrust (force/motion).

8. Medical Applications of Magnetism

The heart and brain in the human body produce magnetic fields.
MRI (Magnetic Resonance Imaging): Images of internal organs can be obtained using strong magnetic fields and radio waves through MRI technology.

9. Domestic Electric Circuits

In domestic wiring, electrical energy is delivered using three main types of insulated wires.

Wire	Insulation colour in the supplied notes	Function / potential
Live wire	Red	High potential (220 V in India)
Neutral wire	Black	Low potential (0 V); completes the circuit
Earth wire	Green	Safety grounding for metallic appliances

Potential difference in India (as stated in these notes): 220 V between the live wire and neutral wire.

Domestic distribution path

Electricity supply pole→Main supply→Electric fuse→Electricity meter→Distribution box→Separate circuits

Key safety concepts and hazards

Earth wire safety

The earth wire protects users from electric shocks in case of current leakage, especially in appliances with metallic bodies. It provides a low-resistance conducting path to the earth for leaked current.

Short circuit

A short circuit occurs when a live wire comes into direct contact with a neutral wire accidentally. The circuit resistance drops drastically, causing a dangerously large electric current to flow.

Overloading

Overloading occurs when the current drawn exceeds the rated current-carrying capacity of the conductor.

Causes of overloading

An accidental increase or surge in the voltage supply.
Connecting more than one high-power appliance to a single electrical socket.

Safety devices

Device	Function
Electric fuse	A safety device that melts and breaks the circuit during excessive current flow.
Earth wire	Provides grounding protection against current leakage.
MCB (Miniature Circuit Breaker)	An automatic switch that trips to interrupt current flow when an overload or short circuit is detected.

Safety reminder: Never experiment with household mains electricity. Practical electrical work should be done only under the supervision of a qualified person.

10. Quick Revision

Topic	Key point to remember
Magnetic poles	Like poles repel; unlike poles attract.
Oersted	Showed that electric current produces a magnetic field.
Bar magnet field	Outside N → S; inside S → N.
Straight conductor	Concentric circular magnetic field lines.
Right-Hand Thumb Rule	Thumb: current; curled fingers: magnetic field.
Circular coil	Field increases with current and number of turns; decreases with radius.
Solenoid	Many circular turns; uniform field inside; can form an electromagnet with soft iron.
Fleming's Left-Hand Rule	Forefinger: field; middle finger: current; thumb: force/motion.
MRI	Uses strong magnetic fields and radio waves.
Short circuit	Live and neutral wires make direct contact.
Overloading	Current exceeds the conductor's rated capacity.
MCB	Trips to interrupt current during overload or short circuit.

Electricity Notes

MG SCHOOL SCIENCE • CLASS 10

Electricity

Chapter 11 • Complete Study Notes, Important Formulae, Activities and Solved Numericals

Class 10 ScienceChapter NotesNumerical ProblemsQuick Revision

Introduction to Electricity

Electricity plays a crucial role in our modern world, powering everything from homes and schools to hospitals and industries. In this chapter, we explore electric circuits, the factors that influence the flow of current, the heating effect of electric current and its practical applications.

Historical origin: The word electricity originates from the Greek word “Elektron” (amber). The Greek philosopher Thales was the first to observe the attracting capacity of certain materials when rubbed together.

1. Electric Current and Circuit

Electricity is one of the most convenient and widely used forms of energy in the world.
Conductors: Substances in which electric charge can flow freely. Metals are conductors. Copper and aluminium are commonly used in electricity.
Insulators: Materials in which electric charges do not move freely. Rubber, glass and plastic are examples.
Current electricity: Deals with moving charges.
Electric circuit: A continuous and closed path of an electric current.

Electric current: The rate of flow of electric charge through a cross-section of a conductor.

I = Q / t

Here, I = electric current, Q = charge flown and t = time.

Flow of Electric Current and Units

The SI unit of electric current is ampere (A).
One ampere is the flow of one coulomb of charge per second: 1 A = 1 C s⁻¹.
The unit is named after the French scientist André-Marie Ampère.
Conventional current is taken opposite to the direction of flow of negatively charged electrons. It is along the direction in which positive charges would move.
In conductors, electric current is due to the flow of electrons. The flow of 6.25 × 10¹⁸ electrons per second across a cross-section constitutes a current of 1 ampere.

