CBSE Class X

Question 3:

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

Answer:

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.

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.

Answer:

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.

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

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

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 (n_w) = 1.33

Refractive index of glass (n_g) = 1.52

Magnification

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.

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

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.

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.

Preparation : Prepared by the method called chlor-alkali process. It is called so because we get chlorine and a base in this process.

• Calcium oxy chloride – CaOCl

     Common Name : Bleaching Power

 use in textile, factories and laundry, used as disinfectant

• Sodium Hydrogen Carbonate – NaHCO₃

     – Common name – Baking Soda

 On heating NaHCO₃ produces :

CO₂ produced causes dough to rise and make cakes, pastries spongy.

 Uses : In household, ingredients of antacid

In making baking power On heating baking powder produces

• Sodium Carbonate – Na₂CO₃

 Common name : Washing Soda

 Preparation : Recrystallisation of sodium carbonate

    Uses
     – Used in glass, soap and paper industry
     – Cleaning agent for domestic purposes.
     – Removal of hardness of water.
     – Manufacturer of borax.

Common Name : Plaster of Paris Calcium Sulphate hemihydrate

• Water of crystallisation : Fixed no. of water molecules present in one formula unit of a salt.

     – On heating copper sulphate crystals water droplets appear, formula of hydrated copper sulphate – CuSO₄.        5H₂O.

    – gypsum also contains water of crystallisation. CaSO₄.2H₂O

    – Preparation : On heating gypsum at 373K it becomes

     – When Plaster of Paris is mixed with water it changes to gypsum.

Uses of plaster of Paris : Making toys, decorative material and smooth surfaces, plaster for fracture bones.

• Strength of an Acid or Base

      Strength of acids and bases depends on the no. of H⁺ions and OH^–ions produced respectively.

      With the help of a universal indicator we can find the strength of an acid or base as it shows different colours       at different concentrations of hydrogen ions in a solution.

      A scale for measuring hydrogen ion conc. in a solution is called pH scale has been developed.

      pH = Potenz in German means power.

      This scale measures from 0 (very acidic) to 14 (very alkaline) 7 Neutral (water in neutral).

      pH paper : Is a paper which is used for measuring pH.

      Variation of PH

      

– strong Acids give rise to more H⁺ions.

      eg. HCl, H₂SO₄ and HNO₃.

– Weak Acids give rise to less H⁺ ions

      eg. CH₃ COOH, H₂ CO₃ (Carbonic acid)

– Strong Bases – Strong bases give rise to more OH^– ions.

     eg. NaOH, KOH, Ca(OH)₂

– Weak Bases : give rise to less OH^– ions.

     eg. NH₄OH

• More about Salts

    Salts and their derivation

    

    Note : NaCl and Na₂ SO₄ belong to the family of sodium salts as they have the same radicals. Similarly NaCl      and KCl belong to the family of chloride salts.

Importance of pH in our daily life

• Importance of pH in our digestive system – Our stomach produces hydrochloric acid. This dilute   hydrochloric acid help in digestion of good. In case of indigestion our stomach produces acid in a very large quantity because of which we feel pain and irritation in our stomach. To get relief from this pain antacids are used. These antacids neutralise the excess acid and we get relief.

• pH of Acid Rain : When pH of rain water is less than 5.6 it is called acid rain. When this acidic rain flows into rivers these were also get acidic, which causes a threat to the survival of aquatic life.

• pH of Soil : Plants require a specific range of pH for their healthy growth. If pH of soil of any particular place is less or more then normal than the farmers add suitable chemicals to it.

• Our body functions between the range of 7.0 to 7.8 living organisms can survive only in the narrow range of pH change.

• Tooth decay and pH : Bacteria present in the mouth produces acids by degradation of sugar and food particles remaining in the mouth. Using toothpaste which is generally basic, can neutralise the excess acid and prevent tooth decay.

• Bee sting or Nettle sting contains methanoic acid which causes pain and irritation. When we use a weak base like baking soda on it, we get relief.

• Chemicals from Common Salt

– Sodium chloride is called as common salt is used in our food. It is derived from seawater.

   – Rock Salt is the brown coloured large crystals. This s mined like coal.

   – Common salt is an important raw material for many materials of daily use such as.

Sodium hydroxide

          Washing Soda

          Bleaching Power.

