Grade 9
  1. Mechanics  1.1. Motion  1.1.1. Types of motion  1.1.2. Distance and displacement  1.1.3. Speed and Velocity  1.1.4. Acceleration  1.1.5. Graphical representation of motion  1.1.6. Equations of motion  1.1.7. Uniform and non-uniform motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Relative speed  1.1.10. Circular motion  1.2. Laws of force and motion  1.2.1. The concept of force  1.2.2. newton's first law of motion  1.2.3. Newton's second law of motion  1.2.4. Newton's third law of motion  1.2.5. Inertia and types of inertia  1.2.6. Motion  1.2.7. Conservation of momentum  1.2.8. Application of Newton's laws in daily life  1.2.9. Types of Forces (Contact and Non-Contact)  1.2.10. Friction and its effects  1.3. Gravitational force  1.3.1. Newton's law of universal gravitation  1.3.2. Importance of Gravitational Force  1.3.3. Acceleration due to gravity  1.3.4. Free fall and weightlessness  1.3.5. Mass and weight  1.3.6. Variation of g with height and depth  1.3.7. Kepler's laws of planetary motion  1.3.8. Satellites and their orbits  1.4. Work, Energy and Power  1.4.1. Concept of work  1.4.2. Positive and negative actions  1.4.3. Work done by constant and variable force  1.4.4. Energy and its forms  1.4.5. Kinetic energy and potential energy  1.4.6. Law of conservation of energy  1.4.8. Commercial unit of energy  1.4.9. Work–energy theorem  1.5. Simple machines  1.5.1. Types of simple machines  1.5.2. Mechanical advantage  1.5.3. Machine efficiency  1.5.4. Levers and their types  1.5.5. Pulleys and Inclined Planes  1.5.6. Gears and their uses
  2. Properties of matter  2.1. States of matter  2.1.1. Solids, liquids and gases  2.1.2. Properties of different states of matter  2.1.3. Change in state of matter  2.1.4. Plasma and Bose–Einstein condensate  2.2. Density and pressure  2.2.1. Concept of density and relative density  2.2.2. Pressure in solids, liquids and gases  2.2.3. Pascal's law and its applications  2.2.4. Atmospheric pressure and its variations  2.2.5. Surface tension and capillarity  2.3. Buoyancy and Archimedes' principle  2.3.1. Buoyant force  2.3.2. Archimedes principle  2.3.3. Applications of Archimedes' Principle  2.3.4. floating and sinking objects  2.3.5. Theory of Flotation and Archimedes' Principle
  3. Heat and Thermodynamics  3.1. Temperature and heat  3.1.1. Concept of heat and temperature  3.1.2. Temperature measurement  3.1.3. Temperature scales  3.2. Heat transfer  3.2.1. Conduction of heat  3.2.2. Convection of heat  3.2.3. heat radiation  3.2.4. Applications of heat transfer  3.2.5. Thermal conductivity  3.3. Thermal expansion  3.3.1. Expansion of solids, liquids and gases  3.3.2. Abnormal expansion of water  3.3.3. Applications of Thermal Expansion  3.4. Specific heat capacity and latent heat  3.4.1. Concept of specific heat capacity  3.4.2. Measurement and applications of specific heat  3.4.3. Latent heat of fusion and vaporization  3.4.4. Heat Engines and Efficiency
  4. Waves and sound  4.1. Waves and their types  4.1.1. Mechanical and electromagnetic waves  4.1.2. Longitudinal and Transverse Waves  4.1.3. Properties of Waves  4.1.4. Wavelength, frequency and speed of the wave  4.1.5. Superimposition of waves  4.2. Sound waves  4.2.1. Nature and transmission of sound  4.2.2. Speed of sound in different mediums  4.2.3. Reflection of sound and echo  4.2.4. Sonar and ultrasound  4.2.5. Resonance and pulsation  4.3. Sound characteristics  4.3.1. Intensity, loudness and quality of sound  4.3.2. Doppler effect in sound
  5. Lighting and Optics  5.1. Reflection of light  5.1.1. Laws of reflection  5.1.2. Reflection from a plane mirror  5.1.3. Reflection from a spherical mirror  5.1.4. Image formation by concave and convex mirrors  5.1.5. Applications of Reflection  5.2. Refraction of light  5.2.1. Laws of refraction  5.2.2. Refractive index  5.2.3. Refraction through a glass slab  5.2.4. Refraction in water and air  5.2.5. Lenses and their types  5.2.6. Image formation by convex and concave lenses  5.2.7. Total internal reflection and its applications  5.3. Dispersion and scattering of light  5.3.1. Spectrum of white light  5.3.2. Prisms and Dispersion  5.3.3. Tyndall effect and blue sky
  6. Electricity and Magnetism  6.1. Electric charge and static electricity  6.1.1. The concept of electric charge  6.1.2. Charging by friction, contact and induction  6.1.3. Electroscope and its working  6.2. Current Electricity  6.2.1. The concept of electric current  6.2.2. Ohm's Law and Resistance  6.2.3. Factors affecting resistance  6.2.4. Series and Parallel Circuits  6.2.5. Heating effect of electric current  6.2.6. Electric power and energy  6.3. Magnetism  6.3.1. Natural and artificial magnets  6.3.2. Properties of magnets  6.3.3. Earth's magnetism  6.3.4. Magnetic field and field lines  6.3.5. Electromagnets and their applications
  7. Modern Physics  7.1. structure of the atom  7.1.1. Atomic Structure and Subatomic Particles  7.1.2. Electrons, Protons, and Neutrons  7.1.3. Rutherford and Bohr model  7.2. Radioactivity  7.2.1. Types of radioactive emissions  7.2.2. Half-life and radioactive decay  7.2.3. Uses and Hazards of Radioactivity
  8. Space science and astronomy  8.1. The universe and its components  8.1.1. Stars and galaxies  8.1.2. Planets and Solar System  8.2. Satellites  8.2.1. Natural and artificial satellites  8.2.2. Use of satellites