📌 Solved Example 1: Charge Calculation

Question: A current of 0.75 A flows through a heater for 8 minutes. Calculate the amount of electric charge that passes through the circuit.

Given: I = 0.75 A; t = 8 min = 480 s

Formula: Q = I × t

Calculation: Q = 0.75 × 480 = 360 C

Result: The electric charge is 360 C.

2. Electric Potential and Potential Difference

The flow of electric charge in a circuit is similar to water flow in a pipe:

The water pipe is analogous to the electric conductor, and the amount of water flowing across a section per second corresponds to electric current.
Just as water flows from higher pressure (level) to lower pressure (level), electric current flows from higher electric potential to lower electric potential.
The potential difference across a conductor is maintained by using a cell or battery.
The chemical action within a cell generates the potential difference between its electrodes, due to which current flows through the circuit.

Potential difference: The work done to move a unit positive charge from one point to another in an electric circuit carrying current.

V_A − V_B = W / Q

SI unit: volt (V), where 1 V = 1 J / 1 C = 1 J C⁻¹.

📌 Solved Example 2: Work Done Calculation

Question: How much work is done in moving a charge of 3 C between two points with a potential difference of 9 V?

Given: Q = 3 C; V = 9 V

Formula: W = V × Q

Calculation: W = 9 × 3 = 27 J

Result: 27 J of work is done in moving the charge.

3. Circuit Diagram

A circuit diagram is a simplified representation of the components of an electrical circuit using either images of distinct parts or standard symbols.

It shows the relative positions of all the elements and their connections to one another.
It is often used to provide a visual representation of the circuit to an electrician or engineer.

4. Ohm’s Law

Georg Simon Ohm established a relationship between the electric current flowing through a conductor and the potential difference across its ends.

Statement: According to Ohm’s law, temperature remaining constant, the current passing through a conductor is directly proportional to the potential difference across its ends.

V ∝ I ⇒ V = I × R or R = V / I

The constant R is known as the resistance of the given conductor.
For a given conductor, its resistance is constant at a given temperature.
Electrical resistance is a measure of the opposition offered by a conductor to the flow of electric charge through it.
The SI unit of electrical resistance is ohm (Ω), where 1 Ω = 1 V / 1 A.

Activity: Verifying Ohm’s Law

Objective: To study the relationship between potential difference (V) across a nichrome wire and current (I) passing through it by varying the number of cells.
Materials: Nichrome wire (0.5 m), ammeter, voltmeter, four 1.5 V cells, connecting wires, switch and circuit board.
Procedure: Connect the nichrome wire in series with an ammeter and in parallel with a voltmeter using one 1.5 V cell. Record current and potential difference. Increase the cells to 2, 3 and 4 successively, recording I and V each time. Plot V against I.
Conclusion: The ratio V/I remains constant in each case. The V-I graph is a straight line passing through the origin, proving V ∝ I.

Important note: Current through a resistor is inversely proportional to its resistance. If resistance is doubled, current gets halved, when the potential difference is unchanged.

5. Factors Affecting Resistance of a Conductor

At a given temperature, the resistance of a conductor depends on:

Length (L): R ∝ L
Area of cross-section (A): R ∝ 1/A
Nature of the material of the conductor.

R = ρ × (L / A)

Here, ρ (rho) is the resistivity of the material.

Resistivity is the resistance offered by a cube of that material of side 1 m when current flows perpendicular to opposite faces.
Unit of resistivity: ohm-metre (Ω·m).
Its value depends only on the nature of the material and temperature, and is independent of dimensions.
Metals and alloys have low resistivity (10⁻⁸ to 10⁻⁶ Ω·m) and are good conductors. Insulators such as rubber and glass have resistivity of 10¹² to 10¹⁷ Ω·m.
Pure metals have very low resistivity. Copper and aluminium are used for transmission lines.
Alloys have higher resistivity and do not oxidise easily. Nichrome is used in heaters, irons and geysers.
Tungsten is used for lamp filaments due to its high melting point.

Rheostat

A variable resistance device used to regulate current without changing the voltage source.

