NCERT Class 10 Science Chapter 10: Light – Reflection and Refraction - A Complete Guide

Introduction to Light – Reflection and Refraction

Welcome, students! Have you ever wondered how we see the world around us? The vibrant colours of a rainbow, your own reflection in a mirror, or the way a straw appears bent in a glass of water – all these phenomena are governed by the fascinating properties of light. Chapter 10 of your NCERT Class 10 Science textbook, "Light – Reflection and Refraction," delves into these very concepts, laying the foundation for the field of optics.

Light is a form of energy that enables our sense of sight. It travels in straight lines, a property known as the rectilinear propagation of light. Interestingly, light exhibits a dual nature, behaving as both a wave and a particle (photons), though in this chapter, we will primarily focus on its straight-line path, represented by rays. This chapter is crucial not only for your board exams but also for understanding how everyday optical instruments like cameras, telescopes, and even our own eyes work. We will explore two primary phenomena: reflection, the bouncing back of light, and refraction, the bending of light as it passes from one medium to another.

Reflection of Light

Reflection is the phenomenon of light bouncing off a surface. When light rays fall on a polished, smooth surface like a mirror, they are sent back. This is what allows us to see our image. Understanding the rules that govern this bouncing back is fundamental to optics.

Laws of Reflection

The reflection of light from any surface, whether smooth or rough, follows two simple laws. To understand these laws, we need to define a few terms:

• Incident Ray: The ray of light that strikes the surface.
• Reflected Ray: The ray of light that bounces back from the surface.
• Normal: An imaginary line drawn perpendicular (at 90°) to the surface at the point where the incident ray strikes.
• Angle of Incidence (∠i): The angle between the incident ray and the normal.
• Angle of Reflection (∠r): The angle between the reflected ray and the normal.

The two laws of reflection are:

1. The angle of incidence is equal to the angle of reflection (∠i = ∠r).
2. The incident ray, the reflected ray, and the normal to the surface at the point of incidence, all lie in the same plane.

These laws are universal and apply to all types of reflecting surfaces, including plane mirrors and curved (spherical) mirrors.

Image Formation by a Plane Mirror

A plane mirror is a flat, smooth reflecting surface. The image you see of yourself in a bathroom mirror is a perfect example. The properties of an image formed by a plane mirror are always consistent:

• Virtual and Erect: The image appears to be behind the mirror and cannot be projected onto a screen. It is upright (erect), not upside down.
• Same Size: The size of the image is exactly the same as the size of the object.
• Same Distance: The image is formed as far behind the mirror as the object is in front of it.
• Laterally Inverted: The image is reversed sideways. This is why the word 'AMBULANCE' is written in reverse on the front of emergency vehicles, so drivers can read it correctly in their rear-view mirrors.

Spherical Mirrors

Unlike plane mirrors, spherical mirrors are curved. They are a part of a hollow sphere. The reflecting surface of a spherical mirror can be curved inwards or outwards, leading to two different types.

Types of Spherical Mirrors

• Concave Mirror: A spherical mirror whose reflecting surface is curved inwards, towards the centre of the sphere. It is also known as a converging mirror because it converges parallel rays of light to a single point. Shaving mirrors and dentist's mirrors are common examples.
• Convex Mirror: A spherical mirror whose reflecting surface is curved outwards. It is known as a diverging mirror because it spreads out (diverges) the light rays that fall on it. Rear-view mirrors in vehicles and security mirrors in shops are examples of convex mirrors.

Important Terms Related to Spherical Mirrors

To study image formation by spherical mirrors, we must first understand some key terminology:

• Pole (P): The centre of the reflecting surface of the spherical mirror.
• Centre of Curvature (C): The centre of the hollow sphere of which the mirror is a part. It is not a part of the mirror itself.
• Radius of Curvature (R): The radius of the sphere of which the mirror is a part. It is the distance between the pole (P) and the centre of curvature (C).
• Principal Axis: The imaginary straight line passing through the pole and the centre of curvature.
• Principal Focus (F): For a concave mirror, it is a point on the principal axis where parallel rays of light converge after reflection. For a convex mirror, it is the point on the principal axis from which parallel rays of light appear to diverge after reflection.
• Focal Length (f): The distance between the pole (P) and the principal focus (F). A crucial relationship connects the focal length and the radius of curvature: f = R/2. The focal length is half the radius of curvature.

