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.

NCERT Chapter Notes Class X Science Light – Reflection and Refraction 3

The ray diagrams given in NCERT Books are also good to be followed.

Image formation by Convex Mirror

Uses of Concave Mirror

1. Used in torches, search light and headlight of vehicle.

2. Used to see large image of face as shaving mirror

3. Used by dentist to see large images of the teeth

4. Large concave mirror used to focus sunlight (heat) in solar furnaces.

Uses of Convex Mirror

1. Used as rear-view mirror in vehicles because it gives erect image. It also helps the driver to view large area.

Sign Convention for Reflection by Spherical Mirror

1. The object is always placed to the left side of mirror.

2. All distance should be measured from pole (P); parallel to principal axis.

3. Take ‘P’ as origin. Distances measured

Right of the origin (+x-Axis) are taken positive

Left of the origin (–x-Axis) are taken negative

Perpendicular to and above principal axis (+y-Axis) are taken positive

Perpendicular to and below principal axis (–y-Axis) are taken negative

NCERT Chapter Notes Class X Science Light – Reflection and Refraction 2

1. Principal axis : Line joining the pole and centre of curvature of the spherical mirror.

2. Pole : The geometrical central point of the reflecting spherical surface. (aperture), denoted by (P).

3. Aperture : The width of reflecting spherical surface.

4. Centre of curvature : The centre of the hollow glass sphere of which the spherical mirror is a part is called as centre of creature.

5. Radius of curvature : The distance between the pole and the centre of curvature. ie. PC = R  or The radius of the hollow sphere of which the mirror is a part.

6. Focus point : The point on the principal axis, where all parallel rays meet after reflection is called as Principal Focus or Focus. It is denoted by letter ‘F’.

7. Focal length : The distance between the pole and focus point i.e. PF = f

8. Relationship between focal length and Radius of curvature. F = R/2

Image formation by Spherical Mirror

Before we learn the formation of image or ray diagram, let us go through few tips

(a) Remember, A say of light which is parallel to principle axis always pass through focus (meet at focus) or vice-versa

(b) A ray of light which passes through centre of curvature (it is also known as normal at the point of incidence on spherical mirror) will retrace their path after reflection

(c) A ray of light falling on pole get reflected at the same angle on the other side of principal axis.

Note : A ray of light passes through centre of curvature reflecting spherical surface is always act as normal at the point of incidence. If we know the normal we can draw angle of incidence and angle of reflection

Note 1 : The image will only form when two or more rays meets at a point. Image formation by a concave mirror for different position of the object.

NCERT Chapter Notes Class X Science Light – Reflection and Refraction 1

Light is a form of energy, which enable us to see the object.

In this chapter we will study the phenomena of reflection and refraction using the property of light i.e. straight line propagation (Light wave travel from one point to another, along a straight line).

Reflection of Light

When the light is allowed to fall on highly polished surface, such as mirror, most of the light gets reflected.

Laws of Reflection

1. The angle of incidence is always equal to angle of reflection.

    ∠i = ∠r

2. The incident ray, reflected ray and thenormal to the reflecting surface at the point of incidence lie in the same plane.

Image formed by Plane Mirror (Plane reflecting surface)

1. Virtual (imaginary) & Erect (Virtual ⇒ The image that do not form on screen.)

2. Laterally inverted (The left side of object appear on right side of image)

3. The size of image is equal to that of object.

4. The image formed is as for behind the mirror as the object is in front of it.

Reflection of light by spherical Mirrors

Mirrors, whose reflecting surface are curved inward or outward spherically are called spherical mirror.

For example – Spoon } → The curved surface of shinning spoon can be considered as curved mirror.

If it is curved inward → Act as concave mirror

If it is curved outward → Act as a convex mirror.