LECTURE 2: CLASS 10 : LIFE PROCESSES : PHOTOSYNTHESIS - I

CLASS X   |    SCIENCE    |    LIFE PROCESSES

      Notes prepared by Subhankar Karmakar

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SCIENCE: CLASS X: CBSE (CLASS NOTES)

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• NUTRITION IN PLANTS
• The process by which green plants make their own food like glucose from carbon di oxide and water by using sunlight energy in the presence of chlorophyll is called photosynthesis.
• Chlorophyll is present in the green coloured bodies called chloroplasts inside the plant cells. 
• The leaves of a plant are green because they contain tiny green coloured organelles called Chloroplasts. 
• The process of photosynthesis
• The chemical reaction of the photosynthesis

6CO₂ + 6H₂O + Light energy (in the presence of chlorophyll) ⟹ C₆H₁₂O₆ + 6O₂

• PHOTOSYNTHESIS

Plants prepare their food (glucose) in the green leaves of the plant by combining carbon-di-oxide and water in the presence of sunlight and chlorophyll. The process is known as Photosynthesis.

• CHLOROPHYLL:

Chlorophyll is a green pigment found in the mesosomes of cyanobacteria and in the chloroplasts of algae and plants. It is needed for the process of photosynthesis.

• CARBON-DI-OXIDE

The plants derive carbon-di-oxide from the air by the plant leaves. Carbon-di-oxide enters the leaves through the small pores in them called stomata. 

• WATER

Water required for food preparation is taken from the soil through the roots. Water is transported to the leaves from the soil through the roots and stem. 

• SUNLIGHT

The sunlight provides the energy required to carry out the chemical reactions involved in the preparation of the food. The energy in the sunlight is absorbed with the help of chlorophyll. 

• Oxygen gas is produced as a by-product during the preparation of food by photosynthesis. This oxygen gas goes into the air. 
• The food prepared by the green leaves of a plant is in the form of a simple sugar called glucose. Glucose thus produced is sent to the different parts of the plant.
• The extra glucose is changed into another food called starch. This starch is stored in the leaves of the plant. Glucose and starch are called carbohydrates. 
• Green plants convert sunlight energy into chemical energy by making carbohydrates. 

• THE PHOTOSYNTHESIS PROCESS
• 1. Absorption of sunlight energy
• 2. Conversion of light energy into chemical energy and splitting of water into hydrogen and oxygen by light energy.
• 3. Reduction of carbon dioxide by hydrogen to form carbohydrate like glucose by utilising the chemical energy obtained by the transformation of light energy. 

• Conditions necessary for photosynthesis by green plants as well as autotrophic nutrition
• 1. Sunlight
• 2. Chlorophyll
• 3. Carbon dioxide
• 4. Water

A. Describe an experiment to show that Sunlight is necessary for photosynthesis

We know that green leaves make starch as food. As starch gives a black-blue colour with iodine solution. Plants store starch in their leaves. The green leaves of a plant are destarched by keeping this plant in a completely dark place in a room for atleast three days. 

• 1. We take a potted plant having Green leaves and place it in a completely dark place for about 3 days to destarch its leaves.
• 2. We take a thin strip of aluminium foil and wrap it in the centre of one leaf on both the sides. The covered part will not receive sunlight.
• 3. We keep this potted plant in bright sunshine for 3 to 4 days. 
• 4. We pluck the partially covered leaf from the plant and remove its Aluminium foil then immerse this leaf in boiling water for a few minutes. This will break down the cell membranes of leaf cells and make the leaf more permeable to iodine solution.
• 5. We put the plucked leaf in a beaker containing some alcohol. Place the beaker containing alcohol and leaf in a water bath and starts to heat it till the leaf becomes colourless. The boiling water will remove the chlorophyll from the green leaf. 
• 6. We remove the colourless leaf from alcohol, wash it in hot water and keep it in a petridish. We drop iodine solution on the leaf. 
• 7. The part which was wrapped in aluminium foil will not turn blue-black but rest of the parts of the leaf will become blue-black. 
• 8. Since the wrapped part didn't get sunlight, it did not produce starch. We can now conclude that 
• (i) sunlight is necessary for the process of photosynthesis.
• (ii) leaves make starch as food by photosynthesis.

• Variegated leaves:

The leaves which are partly green and partly white are called variegated leaves. The white part of the leaves doesn't contain chlorophyll. 

