NCERT Solutions to Class X Mathematics

Polynomials NCERT Solutions

Pair of Linear Equations in Two Variables NCERT Solutions

Quadratic Equations NCERT Solutions

Arithmetic Progressions NCERT Solutions

Triangles NCERT Solutions

Coordinate Geometry NCERT Solutions

Introduction to Trigonometry NCERT Solutions

Some Applications of Trigonometry NCERT Solutions

Circles NCERT Solutions

Constructions NCERT Solutions

Areas Related to Circles NCERT Solutions

Surface Areas and Volumes NCERT Solutions

Statistics NCERT Solutions

Probability NCERT Solutions

NCERT Solution to Class X Science

Chapter Notes: Acid, Bases and Salts Solutions

Chapter Notes: Light – Reflection and Refraction Solutions

Chemical Reactions and Equations Solutions

Acids Bases and Salts Solutions

Metals and Non-metals Solutions

Carbon and its Compounds Solutions

Periodic Classification of Elements Solutions

Life Processes Solutions

Control and Coordination Solutions

How do Organisms Reproduce Solutions

Heredity and Evolution Solutions

Light – Reflection and Refraction Solutions

Human Eye and Colourful World Solutions

Electricity Solutions

Magnetic Effects of Electric Current Solutions

Sources of Energy Solutions

Management of Natural Resources Solutions

NCERT Solution Class X Mathematics Coordinate Geometry Question 3 (Ex 7.1)

Question 3:

Determine if the points (1, 5), (2, 3) and (− 2, − 11) are collinear.


Let the points (1, 5), (2, 3), and (−2, −11) be representing the vertices A, B, and C of the given triangle respectively.

Let A = (1,5), B = (2,3), C = (−2, −11)

Therefore, the points (1, 5), (2, 3), and (−2, −11) are not collinear.

NCERT Solution Class X Mathematics Coordinate Geometry Question 2 (Ex 7.1)

Question 2:

Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.


Distance between points (0,0) and (36,15)

Yes, we can find the distance between the given towns A and B.

Assume town A at origin point (0, 0).

Therefore, town B will be at point (36, 15) with respect to town A.

And hence, as calculated above, the distance between town A and B will be 39 km.

NCERT Chapter Notes Class X Science Light – Reflection and Refraction 7

Sign Convention for Refraction by spherical lens

Similar to that of spherical mirror, only the difference is that all the measurement are made from optical centre ‘O’


Few Tips to Remember Sign Convention for Spherical Lens

Lens : f – u – v

Concave :       –ve     –ve     –ve (Real)

                                                    +ve (virtual)

Convex :         +ve,    –ve      +ve,

h – is always +ve

n´ –                  –ve for Real and

                           +ve for virtual & Errect.

Power of Lens

The degree of convergence or divergence of light ray achieved by a lens is known as power of a lens.

It is defined as the reciprocal of its focal length Represented by P.

SI unit of power of a lens is “dioptre” denoted by ‘D’

I dioptre or ID → It is the power of lens whose focal length is 1m

Power convex lens or converging lens is always positive

Power of concave lens or diverging lens is always negative

If any optical instrument have many lens, then net power will be

NCERT Chapter Notes Class X Science Light – Reflection and Refraction 6

Spherical Lens

A transparent material bound by two surface, of which one or both surfaces are spherical, forms a lens.

Convex Lens

A lens may have two spherical surfaces, bulging outwards, is called double convex lens (or simply convex lens.

It is also known as converging lens because it converges the light.

Concave Lens

A lens bounded by two spherical surfaces, curved inwards is known as double concave lens (or simply concave lens)

It is also known as diverging lens because it diverges the light.

Few Basic Terms Related to Spherical Lens.

1. Centre of curvature : A lens, either a convex lens or a concave lens is a combination of two spherical surfaces. Each of these surfaces form a part of sphere. The centre of these two spheres are called centre of curvature represented by C1 and C2.

2. Principal axis : Imaginary straight line passing through the two centres of curvature

3. Optical Centre : The central point of lens is its optical centre (O). A ray of light, when passes through ‘O’ it remains undeviated i.e. it goes straight.

4. Aperture : The effective diameter of the circular outline of a spherical lens.

5. Focus of lens : Beam of light parallel is principal axis, after refraction from

     1. Convex lens, converge to the point on principal axis, denoted by F, known as Principal focus

   2. Concave lens, appear to diverge from a point on the principal axis, known as principal focus.

The distance OF2 and OF1 is called as focal length

Tips for drawing Ray diagram

(a) After refraction, a ray parallel to principal axis will pass through F.

(b) A ray passes through F, after refraction will emerge parallel to principal axis.

(c) A ray passes through optical centre ‘O’, passes without any deviation.

Image formation by concave lens

NCERT Chapter Notes Class X Science Light – Reflection and Refraction 5

When a incident ray of light AO passes from a rarer medium (air) to a denser medium (glass) at point. O on interface KL, it will bends towards the normal. At point O1, on interface NM the light ray entered from denser medium (glass) to rarer medium (air) here the light ray will bend away from normal OO1is a refracted ray OB is an emergent ray. If the incident ray is extended to C, we will observe that emergent ray O1B is parallel to incident ray. The ray will slightly displaced laterally after refraction.

Note : When a ray of light is incident normally to the interface of two media it will go straight, without any deviation.

Laws of refraction of light

1. The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.

2. The ratio of sine of angle of incidence to the sine of angle of refraction is a constant i.e.

for given colour and pair of media, this law is also known as Snells Law

Constant n is the refractive index for a given pair of medium. It is the refractive index of the second medium with respect to first medium.

Refractive Index

The refractive index of glass with respect to air is given by ratio of speed of light in air to the speed of light in glass.

C → Speed of light in vacuum = 3•108 m/s speed of light in air is marginally less, compared to that in vacuum.

Refractive index of air with respect to glass is given by

The absolute refractive index of a medium is simply called refractive index

Refractive index of water (nw) = 1.33

Refractive index of glass (ng) = 1.52

NCERT Chapter Notes Class X Science Light – Reflection and Refraction 4


It is expressed as the ratio of the height of the image to height of the object

Few tips to remember sign convention for Spherical mirror

Refraction of Light

Refraction of Light : Happens in Transparent medium when a light travels from one medium to another, refraction takes place.

A ray of light bends as it moves from one medium to another

Refraction is due to change in the speed of light as it enters from one transparent medium to another.

Speed of light decreases as the beam of light travel from rarer medium to the denser medium.

Some Commonly observed phenomenon due to Refraction

1. The stone at the bottom of water tub appears to be raised.

2. A fish kept in aquarium appears to be bigger than its actual size.

3. A pencil partially immersed in water appears to be displaced at the interface of air and water.