Ammeter

An instrument connected in series to measure current.

Voltmeter

An instrument connected in parallel to measure potential difference.

📌 Solved Example 3: Resistivity Calculation

Question: The resistance of a metal wire of length 1.5 m is 30 Ω at 25°C. If its diameter is 0.4 mm, find resistivity at 25°C.

Given: R = 30 Ω; d = 0.4 mm = 4 × 10⁻⁴ m; l = 1.5 m

Formula: ρ = R × A / l = R × (πd²/4) / l

Calculation: ρ = (30 × 3.1416 × (4 × 10⁻⁴)²) / (4 × 1.5) = 2.51 × 10⁻⁶ Ω·m

Result: Resistivity of the metal at 25°C is 2.51 × 10⁻⁶ Ω·m.

📌 Solved Example 4: Resized Wire Resistance

Question: A wire of length l and cross-sectional area A has resistance 6 Ω. What is the resistance of another wire of the same material with length l/3 and cross-sectional area 3A?

For wire 1: R₁ = ρ(l/A) = 6 Ω

For wire 2: R₂ = ρ((l/3)/(3A)) = ρ(l/9A) = (1/9) × R₁

R₂ = (1/9) × 6 Ω = 0.67 Ω (approximately).

Result: The new wire has resistance 0.67 Ω (approximately; the source notes also give a simplified rounded value of 1 Ω).

6. Resistance of System of Resistors

Resistors in an electric circuit can be connected in series or parallel arrangement.

Series Combination

Current flowing through all resistors is the same.
Total voltage equals the sum of voltage drops: V = V₁ + V₂ + V₃.
Total equivalent resistance:

R_s = R₁ + R₂ + R₃ + ...

Parallel Combination

Voltage across each resistor is the same and equals the total applied voltage.
Current divides among resistors inversely proportional to resistance. I = I₁ + I₂ + I₃.
Reciprocal of equivalent resistance:

1/R_p = 1/R₁ + 1/R₂ + 1/R₃ + ...

For two resistors:

R_p = (R₁ × R₂) / (R₁ + R₂)

Why Parallel Connection is Preferred in Household Circuits

In series, if one component fails, the circuit breaks and all components stop working.
In series, the same current flows through all appliances regardless of their requirement.
Parallel circuits divide current so each appliance draws the required current with separate switches, and total circuit resistance decreases.

📌 Solved Example 5: Series Circuit and Power Analysis

Question: An electric lamp of resistance 20 Ω and a conductor of 4 Ω are connected in series to a 6 V battery. Calculate (a) total resistance, (b) circuit current, (c) potential difference across the lamp and conductor, and (d) power of the lamp.

Given: R₁ = 20 Ω; R₂ = 4 Ω; V = 6 V

Total resistance: R = R₁ + R₂ = 20 + 4 = 24 Ω.
Current: I = V/R = 6/24 = 0.25 A.
Voltage across lamp: V₁ = I × R₁ = 0.25 × 20 = 5 V.
Voltage across conductor: V₂ = I × R₂ = 0.25 × 4 = 1 V.
Power of lamp: P = V₁ × I = 5 × 0.25 = 1.25 W.

Results: Total resistance = 24 Ω; current = 0.25 A; voltage drops = 5 V and 1 V; lamp power = 1.25 W.

7. Heating Effect of Electric Current

According to Joule’s law of heating, when current I flows through resistance R for time t under voltage V, the electrical energy consumed or heat produced is:

H = W = Q × V = V × I × t = I² × R × t = (V² × t) / R

Unit: Joule (J).

Formula H = I²Rt is preferred for series circuits (constant current I).
Formula H = (V²t)/R is preferred for parallel circuits (constant voltage V).

📌 Solved Example 6: Electric Heater Power and Resistance

Question: An electric heater uses 900 W at maximum heat and 400 W at minimum heat, operating at 240 V. Calculate current and resistance in each case.

Formulae: I = P/V and R = V/I

(a) Maximum heating: P = 900 W, V = 240 V

Current I = 900/240 = 3.75 A
Resistance R = 240/3.75 = 64 Ω

(b) Minimum heating: P = 400 W, V = 240 V

Current I = 400/240 = 1.67 A
Resistance R = 240/1.67 ≈ 144 Ω

Result: Maximum heat → 3.75 A, 64 Ω. Minimum heat → 1.67 A, 144 Ω.