• Sodium Hydroxide : NaOH, Common Name – caustic soda.

• Action of Acids with metal Carbonates and metal bicarbonates

      Metal Carbonate + Acid → Salt + Carbondioxide + Water

      Na₂CO_3(S) + 2HCl_(aq) → 2NaCl_(aq) + H₂O(l) + CO_2(g)

     Metal bicarbonate + Acid → Salt + Carbondioxide + Water

     NaHCO₃ + HCl → NaCl + CO₂ + H₂O

• Lime water Test : On passing the evolved CO₂ gas is Passed through lime water,

• Reaction of acids and bases with each other.

• Neutralisation Reactions

     Base + Acid → Salt + Water

     NaOH_(aq) + HCl_(aq) → NaCl_(aq) + H₂O(l)

Neutralisation reaction : The reaction between an acid and a base to give salt and waste is called as neutralization reaction takes place when the effect of a base is nullified by an acid and vice versa to give salt and water.

• Reactions of metal oxides with acids

Note : Appearance of blue green colour of the solution because of formation of CuCl₂.

Metallic oxides are said to be basic oxides because they give salt and water on reacting with acids.

• Reaction of Non Metallic Oxide with Base

     Non metallic oxide + Base → Salt + Water

     Ca(OH)₂ + CO₂ → CaCO₃ + H₂O

Note : Non Metallic oxides are said to be acidic in nature because on reacting with a base they produce salt and water.

• All acidic solutions conduct electricity because of formation of (H⁺ions in eq, solution.)

      Refer activity 2.3 on page 22 of NCERT Book

     – Glowing of bulb indicates that there is a flow of electric current through the solution.

• Acids or bases in a Water Solution

   Acids produce H⁺ ions in the presence of water

   HCl + H₂O → H₃O⁺ + Cl^–

   H₃O⁺ – Hydronium ion.

               – H⁺ion cannot exist alone. It exists as H⁺(aq) or (H₃O⁺) hydronium ion.

   H⁺ + H₂O → H₃O⁺

– Bases provide (OH^–) ions in the presence of water

• Alkalis

  All bases donot dissolve in water. An alkali is a base that dissolves in water. Common alkalis are

    NaOH           Sodium hydroxide

    KOH             Potassium hydroxide

    Ca(OH)₂     Calcium hydroxide

    NH₄OH      Ammonium hydroxide

    Note : All alkalis are bases but all bases are not alkalis.

• Precaution must be taken while mixing acid or base with water. The acid must always be added to water with        constant stirring as it is a highly exothermic reaction.

    When an acid or a base is mixed with water they become dilute. This results in the decrease in the           concentration of H₃O⁺ or OH^– per unit volume in acids and bases respectively.

• Some naturally occuring acids

       Vinegar – Acetic Acid

        Orange – Citric Acid

        Lemon – Citric Acid

       Tamarind – Tartaric Acid

       Tomato – Oxalic Acid

       Sour milk (Curd) – Lactic Acid

      Ant and Nettle sting – Methanoic Acid

• Acid – Base Indicators – Indicate the presence of an acid or base in a solution.

• Litmus solution – It is a natural indicator. It is a purple dye extracted from Lichens. Other examples are Red Cabbage and coloured petals of Petunia and turmeric.

• Olfactory indicators – Show odour changes in acidic or basic media.

      eg. onion and clove.

• Acid – Base Indicators

     

• Dilute Acid : Contains only a small amounts of acid and a large amount of water.

• Concentrated Acid : A concentrated acid contains a large amount of acid and a small amount of water.

• Chemical Properties of Acids and Bases

(i) Reaction with metal

     Acid + Metal → Salt + Hydrogen

    2HCl + Zn → ZnCl₂ + H₂

    2HNO₃ + Zn → Zn (NO₃)₂ + H₂

    H₂SO₄ + Zn → ZnSO₄ + H₂

   2CH₃COOH + Zn → (CH₃COO)₂ Zn + H₂

• Pop test : When a burning candle is brought near a test tube containing hydrogen gas it burns with a ‘Pop’ sound. This test is conducted for examining the presence of hydrogen gas.

• Base + Metal → Salt + Hydrogen

      NaOH + Zn → Na₂ZnO₂ + H₂
                             Sodium Zincate

     Note – Such reactions are not possible with all the metals.

