- A concave mirror has an inward-curved reflecting surface, while a convex mirror has an outward-curved reflecting surface.
- Important parts of a spherical mirror: Pole (P), Centre of Curvature (C), Principal Axis, and Principal Focus (F).
- For spherical mirrors, the relation is R = 2f, where R is the radius of curvature and f is the focal length.
- In concave mirrors, parallel rays converge at the focus; in convex mirrors, they appear to diverge from the focus behind the mirror.
Topics
Electrostatics
Electric Charges and Fields
- Electric Charge
- Positive and Negative Charges
- Electron Theory of Electrification
- Conductors and Insulators
- Electrostatic Induction
- Important Properties of Electric Charge
- Scalar Form of Coulomb’s Law
- Coulomb's Law in Vector Form
- Principle of Superposition
- Equilibrium of Charge and System of Charges
- Electric Field
- Electric Field Intensity Due to a Point-Charge
- Intensity of Electric Field due to a Continuous Charge Distribution
- Electric Lines of Force
- Electric Dipole
- Electric Field due to an Electric Dipole
- Torque on a Dipole in a Uniform Electric Field
Current Electricity
Gauss' Theorem
- Gauss’s Law
- Electric Flux
- Gauss' Theorem
- Applications of Gauss' Theorem
- Overview: Gauss' Theorem
Magnetic Effects of Current and Magnetism
Electric Potential
- Electric Potential
- Potential and Potential Difference
- Potential Gradient
- Equipotential Surfaces
- Potential Due to an Electric Dipole
- Electric Potential Energy of an Electric Dipole in an Electrostatic Field
- Overview: Electric Potential
Capacitors and Dielectrics
- Conductors and Insulators
- Capacitance of a Conductor
- Capacitors
- Capacitance of a Capacitor
- Combination of Capacitors
- Energy Stored in a Charged Capacitor
- Dielectrics
- Electric Polarisation of Matter
- Effect of Introducing a Dielectric between the Plates of a Charged Capacitor
- Overview: Capacitors and Dielectrics
Electromagnetic Induction and Alternating Currents
Electric Resistance and Ohm's Law
- Electric Current
- Current Density
- Mechanism of Flow of Charge in Metals
- Transport Properties of Free Electrons
- Mobility of Electrons
- Relation between Drift Velocity of Free Electrons and Electric Current
- Electric Resistance
- Ohm's Law
- Experimental Verification of Ohm’s Law
- Ohmic and Non-ohmic Resistors
- Exceptions to Ohm's Law
- Dynamic Resistance
- Derivation of Ohm's Law
- Specific Resistance or Electrical Resistivity
- Ohm's law in Vector Form
- Resistance and Conductor Dimensions
- Effect of Temperature on Resistivity
- Colour Code of Carbon Resistors
- Combinations of Resistances
- Derivation Using Series and Parallel Connections
- Electric Energy and Power
- Commercial Units of Electricity Consumption
- Overview: Electric Resistance and Ohm's Law
Electromagnetic Waves
DC Circuits and Measurements
- Electric cell
- Electromotive Force (emf)
- Terminal Potential Difference
- Internal Resistance of a Cell
- Relation between E, V, and r
- Combinations of Cells
- Kirchhoff’s Laws
- Wheatstone Bridge
- Rheostat
- Metre Bridge: Slide-Wire Bridge
- Potentiometer
- Overview: DC Circuits and Measurements
Optics (Ray and Wave Optics)
Dual Nature of Radiation and Matter
Moving Charges and Magnetic Field
- Magnetic Field
- Oersted's Experiment
- Biot-Savart Law
- Comparison of Coulomb's Law and Biot-Savart's Law
- Rules to Determine the Direction of Developed Magnetic Field
- Applications of Biot-Savart's Law > Magnetic Field due to a Finite Straight Current-Carrying Wire
- Applications of Biot-Savart's Law > Magnetic Field on the Axis of a Circular Current-Carrying Loop
- Applications of Biot-Savart's Law > Magnetic Field at the Centre of a Circular Loop
- Ampere’s Circuital Law
- Applications of Ampere’s Circuital Law > Magnetic Field of a Long Straight Solenoid
- Applications of Ampere’s Circuital Law > Magnetic Field of a Long Straight Thin Wire
- Applications of Ampere’s Circuital Law > Magnetic Field of a Toroidal Solenoid
- Force on a Moving Charge in a Uniform Magnetic Field
- Magnetic Field Defined by Magnetic Force
- Motion of Charged Particles in a Uniform Magnetic Field
- Lorentz Force
- Cyclotron
- Force on a Current - Carrying Conductor in a Uniform Magnetic Field
- Ampere: Based on Force Between Currents
- Overview: Moving Charges and Magnetic Field
Atoms and Nuclei
Torque on a Current-Loop : Moving-Coil Galvanometer
- Torque on a Current-Loop in a Uniform Magnetic Field
- Magnetic Moment of a Coil
- Moving Coil Galvanometer
- Sensitivity of a Galvanometer
- Conversion of a Galvanometer into an Ammeter
- Conversion of a Galvanometer into a Voltmeter
- Overview: Torque on a Current-Loop : Moving-Coil Galvanometer
Magnetic Field and Earth's Magnetism
- Current Loop as a Magnetic Dipole: Magnetic Dipole Moment of Current Loop