B. Describe an experiment to show that Chlorophyll is necessary for photosynthesis.

• 1. We take a potted plant having variegated leaves like a croton plant. The white part of the leaves doesn't contain chlorophyll whereas the green part contains chlorophyll. 
• 2. We place the plant in a completely dark place for about three days. 
• 3. We take out the plant and keep it under bright sun for 3 to 4 days 
• 4. We pluck the variegated leaf from the plant , boil it in water for few minutes, and then remove its green colour  chlorophyll by boiling in alcohol. The green part of the leaf  get decolourised.
• 5. We wash the decolourised leaf with hot water to soften and remove left-over Chlorophyll. 
• 6. We now pour iodine solution over the colourless leaf and observe the change in colour of the leaf. 
• 7. The inner part of leaf which was originally green turns blue black on adding iodine. 
• Chlorophyll is necessary for the process of photosynthesis to take place. 

C. Describe an experiment to show that Carbon Dioxide is necessary for photosynthesis.

• 1. We take a potted plant having narrow leaves and place it in a completely dark place for about three days to destarch its leaves. 
• 2. Take a glass bottle having a wide mouth and put some potassium hydroxide solution in it. 
• 3. Take a rubber cork which fits tightly into the mouth of the glass bottle and cut it into two halves. 
• 4. We put the destarched leaves in such a way, that upper half of the leaf should remain outside the glass bottle and only the lower half of the leaf should be inside the glass bottle.
• 5. The potted plant is kept in sunlight for 3 to 4 days. Upper half gets the carbon dioxide from air but lower half didn't get carbon dioxide as potassium hydroxide absorbed the carbon dioxide of the inside jar. 
• 6. We pluck the leaf and boiled it in alcohol then wash it with water.
• 7. We pour iodine solution over the colourless leaf. We observe that lower part of the leaf doesn't turned blue-black but the upper part became blue-black. 
• The photosynthesis to make starch in the leaf does not take place without carbon dioxide. 

Raw Materials for photosynthesis

The preparation of carbohydrates by plants by the process of photosynthesis requires two materials a. Carbon dioxide and b. Water

HOW THE PLANTS OBTAIN CARBON DIOXIDE

• STOMATA

There are large number of tiny pores called stomata on the surface of the leaves of plants. and green stem. The green plants take carbon dioxide from air for photosynthesis. The carbon dioxide gas enters the leaves of the plant through the stomata present on their surface. 

• STOMATAL PORES AND GUARD CELLS

STOMATAL PORES & GUARD CELL

• Each stomatal pore is surrounded by a pair of guard cells. The opening and closing of stomatal pore is controlled by the guard cells. 
• • When water flows into the guard cells, they swell, become curved and cause the pore to open. 
• • When guard cells lose water, they shrink, become straight and close the stomatal pore. 
• Plant losses water through the open stomatal pores hence when carbon dioxide is not needed by the plants, these pores are closed. 
• Oxygen gases produced during photosynthesis also goes out through the stomatal pores. 
• In most of the broad-leaved plants, stomata occur only on the lower surface of the leaf but in narrow-leaved plants, stomata are equally distributed on the both sides of the leaf. 
• Aquatic plants use the carbon dioxide gas dissolved in water for carrying out photosynthesis. 

HOW THE PLANTS OBTAIN WATER FOR PHOTOSYNTHESIS

• The water required by the plants for photosynthesis is absorbed by the roots of the plants from the soil through the process of osmosis. The water is absorbed by the roots of the plants is transported upward through the xylem vessels to the leaves. 
• Other nutrients like nitrogen, phosphorus, iron and magnesium etc. by the plants for its growth are taken by the plants from the soil through the roots of the plants. 

SITE OF PHOTOSYNTHESIS: CHLOROPLASTS

• Chloroplasts are the disc-like cell organelles of the photosynthetic cells of green plants which contain chlorophyll. At Chloroplasts photosynthesis take place. 
• The middle layer of the leaves are palisade layer and spongy layer and they contain photosynthetic cells which are called mesophyll cells. 
• Carbon dioxide enters through stomata and diffuses into the mesophyll cells and reaches the Chloroplasts. 
• Water is carried to the leaf by xylem and passes into the mesophyll cells by diffusion and reaches the Chloroplasts. 
• To reduce the water loss, there is a thin waxy protective layer called cuticle above and below a leaf. 

LECTURE 1 : CLASS XII: PHYSICS : ELECTRIC CHARGE & FIELD

CLASS XII   |    PHYSICS    |    ELECTRIC CHARGE

      Notes prepared by Subhankar Karmakar

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ELECTRIC CHARGE

Electric charge is an intrinsic property of elementary particles of matter which gives rise to electric force between various objects.

• Electric charge is a scalar quantity.
• SI unit of electric charge is coulomb (C).
• There are two types of charges- a. Positive charge and b. Negative charge.
• A proton has a positive charge (+e) and an electron has a negative charge (-e).
• Magnitude of charge of a proton and an electron are same.
• Charge of a proton = + 1.6 x 10⁻¹⁹ C
• Charge of an electron = - 1.6 x 10⁻¹⁹ C

POLARITY OF CHARGE

• The property which distinguishes the two kinds of charges is called the polarity of charge.