Question 7:

On the basis of the issues raised in this chapter, what changes would you

incorporate in your life-style in a move towards a sustainable use of our

resources?

Answer:

One should incorporate the following changes in life-style in a move towards

a sustainable use of our resources:

(i) Stop cutting trees and practice plantation of trees.

(ii) Stop using plastic and polythene bags for carrying goods.

(iii) Use recycled paper.

(iv) Throw biodegradable and non-biodegradable waste into separate bins.

(v) Waste minimum amount of water while using and repair leaking taps.

(vi) Practice rainwater harvesting.

(vi) Avoid using vehicles for short distances. Instead, one can walk or cycle

to cover short distances. To cover long distances, one should take a bus

instead of using personal vehicles.

(vii) Switch off electrical appliances when not in use.

(viii) Use fluorescent tubes in place of bulbs to save electricity.

(ix) Take stairs and avoid using lifts.

(x) During winters, wear an extra sweater to avoid using heaters.

Question 6:

List five things you have done over the last one week to −

(a) conserve our natural resources

(b) increase the pressure on our natural resources

Answer:

(a) To conserve our natural resources:

(i) Travel by a CNG bus for long distances and walk for short distances.

(ii) Use recycled paper

(iii) Throw biodegradable and non-biodegradable waste into separate bins

(iv) Plant trees

(v) Harvest rainwater

(b) To increase the pressure on our natural resources:

(i) Use non-renewable resources of energy

(ii) Waste water

(iii) Waste electricity

(iv) Use plastics and polythene bags for carrying goods

(v) Use escalators

Question 5:

What can you as an individual do to reduce your consumption of the various

natural resources?

Answer:

Natural resources such as water, forests, coal and petroleum, etc. are important

for the survival of human beings. The ways in which we can reduce the

consumption of various natural resources are as follows:

(i) We should stop the cutting of trees (deforestation).

(ii) We should use recycled paper to reduce the cutting down of trees.

(iii) We should not waste water.

(iv) We should practice rainwater harvesting.

(v) We should practice car pooling to avoid the excessive use of petroleum.

(vi) We should use alternative sources of energy such as hydro-energy and

solar energy.

Question 4:

How can you as an individual contribute or make a difference to the management

of (a) forests and wildlife, (b) water resources and (c) coal and petroleum?

Answer:

(a) Forest and wildlife:

(i) We should protest against the cutting of trees (deforestation).

(ii) We should protest against the poaching of wild animals.

(iii) We should stop the annexation of forest land for our use.

(b) Water resources:

(i) Turn the taps off while brushing or bathing and repair leaking taps.

(ii) We should practice rainwater harvesting.

(iii) We should avoid the discharge of sewage and other wastes into rivers

and other water resources.

(c) Coal and petroleum:

(i) We should take a bus or practice car pooling to avoid excessive use

of petroleum.

(ii) We should stop using coal as a fuel (angithis).

(iii)We should use alternative sources of energy such as hydro-energy and

solar energy instead of depending largely on coal and petroleum.

Question 3:

We saw in this chapter that there are four main stakeholders when it comes

to forests and wildlife. Which among these should have the authority to

decide the management of forest produce? Why do you think so?

Answer:

The forest department of the government should have the authority to decide

the management of forest produces. This is because the forest department

is the care taker of the forest land and is responsible for any damage to

the forest.

Question 2:

Can you suggest some changes in your school which would make it

environment friendly?

Answer:

Changes that can be undertaken in our schools to make it environment friendly

are listed below:

(i) Electricity can be saved by switching off lights and fans when not required.

(ii) Turn the taps off when not in use.

(iii) Biodegradable and non-biodegradable wastes should be thrown into

separate bins.

Question 1:

What changes would you suggest in your home in order to be environment-friendly?

Answer:

Changes that can be undertaken in our homes to be environment-friendly are

listed below:

(i)Switch off the electrical appliances when not in use.

(ii)Turn the taps off while brushing or bathing and repair the leaking taps.

(iii)Throw biodegradable and non-biodegradable waste into separate bins.

(iv)Construct composting pits.

(v)Food items such as jam, pickles, etc., come packed in plastic bottles.

These bottles can later be used for storing things in the kitchen.