Image Formation by Spherical Mirrors

The location, size, and nature (real or virtual) of the image formed by a spherical mirror depend on the position of the object. We can determine this using ray diagrams.

Rules for Drawing Ray Diagrams

To construct accurate ray diagrams, we use at least two of the following four rules:

1. A ray parallel to the principal axis: After reflection, this ray will pass through the principal focus (F) in a concave mirror or appear to diverge from the principal focus (F) in a convex mirror.
2. A ray passing through the principal focus (F): After reflection, this ray will emerge parallel to the principal axis.
3. A ray passing through the centre of curvature (C): This ray reflects back along the same path because it strikes the mirror normally (at 90°).
4. A ray incident obliquely to the principal axis at the pole (P): This ray is reflected obliquely, following the laws of reflection (∠i = ∠r), with the principal axis acting as the normal.

Image Formation by a Concave Mirror

Concave mirrors can form both real and virtual images depending on the object's position. The various cases are summarized below:

Uses of Concave Mirrors: Used in torches and vehicle headlights to produce a powerful parallel beam of light, as shaving mirrors to see a larger image of the face, and by dentists to see an enlarged image of teeth.

Image Formation by a Convex Mirror

A convex mirror always forms a virtual, erect, and diminished image, regardless of the object's position. This property makes them incredibly useful.

• Object at infinity: The image is formed at the focus (F) behind the mirror. It is highly diminished and virtual.
• Object between infinity and the pole (P): The image is formed between P and F behind the mirror. It is diminished, virtual, and erect.

Uses of Convex Mirrors: Primarily used as rear-view (wing) mirrors in vehicles. This is because they always give an erect, diminished image and have a wider field of view, allowing the driver to see much more of the traffic behind them.

Sign Convention for Reflection by Spherical Mirrors

To solve numerical problems involving mirrors, we use a consistent set of sign conventions called the New Cartesian Sign Convention. The rules are:

1. The object is always placed to the left of the mirror.
2. All distances are measured from the pole (P) of the mirror.
3. Distances measured in the same direction as the incident light (to the right of P) are taken as positive.
4. Distances measured against the direction of the incident light (to the left of P) are taken as negative.
5. Heights measured upwards and perpendicular to the principal axis are taken as positive.
6. Heights measured downwards and perpendicular to the principal axis are taken as negative.

Based on this convention: object distance (u) is always negative. The focal length (f) of a concave mirror is negative, while for a convex mirror, it is positive.

Mirror Formula and Magnification

The Mirror Formula

The mirror formula is a mathematical relationship between the object distance (u), the image distance (v), and the focal length (f) of a spherical mirror. It is expressed as:

1/v + 1/u = 1/f

This formula is valid for all spherical mirrors for all positions of the object. Remember to use the correct signs for u, v, and f when solving problems.

Magnification (m)

Magnification tells us how large or small the image is relative to the object. It is the ratio of the height of the image (h') to the height of the object (h).

m = h'/h

Magnification is also related to the object and image distances:

m = -v/u

• If m is negative, the image is real and inverted.
• If m is positive, the image is virtual and erect.
• If |m| > 1, the image is magnified (enlarged).
• If |m| < 1, the image is diminished (smaller).
• If |m| = 1, the image is the same size as the object.

Refraction of Light

We now move to the second major phenomenon: refraction. Refraction is the bending of light when it travels from one transparent medium to another (e.g., from air to water). This bending occurs because the speed of light is different in different media. Light travels fastest in a vacuum and slower in denser media like water or glass.

The extent of bending depends on the optical density of the media. A medium in which the speed of light is lower is called an optically denser medium, while one where the speed is higher is an optically rarer medium.