Practical Applications of Heating Effect

Electric lighting – Electric bulb: The filament is made of high melting-point tungsten. It is filled with inert nitrogen and argon gas to prolong filament life.
Electric fuse: A safety device placed in series. It consists of a wire with an appropriate low melting point. Excess current heats the wire beyond its melting point, breaking the circuit.

8. Electric Power

Definition: Electric power is defined as the time rate of doing electrical work.

P = W/t = V × I = I² × R = V² / R

SI unit: Watt (W), where 1 watt = 1 volt × 1 ampere = 1 VA.
Commercial unit of electrical energy: Kilowatt-hour (kWh).
Conversion: 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J.

⚡ Quick Formula Revision

Quantity / Concept	Formula	SI Unit
Electric current	I = Q/t	Ampere (A)
Electric charge	Q = I × t	Coulomb (C)
Potential difference	V = W/Q	Volt (V)
Ohm’s law	V = I × R	—
Resistance	R = V/I	Ohm (Ω)
Resistivity relation	R = ρL/A	Ω·m for ρ
Series resistance	R_s = R₁ + R₂ + ...	Ohm (Ω)
Parallel resistance	1/R_p = 1/R₁ + 1/R₂ + ...	Ohm (Ω)
Heat produced	H = I²Rt	Joule (J)
Electric power	P = VI = I²R = V²/R	Watt (W)
Electrical energy	E = P × t	Joule (J) or kWh

Study tip: Before solving a numerical, write the given quantities, convert all values into SI units, select the correct formula, substitute the values and include the final unit.

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Class 10 Science | Notes

Human Eye And Colourful World Notes

1. Introduction

2. How Our Eyes Work Like a Camera Lens

3. The Human Eye

Structure and functions

4. Power of Accommodation

Near point and far point

Cataract

5. Defects of Vision and Their Correction

Comparison of refractive defects

6. Refraction of Light Through a Prism

7. Dispersion of White Light by a Glass Prism

8. Recombination of White Light

9. Rainbow Formation

10. Atmospheric Refraction

Apparent flickering behind a hot surface

Stars near the horizon

Advanced sunrise and delayed sunset

Twinkling of stars

Why do planets not twinkle?

11. Scattering of Light

Tyndall Effect

Why is the clear sky blue?

Quick Revision • Important Facts

Practice Test • Check Your Understanding

Light - Reflection And Refraction Notes

Common phenomena associated with light

Properties of light

Laws of reflection

Real and virtual images

Image formed by a plane mirror

Common terms for spherical mirrors

Rules for ray diagrams in spherical mirrors

Image formation by a concave mirror

Uses of concave mirrors

Image formation by a convex mirror

Uses of convex mirrors

New Cartesian sign convention for reflection

Mirror formula and magnification

Key rules for magnification (m)

Speed of light and media density

Laws of refraction

Bending behaviour of light

Refractive index (n)

Key terminologies for lenses

Rules for ray diagrams in lenses

Image formation for a convex lens

Image formation for a concave lens

Sign convention for lenses

Lens formula

Rules for applying lens formula

Magnification of lens

Power of a lens

Combination of thin lenses

⚡ Quick Formula Revision

📝 Self-check Quiz

Magnetic Effect Of Electric Current Notes

1. Introduction to Magnetism

Electric current and magnetism

Bar magnet

2. Properties of Magnets

3. Magnetic Field and Field Lines

Characteristics of magnetic field lines

Oersted's discovery

4. Magnetic Field Due to Current Through a Straight Conductor

Right-Hand Thumb Rule

5. Magnetic Field Due to Current Through a Circular Loop

Factors affecting the magnetic field of a circular current-carrying coil

6. Magnetic Field Due to Current in a Solenoid

7. Force on a Current-Carrying Conductor in a Magnetic Field

Fleming's Left-Hand Rule

8. Medical Applications of Magnetism

9. Domestic Electric Circuits

Domestic distribution path

Key safety concepts and hazards

Causes of overloading

Safety devices