- Magnetic Dipole Moment of a Revolving Electron
- Magnetic Field of a Magnetic Dipole (Small Bar Magnet)
- Torque on a Magnetic Dipole (Bar Magnet) in a Uniform Magnetic Field
- Potential Energy of a Magnet in a Magnetic Field
- Current-Carrying Solenoid as an Equivalent to a Bar Magnet
- Magnetic Lines of Force
- Earth’s Magnetic Field
- Elements of the Earth's Magnetic Field > Angle of Declination
- Elements of the Earth's Magnetic Field > Angle of Dip or Magnetic Inclination
- Elements of the Earth's Magnetic Field > Horizontal Component of Earth's Magnetic Field
- Overview: Magnetic Field and Earth's Magnetism
Electronic Devices
Communication Systems
Magnetic Classification of Substances
- Classification of Substances According to their Magnetic Behaviour
- Terms Used in Magnetism
- Properties of Dia-, Para-, and Ferromagnetic Substances
- Explanation of Dia-, Para-, and Ferromagnetism based on the Atomic Model of Magnetism
- Hysteresis: Retentivity and Coercivity
- Differences in Magnetic Properties of Soft Iron and Steel
- Magnetic Materials
- Overview: Magnetic Classification of Substances
Electromagnetic Induction
- Magnetic Flux
- Electromagnetic Induction
- Faraday's Laws of Electromagnetic Induction
- Induced Current and Induced Charge
- Methods of Changing the Magnetic Flux
- Motion of a Straight Conductor in a Uniform Magnetic Field (Motional EMF)
- Explanation of Electromagnetic Induction in Terms of Lorentz Force: Proof of Faraday's Law
- Motional emf in Rotating a Conducting Rod in a Uniform Magnetic Field
- Self – Induction
- Self-Inductance of a Long Solenoid
- Energy Stored in an Inductor
- Examples of the Effects of Self-Induced Current
- Mutual Induction
- Mutual Inductance
- Eddy Currents or Foucault Currents
- Overview: Electromagnetic Induction
Alternating Current
- Alternating Voltage and Current in a Rotating Coil
- Definitions Regarding Alternating Voltage and Current
- Mean (or Average) Value of Alternating Current (or Voltage)
- Root-Mean-Square Value of Alternating Current
- Phasors and Phasor Diagrams
- Types of AC Circuits
- Circuit containing Resistance Only
- Circuit containing Inductance Only
- Circuit containing Capacitance Only
- Circuit containing Inductance and Resistance in Series (L-R Series Circuit)
- Circuit containing Capacitance and Resistance in Series (C-R Series Circuit)
- Circuit containing Inductance and Capacitance (L-C Circuit)
- Circuit containing Inductance, Capacitance and Resistance in Series (L-C-R Series Circuit)
- Power in AC Circuit
- Wattless Current
- Half Power Points, Bandwidth and Q-Factor
- Choke Coil
- Electrical Oscillations in L-C Circuit
- Resonant Circuits
- Frequency Response of AC Circuits
- A.C. Generator
- Transformers
- Utility of Alternating Current in Comparison to Direct Current
- Overview: Alternating Current
Electromagnetic Waves
- Displacement Current
- Relation between Conduction and Displacement Current
- Maxwell's Equation
- EM Wave
- Field Magnitude Relation in Free Space
- Energy Density in Electromagnetic Waves
- Transverse Nature of Electromagnetic Waves
- Electromagnetic Spectrum
- Overview: Electromagnetic Waves
Reflection of Light: Spherical Mirrors
- Spherical Mirrors
- Fundamental Terms Related to Spherical Mirrors
- Relation Between Focal Length and Radius of Curvature of a Spherical Mirror
- Rules to Trace the Image Formed by Spherical Mirrors
- Conditions of Image Formation
- Position and Nature of Image Formed by Spherical Mirrors
- Sign Convention
- Mirror Formula for Concave Mirror
- Mirror Formula for Convex Mirror
- Linear Magnification by Spherical Mirrors
- Uses of Spherical Mirrors
- Overview: Reflection of Light: Spherical Mirrors
Refraction of Light at a Plane Interface : Total Internal Reflection : Optical Fibre
- Refraction of Light
- Laws of Refraction
- Cause of Refraction
- Physical Significance of Refractive Index
- Reversibility of Light
- Refraction of Light Through a Rectangular Glass Block
- Refraction through Parallel Multiple Media
- Real and Apparent Depths: Normal Displacement
- Critical Angle
- Total Internal Reflection
- Applications of Total Internal Reflection
- Overview: Refraction of Light at a Plane Interface
Refraction of Light at Spherical Surfaces : Lenses
- Coordinate Geometry Sign Convention for Measuring Distances and Lengths
- Refraction at Concave Spherical Surface
- Refraction at a Convex Spherical Surface
- Concept of Lenses
- Converging and Diverging Actions of Lenses
- Lens Maker's Formula
- Factors Affecting Focal Length of a Lens
- Image Formation by Thin Lenses
- Ray Diagrams for Formation of Image by a Convex Lens
- Ray Diagram for Formation of Image by a Concave Lens
- Linear Magnification by Spherical Lenses
- Power of a Lens
- Combined Focal Length of Two Thin Lenses in Contact