• When light enters from a rarer to a denser medium, it bends towards the normal.
• When light enters from a denser to a rarer medium, it bends away from the normal.

Refraction through a Rectangular Glass Slab

When a ray of light passes through a rectangular glass slab, it gets refracted twice: once when entering the glass from air, and again when exiting the glass back into the air. The emergent ray is parallel to the incident ray, but it is slightly shifted sideways. This perpendicular shift is called lateral displacement. In this case, the angle of incidence is equal to the angle of emergence (∠i = ∠e).

Laws of Refraction

Similar to reflection, refraction also follows two laws:

1. The incident ray, the refracted ray, and the normal to the interface of the two transparent media at the point of incidence, all lie in the same plane.
2. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for the light of a given colour and for the given pair of media. This law is known as Snell's Law.

Mathematically, Snell's Law is expressed as: sin(i) / sin(r) = constant = n₂₁

This constant value is called the refractive index of the second medium with respect to the first medium.

Refractive Index (n)

The refractive index is a measure of how much a medium can bend light. It is defined as the ratio of the speed of light in a vacuum (c) to its speed in a given medium (v).

n = c / v

This is called the absolute refractive index. The relative refractive index (n₂₁) compares the speeds of light in two different media: n₂₁ = v₁ / v₂. The higher the refractive index, the optically denser the medium and the slower the light travels in it.

Refraction by Spherical Lenses

A lens is a piece of transparent material (like glass) bound by two surfaces, at least one of which is curved. We will focus on spherical lenses, which have two spherical surfaces.

Types of Spherical Lenses

• Convex Lens: It is thicker at the centre and thinner at the edges. It is a converging lens because it brings parallel rays of light together at a single point.
• Concave Lens: It is thinner at the centre and thicker at the edges. It is a diverging lens because it spreads out the parallel rays of light that pass through it.

Important Terms Related to Spherical Lenses

• Optical Centre (O): The central point of a lens. A ray of light passing through it emerges without any deviation.
• Centre of Curvature (C): A lens has two spherical surfaces, so it has two centres of curvature (C₁ and C₂).
• Principal Axis: The imaginary line passing through the two centres of curvature.
• Principal Focus (F): A lens has two principal foci (F₁ and F₂). For a convex lens, F₂ is where parallel rays converge. For a concave lens, F₁ is the point from which parallel rays appear to diverge.
• Focal Length (f): The distance from the optical centre (O) to the principal focus (F).

Image Formation by Lenses

The principles of image formation by lenses are similar to those for mirrors, relying on ray diagrams.

Rules for Drawing Ray Diagrams for Lenses

1. A ray parallel to the principal axis: After refraction from a convex lens, it passes through the principal focus (F₂) on the other side. For a concave lens, it appears to diverge from the principal focus (F₁) on the same side.
2. A ray passing through the principal focus: After refraction from a convex lens, it will emerge parallel to the principal axis. A ray directed towards the principal focus of a concave lens will emerge parallel to the principal axis.
3. A ray passing through the optical centre (O): It will emerge from the lens without any deviation.

Image Formation by a Convex Lens

A convex lens can form both real and virtual images. The characteristics of the image depend on the object's position.

Image Formation by a Concave Lens

A concave lens always forms a virtual, erect, and diminished image, irrespective of the object's position.

Sign Convention for Spherical Lenses

The sign convention is similar to that for mirrors, but all distances are measured from the optical centre (O).

• Object distance (u) is always negative.
• For a convex lens, focal length (f) is positive.
• For a concave lens, focal length (f) is negative.

Lens Formula and Magnification

The Lens Formula

This formula relates the object distance (u), image distance (v), and focal length (f) for a spherical lens:

1/v - 1/u = 1/f

Note the minus sign, which is different from the mirror formula.

Magnification (m)

The formula for magnification is similar, but without the negative sign in the v/u ratio.

m = h'/h = v/u

The interpretation of the sign and magnitude of 'm' remains the same as for mirrors.

