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

Introduction to Light – Reflection and Refraction

Welcome, students, to a fascinating journey into the world of light! Chapter 10 of your NCERT Class 10 Science textbook, "Light – Reflection and Refraction," unveils the principles that govern how we see the world around us. Light is a form of energy that creates the sensation of vision. Without it, our world would be a canvas of darkness. From the simple act of looking into a mirror to the complex workings of a telescope, the phenomena of reflection and refraction are at play. This chapter is not just crucial for your board exams but also for building a fundamental understanding of physics. It explains why a pencil appears bent in a glass of water, how magnifying glasses work, and why the rear-view mirrors in cars are shaped the way they are. In this comprehensive guide, we will break down every concept, formula, and diagram from this chapter, ensuring you have a clear and thorough understanding.

Reflection of Light

Reflection is the phenomenon that allows us to see non-luminous objects. When light falls on a surface, it bounces back. This bouncing back of light into the same medium is called reflection. A highly polished surface, like a mirror, reflects most of the light falling on it, leading to the formation of a clear image.

Key Terms in Reflection

Before diving into the laws of reflection, let's understand some basic terms associated with it, typically explained using a plane mirror as an example:

• Incident Ray: The ray of light that falls on the reflecting surface.
• Point of Incidence: The point on the surface where the incident ray strikes.
• Reflected Ray: The ray of light that is sent back by the surface after reflection.
• Normal: An imaginary line drawn perpendicular (at 90°) to the surface at the point of incidence.
• 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.

Laws of Reflection

The reflection of light from any surface, whether smooth or rough, abides by two fundamental laws:

1. The First Law of Reflection: The angle of incidence is always equal to the angle of reflection. (∠i = ∠r)
2. The Second Law of Reflection: 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

When you stand in front of a plane mirror, you see an image of yourself. The characteristics of this image are always consistent:

• Virtual and Erect: The image cannot be formed on a screen, hence it is 'virtual'. It appears upright, just as the object is, so it is 'erect'.
• 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 right side of the object appears as the left side of the image, and vice versa. 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 have a curved reflecting surface. They are a part of a hollow sphere of glass. Depending on which side is polished, spherical mirrors are of two 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 at a point.
• Convex Mirror: A spherical mirror whose reflecting surface is curved outwards. It is also known as a diverging mirror because it diverges the parallel rays of light that fall on it, making them appear to come from a point behind the mirror.

Important Terms for Spherical Mirrors

Understanding the following terms is essential for studying image formation by spherical mirrors:

• Pole (P): The centre of the reflecting surface of the spherical mirror. It lies on the surface of the 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; it lies in front of a concave mirror and behind a convex mirror.
• 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 of a spherical mirror.
• Principal Focus (F):
  • For a concave mirror, it is a point on the principal axis where the rays of light initially parallel to the principal axis meet (converge) after reflection.
  • For a convex mirror, it is a point on the principal axis from which the rays of light initially parallel to the principal axis appear to diverge after reflection.
• Focal Length (f): The distance between the pole (P) and the principal focus (F). For spherical mirrors with a small aperture, the radius of curvature is found to be twice the focal length: R = 2f.

Image Formation by Concave Mirrors

The nature, position, and size of the image formed by a concave mirror depend on the position of the object. There are six possible cases, which can be determined using ray diagrams. The standard rays used are: (1) A ray parallel to the principal axis, which passes through the focus after reflection. (2) A ray passing through the focus, which becomes parallel to the principal axis after reflection. (3) A ray passing through the centre of curvature, which reflects back along the same path.

Here is a summary of the image formation by a concave mirror:

Image Formation by Convex Mirrors

A convex mirror always produces a virtual, erect, and diminished image, irrespective of the object's position. This property makes it very useful. There are two main cases:

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

Uses of Concave and Convex Mirrors

Concave Mirrors:

• Used in torches, searchlights, and vehicle headlights to get powerful parallel beams of light.
• Used by dentists to see an enlarged image of the teeth.
• Used as shaving mirrors to see a larger image of the face.
• Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces.

Convex Mirrors:

• Commonly used as rear-view (wing) mirrors in vehicles. They give an erect, diminished image and have a wider field of view, allowing the driver to see more of the traffic behind.
• Used at blind turns and in shops for security purposes.

Sign Convention for Spherical Mirrors

To solve numerical problems related to mirrors, we use the New Cartesian Sign Convention. The rules are:

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

Based on this convention: object distance (u) is always negative. For a concave mirror, focal length (f) is negative. For a convex mirror, focal length (f) is positive.

Mirror Formula and Magnification

The relationship between the object distance (u), image distance (v), and focal length (f) of a spherical mirror is given by the mirror formula:

1/v + 1/u = 1/f

Magnification (m) produced by a spherical mirror gives the relative extent to which the image of an object is magnified with respect to the object size. It is expressed as 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 distance (u) and image distance (v):

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.
• If |m| < 1, the image is diminished.
• If |m| = 1, the image is of the same size.

Refraction of Light

While reflection is the bouncing of light, refraction is the bending of light. Refraction occurs when light travels from one transparent medium to another (e.g., from air to water). The primary cause of refraction is the change in the speed of light as it enters a different medium. The speed of light is maximum in a vacuum (approximately 3 × 10⁸ m/s) and is less in other media like glass or water.

Refraction through a Rectangular Glass Slab

A common experiment to demonstrate refraction is passing a ray of light through a glass slab. When a ray of light enters the glass slab from air, it bends towards the normal (as it moves from a rarer to a denser medium). When it emerges from the slab back into the air, it bends away from the normal (as it moves from a denser to a rarer medium). The emergent ray is parallel to the incident ray, but it is slightly shifted sideways. This shift is called lateral displacement.