Grade 9 → Lighting and Optics → Reflection of light ↓


Reflection from a spherical mirror


Reflection is the change in the direction of a wavefront at an interface between two different media so that the wavefront returns to the medium from which it originated. In grade 9 physics, when we study reflection in light, one of the topics is reflection from spherical mirrors. In this lesson, we will explore the features, rules and calculations associated with spherical mirrors and understand their applications.

Understanding spherical mirrors

Spherical mirrors are mirrors with a curved surface that forms part of a sphere. They can be concave or convex:

  • Concave mirror: This mirror is curved inwards and looks like the inside of a sphere.
  • Convex mirror: This mirror is bulged outwards, and looks like the outer part of a sphere.

Let us imagine these types of mirrors:

Illustration of a concave mirror

Reflective Surface Non-reflective surface P

Illustration of a convex mirror

Reflective Surface Non-reflective surface P

The principal axis of these mirrors is called the principal axis, and the midpoint of the mirror is called the pole (denoted by P).

Key terms and concepts

  • Pole (P): The centre of the mirror surface.
  • Centre of curvature (C): The centre of the sphere from which the mirror is separated.
  • Radius of curvature (R): Distance between C and P.
  • Principal axis: Line passing through C and P, and normal to the mirror at P.
  • Principal focus (F): The point on the principal axis where rays parallel to the axis converge (concave) or appear to diverge (convex).
  • Focal length (f): The distance between P and F.

To understand how light interacts with spherical mirrors, it is important to understand these concepts, as they are fundamental to all calculations and descriptions of reflected light behavior.

Reflection laws for spherical mirrors

Reflection of light from spherical mirrors follows some basic rules. These are important in finding the possible light path diagrams:

Concave mirror rule

  • Any ray parallel to the principal axis gets reflected through the focus.
  • Any ray passing through the centre of curvature reflects back along the same path.
  • Any ray passing through the focus is reflected parallel to the principal axis.
  • Any incident ray falling on the pole is reflected symmetrically about the principal axis.