Power of a Lens

The power of a lens (P) is a measure of its ability to converge or diverge light rays. It is defined as the reciprocal of its focal length (f) in metres.

P = 1/f

The SI unit of power is the dioptre (D). 1 D is the power of a lens whose focal length is 1 metre.

• The power of a convex lens is positive.
• The power of a concave lens is negative.

For a combination of lenses placed in contact, the total power is the simple algebraic sum of their individual powers: P = P₁ + P₂ + P₃ + ...

Important Questions and Answers

Question 1: Define the principal focus of a concave mirror.

Answer: The principal focus of a concave mirror is a point on its principal axis where light rays that are initially parallel to the principal axis converge after being reflected from the mirror.

Question 2: A convex mirror used for rear-view on an automobile has a radius of curvature of 3.00 m. If a bus is located at 5.00 m from this mirror, find the position, nature, and size of the image.

Answer:
Given:
Radius of curvature, R = +3.00 m (Convex mirror, so R is positive)
Object distance, u = -5.00 m (Object is always on the left)
Calculations:
Focal length, f = R/2 = +3.00 / 2 = +1.50 m
Using the mirror formula: 1/v + 1/u = 1/f
1/v + 1/(-5.00) = 1/(1.50)
1/v = 1/1.50 + 1/5.00
1/v = (5.00 + 1.50) / (1.50 * 5.00) = 6.50 / 7.50
v = 7.50 / 6.50 = +1.15 m
The image is formed 1.15 m behind the mirror (positive sign indicates this).
Magnification:
m = -v/u = - (1.15) / (-5.00) = +0.23
Nature and Size:
Since 'v' is positive, the image is virtual.
Since 'm' is positive (+0.23), the image is erect.
Since |m| is 0.23 (which is less than 1), the image is diminished (0.23 times the size of the object).

Question 3: A concave lens has a focal length of 15 cm. At what distance should the object from the lens be placed so that it forms an image at 10 cm from the lens? Also, find the magnification produced by the lens.

Answer:
Given:
Focal length, f = -15 cm (Concave lens)
Image distance, v = -10 cm (A concave lens always forms a virtual image on the same side as the object)
Calculations:
Using the lens formula: 1/v - 1/u = 1/f
1/(-10) - 1/u = 1/(-15)
-1/10 - 1/u = -1/15
-1/u = -1/15 + 1/10
-1/u = (-2 + 3) / 30 = 1/30
u = -30 cm
The object should be placed 30 cm in front of the lens.
Magnification:
m = v/u = (-10) / (-30) = 1/3 = +0.33
The positive sign of 'm' indicates that the image is virtual and erect. The value 0.33 (less than 1) indicates that the image is diminished.

Question 4: Find the power of a concave lens of focal length 2 m.

Answer:
Given:
Focal length, f = -2 m (Concave lens has a negative focal length)
Calculation:
Power, P = 1/f
P = 1 / (-2 m) = -0.5 D
The power of the lens is -0.5 dioptres.

Chapter Summary

Here are the key takeaways from this comprehensive exploration of light:

• Light travels in straight lines and exhibits both reflection and refraction.
• Laws of Reflection: ∠i = ∠r, and the incident ray, reflected ray, and normal all lie in the same plane.
• Spherical mirrors are of two types: concave (converging) and convex (diverging).
• The Mirror Formula (1/v + 1/u = 1/f) and Magnification (m = -v/u) are used to solve numerical problems related to mirrors.
• Refraction is the bending of light as it passes from one medium to another, caused by a change in the speed of light.
• Snell's Law (sin i / sin r = constant) governs the phenomenon of refraction. The constant is the refractive index.
• Spherical lenses are of two types: convex (converging) and concave (diverging).
• The Lens Formula (1/v - 1/u = 1/f) and Magnification (m = v/u) are used for calculations involving lenses.
• The Power of a lens (P = 1/f) is measured in dioptres (D) and indicates its degree of convergence or divergence.