Laws of Refraction

Similar to reflection, refraction also follows two specific laws:

1. The First Law of Refraction: 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 Second Law of Refraction (Snell's Law): 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 constant value is called the refractive index of the second medium with respect to the first.

Mathematically, Snell's Law is expressed as: sin(i) / sin(r) = constant = n₂₁ (where n₂₁ is the refractive index of medium 2 with respect to medium 1).

Refractive Index

The refractive index (n) of a medium is a measure of how much the speed of light is reduced inside that medium. The more the light slows down, the higher the refractive index.

• Absolute Refractive Index: When the first medium is a vacuum or air, the refractive index of the second medium is called its absolute refractive index. It is given by n = c/v, where 'c' is the speed of light in a vacuum and 'v' is the speed of light in the medium.
• Relative Refractive Index: The refractive index of medium 2 with respect to medium 1 (n₂₁) is given by the ratio of the speed of light in medium 1 (v₁) to the speed of light in medium 2 (v₂). So, n₂₁ = v₁/v₂.

A medium with a higher refractive index is called an optically denser medium, while a medium with a lower refractive index is called an optically rarer medium.

Refraction by Spherical Lenses

A lens is a piece of transparent material bound by two curved surfaces. Lenses work on the principle of refraction. They are broadly classified into two types.

Types of Spherical Lenses

• Convex Lens: It is thicker at the centre and thinner at the edges. It converges parallel rays of light, so it is also called a converging lens.
• Concave Lens: It is thinner at the centre and thicker at the edges. It diverges parallel rays of light, so it is also called a diverging lens.

Image Formation by Convex Lenses

The image formation by a convex lens is very similar to that of a concave mirror. The position, nature, and size of the image depend on the object's position.

Image Formation by Concave Lenses

Similar to a convex mirror, a concave lens always forms a virtual, erect, and diminished image, regardless of the object's position.

Lens Formula and Magnification

The relationship between object distance (u), image distance (v), and focal length (f) for a spherical lens is given by the lens formula:

1/v - 1/u = 1/f

Note the minus sign, which is different from the mirror formula. The sign conventions for lenses are the same as for mirrors, except that all distances are measured from the optical centre (O).

Magnification (m) for a lens is given by:

m = h'/h = v/u

Note that there is no negative sign in the v/u ratio for the lens magnification formula. The interpretation of the sign and magnitude of 'm' remains the same as for mirrors.

Power of a Lens

The power of a lens is a measure of its ability to converge or diverge light rays. A lens with a short focal length bends light more and has a higher power. Power (P) is defined as the reciprocal of the focal length (f).

P = 1/f

Important: For this formula, the focal length 'f' must be in meters (m).

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

• The power of a convex lens is positive (as its focal length is positive).
• The power of a concave lens is negative (as its focal length is negative).

If multiple thin lenses are placed in contact, the total power of the combination 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 meet or converge after being reflected from the mirror. It is denoted by the letter 'F'.

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 (A convex mirror has a positive R)
Object distance, u = -5.00 m (Object is always on the left)

First, find the focal length (f):
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 + 1.5) / 7.5
1/v = 6.5 / 7.5
1/v = 13/15
v = 15/13 = +1.15 m

The positive sign of 'v' indicates the image is formed behind the mirror. The image is at a distance of 1.15 m from the pole.

Now, find the magnification (m):
m = -v/u = -(1.15) / (-5.00) = +0.23

Nature and Size:
Since 'm' is positive, the image is virtual and erect.
Since |m| = 0.23, which is less than 1, the image is diminished (smaller than the object by a factor of 0.23).

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:
A concave lens always forms a virtual image on the same side as the object.
Focal length, f = -15 cm (Concave lens has negative f)
Image distance, v = -10 cm (Virtual image on the left)

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/u = 1/30
u = -30 cm

The object should be placed at a distance of 30 cm from the lens.

Now, find the magnification (m):
m = v/u = (-10) / (-30) = +1/3 ≈ +0.33

The positive sign of 'm' indicates the image is virtual and erect. The magnification of +0.33 indicates the image is diminished to one-third the size of the object.

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

Answer:
Given:
Focal length, f = -2 m (Concave lens has negative f)

The power (P) of a lens is given by the formula P = 1/f, where f is in meters.
P = 1 / (-2 m)
P = -0.5 D

The power of the concave lens is -0.5 dioptres.

Chapter Summary

Here are the key takeaways from the chapter on Light – Reflection and Refraction:

• Light is a form of energy that enables vision and travels in straight lines.
• Reflection is the bouncing back of light. It follows two laws: ∠i = ∠r, and the incident ray, reflected ray, and normal all lie in the same plane.
• Plane mirrors form virtual, erect, same-sized, and laterally inverted images.
• Spherical mirrors are of two types: concave (converging) and convex (diverging).
• The Mirror Formula is 1/v + 1/u = 1/f.
• Magnification by a mirror is m = -v/u.
• Refraction is the bending of light when it passes from one medium to another, caused by a change in its speed.
• Snell's Law of Refraction states that sin(i)/sin(r) is a constant, known as the refractive index.
• Spherical lenses are of two types: convex (converging) and concave (diverging).
• The Lens Formula is 1/v - 1/u = 1/f.
• Magnification by a lens is m = v/u.
• The Power of a lens (P) is the reciprocal of its focal length in meters (P = 1/f). Its unit is the dioptre (D).