Convex mirror rule

  • Any ray that is parallel to the principal axis is reflected and appears to diverge from the focal point.
  • Any incident ray directed towards the centre of curvature is reflected back along the same path.
  • Any incident ray directed towards the focus is reflected parallel to the principal axis.
  • Any incident ray falling on the pole is reflected at the same angle with respect to the principal axis.

Understanding these laws is fundamental to drawing ray diagrams and predicting the behavior of light in optics.

Ray diagram and image formation by spherical mirror

Ray diagram for a concave mirror

Let us visualise how a concave mirror forms an image with ray diagrams. Consider an object placed beyond the centre of curvature:

C F P

In this ray diagram, the object is placed beyond the centre of curvature, and the image is formed between C and F, which is diminished, inverted and real. Similar diagrams can be drawn by placing the object in different positions to show different image characteristics.

Ray diagram for a convex mirror

Now, consider the ray diagram for a convex mirror. When an object is placed in front of a convex mirror, the reflected rays appear to diverge. Here is an example:

F C P

In this ray diagram the object appears small, erect and virtual. The virtual image is located behind the mirror.

Mirror formula and magnification

The behavior of mirrors is measured using formulas. The two main equations are the mirror formula and the magnification formula. These help us understand the relationship between object distance (u), image distance (v) and focal length (f).

Mirror formula

1/f = 1/v + 1/u

Here, f is the focal length of the mirror, v is the image distance, and u is the object distance. This formula applies to all spherical mirrors. Here's how you use the formula:

  • For a concave mirror, f is negative.
  • For a convex mirror f is positive.

Magnification formula

Magnification is how large or small the image is compared to the object:

m = -v/u

In this formula, m is the magnification, v is the image distance, and u is the object distance. A negative value of magnification indicates an inverted image, while a positive value indicates an erect image.

Examples and exercises

Example 1: Concave mirror

An object is placed at a distance of 30 cm in front of a concave mirror of focal length 10 cm. Where is the image formed and what is its nature?

Given:

  • u = -30 cm
  • f = -10 cm

Use of Mirror Formula:

1/f = 1/v + 1/u 1/-10 = 1/v + 1/(-30)

Solving for v gives:

1/v = 1/-10 + 1/30 1/v = (-3 + 1)/30 1/v = -2/30 v = -15 cm

The image is formed at a distance of 15 cm in front of the mirror, which shows that it is real and inverted.

Example 2: Convex mirror

An object is placed at a distance of 20 cm in front of a convex mirror of focal length 15 cm. Where is the image formed?

Given:

  • u = -20 cm
  • f = 15 cm

Use of Mirror Formula:

1/f = 1/v + 1/u 1/15 = 1/v + 1/(-20)

Solving for v gives:

1/v = 1/15 + 1/20 1/v = (4 + 3)/60 1/v = 7/60 v = 60/7 cm ≈ 8.57 cm

The image is virtual, erect and formed at a distance of about 8.57 cm behind the mirror.

Applications of spherical mirrors

Spherical mirrors have wide usage in various fields. Here are some examples:

  • Concave mirrors: They are used in applications such as reflecting telescopes, shaving mirrors, and to focus light in vehicle headlights.
  • Convex mirrors: These mirrors are commonly used as rear-view mirrors in vehicles, giving drivers a wide-angle view of the road behind them.

Conclusion

Understanding reflection from spherical mirrors is a fundamental aspect of optics and physics. The behavior and rules governing how light reflects from these surfaces enable us to use and manipulate light for many practical applications. By mastering the concepts of ray diagrams, mirror formulas, and magnification, we not only appreciate the physics in everyday objects, but also develop the analytical skills necessary for advanced study in optics and related fields. Keep practicing with examples and exercises to strengthen your understanding of these fascinating aspects of reflection and optics.


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Reflection from a plane mirror
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Reflection from a spherical mirror

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