- Combination of Lenses and Mirrors
- Overview: Refraction of Light at Spherical Surfaces: Lenses
Refraction and Dispersion of Light through a Prism
Optical Instruments
Wave Nature of Light : Huygens' Principle
Interference of Light
Diffraction of Light
Polarisation of Light
Photoelectric Effect
Matter Waves
X-Rays
Atom, Origin of Spectra : Bohr's Theory of Hydrogen Atom
Nuclear Structure
Radioactivity
Mass-Energy Equivalence : Nuclear Binding Energy
Nuclear Fission and Nuclear Fusion : Sources of Energy
Semiconductor Electronics
Junction Diodes
Junction Transistors
Logic Gates
Communication Systems
- Definition: Spherical Mirror
- Definition: Concave Mirror
- Definition: Convex Mirror
- Definition: Pole
- Definition: Centre of Curvature
- Definition: Radius of Curvature
- Definition: Principal Axis
- Introduction
- Types of Spherical Mirrors
- Activity
- Key Points: Spherical Mirrors
Maharashtra State Board: Class 9
Introduction:
Spherical mirrors are curved mirrors that form images different from those formed by plane mirrors. Unlike the flat mirrors commonly used at home, spherical mirrors distort images depending on their shape. For example, mirrors in a laughing chamber create distorted reflections due to their curved surfaces.
Laughing Chamber
These mirrors are also used in practical applications, such as rearview mirrors in cars, which allow drivers to see vehicles approaching from behind. The unique properties of spherical mirrors make them useful in various scientific, entertainment, and safety applications.
CBSE: Class 10
CISCE: Class 12
CISCE: Class 12
Definition: Spherical Mirrors
Mirrors whose reflecting surfaces are spherical are called spherical mirrors.
OR
A spherical mirror is a part of a hollow sphere, whose one side is silvered and coated with red oxide and the other side is the reflecting surface.
CBSE: Class 10
CISCE: Class 12
CISCE: Class 12
Definition: Concave Mirror
A spherical mirror, whose reflecting surface is curved inwards, that is, faces towards the centre of the sphere, is called a concave mirror.
OR
A concave mirror is one whose reflecting surface is towards the centre of the sphere of which the mirror is a part.
CBSE: Class 10
CISCE: Class 12
CISCE: Class 12
Definition: Convex Mirror
A spherical mirror whose reflecting surface is curved outwards, is called a convex mirror.
OR
A convex mirror is one whose reflecting surface is away from the centre of the sphere of which the mirror is a part.
CBSE: Class 10
CISCE: Class 12
CISCE: Class 12
Definition: Pole
The centre of the reflecting surface of a spherical mirror is a point called the pole. The pole is usually represented by the letter P.
OR
The central point of the reflecting surface of the mirror is called the 'pole' of the mirror.
CBSE: Class 10
CISCE: Class 12
CISCE: Class 12
Definition: Centre of Curvature
The reflecting surface of a spherical mirror forms a part of a sphere. This sphere has a centre. This point is called the centre of curvature of the spherical mirror. It is represented by the letter C.
OR
The centre of the sphere of which the mirror forms a part, is called the ‘centre of curvature' of the mirror.
CBSE: Class 10
CISCE: Class 12
CISCE: Class 12
Definition: Radius of Curvature
The radius of the sphere of which the reflecting surface of a spherical mirror forms a part is called the radius of curvature of the mirror. It is represented by the letter R.
OR
The radius of the sphere of which the mirror forms a part, is called the 'radius of curvature' of the mirror.
CBSE: Class 10
CISCE: Class 12
CISCE: Class 12
Definition: Principal Axis
A straight line passing through the pole and the centre of curvature of a spherical mirror. This line is called the principal axis.
OR
The straight line joining the pole and the centre of curvature of the mirror and extended on both sides is called the 'principal axis' of the mirror.
Maharashtra State Board: Class 9
Activity
Formation and Reflection in Spherical Mirrors:
- Cut a rubber ball into two equal halves and observe the curved surfaces.
- The inner surface is concave, resembling a concave mirror, where light reflects inside the curve.
- The outer surface is convex, resembling a convex mirror, where light reflects outward.
- In real spherical mirrors, either the inner or outer surface of a hollow glass sphere is coated with a reflective material like silver or aluminium.
- Concave mirrors focus light and are used in headlights and magnifying mirrors, while convex mirrors spread light and are used in vehicle side mirrors and security mirrors.
- This activity demonstrates how spherical mirrors are formed and how light reflects differently depending on the curved surface.
Creation of spherical mirrors
CBSE: Class 10
Key Points: Spherical Mirrors
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