FUNDAMENTAL LAW OF ELECTROSTATICS: 

• Like charges repel and unlike charges attract each other.

• The charge developed on a glass rod when rubbed with silk is called positive charge.
• The charge developed on a plastic rod rubbed with wool is called negative charge. 

CONDUCTORS AND INSULATORS

• Conductors: The substances through which electric charges can flow easily are called conductors. 
• Insulators: the substances through which electric charges cannot flow easily are called insulators.
• When some charge is transferred to a conductor, it really gets distributed over his entire surface. 
• If some charge is put on an insulator, It stays at same place. 
• The process in which a body shares its charges with the earth is called grounding or earthing.

ELECTROSTATIC INDUCTION

• It is the phenomenon of temporary electrification of a conductor in which opposite charges appear at its closure and and similar charges appear at its further and in the presence of a nearby charged body. 
• When two conductors one or both are charged are in contact with each other total charge is divided into two equal parts. 
• Suppose a conductor A has charge Q and another conductor B has charged q and they are connected with each other, then each of them will have a charge equal to (Q + q)/2.
• Suppose a conductor A has charge Q and another uncharged conductor B are connected with each other, then each of them will have a charge equal to (Q/2).

CHARGING OF TWO SPHERES BY INDUCTION

Steps for charging of two spheres by induction.

1. We hold the two metal spheres on insulating stands and place them in contact.
2. We bring a positively charged glass rod near the left sphere. The left sphere then becomes negatively charged and the right sphere becomes positively charged.
3. We separate the spheres and they now have opposite charges. 
4. We remove the glass rod. The charges on the spheres get redistributed. Positive and negative charges now face each other. 
5. When the spheres are separated quite apart, the charges on them get uniformly distributed. 

CHARGING OF A SPHERE BY INDUCTION

Steps for charging of a sphere by induction

1. We take a metal sphere on an insulating stand and keep a negatively charged plastic rod near it. The near end of the sphere becomes positively charged and far end of the sphere becomes negatively charged.
2. Far end of the sphere is connected to the ground by a connecting wire to the ground. 
3. When the sphere is disconnected from the ground, the positive charge remain in the near end. 
4. When the plastic rod is removed, the positive charge is uniformly distributed on the sphere. 

BASIC PROPERTIES OF CHARGE:

• There are three basic properties of charge. They are 1. Additivity, 2. Quantization and 3. Conservation of Charge. 
• Additivity: Additivity of electric charge means that the total charge of a system is the algebraic sum of all the individual charges located at different points inside the system.
• Quantisation: The quantization of electric charge means that the total charge (q) of a body is always an integral multiple of a basic quantum of charge (e).

∴ q = ne, where n = ±1, ±2, ±3, ±4,.........

• Conservation: The laws of conservation of charge states that 
• The total charge of an isolated system remains constant. 
• The electric charges can neither be created nor destroyed, they can only be transferred from one body to another body. 

COULOMB'S LAW OF ELECTRIC FORCE:

Coulomb's law states that the force of attraction or repulsion between two stationary point charges is

1. Directly proportional to the product of the magnitude of the two charges.
2. Inversely proportional to the square of the distance between them and the force acts along the line joining the two charges. 

q₁ ⁕--------------- r ------------------⁕ q₂

If two point charges q₁ and q₂ are separated by a distance r, then the force F of attraction or repulsion between them is such that

 F ∝ q₁q₂  and  F ∝ 1 /r²

F = k q₁q₂/r²

[ Electrostatic force constant (k) ]

Where k is a constant of proportionality and it is called electrostatic force constant. 

The value of k depends on the nature of the medium between the two charges and the system of units used to represent the physical quantities. 

For the two charges located in free space and in SI units, 

 k = 1/(4πεₒ) = 9 x 10⁹ Nm²/C²

Where εₒ is called permittivity of free space. 

εₒ =  8.85 x 10⁻² C² N⁻¹m⁻²

Dimension of εₒ = [M⁻¹L⁻³T⁻⁴A²]

UNITS OF CHARGE

1. The SI unit of charge is Coulomb and denoted by C. 

2. CGS unit of Charge is two types

(i) in electrostatic CGS unit: statcoulomb or e.s.u. 

1 C = 3 x 10⁹ e.s.u. of charge. 

(ii) in electromagnetic CGS unit: abcoulomb or e.m.u. of charge.

1 C = 0.1 abcoulomb or e.m.u. of charge.

COULOMB'S LAW IN VECTOR FORM

RELATIVE PERMITTIVITY AND DIELECTRIC CONSTANT 

Permittivity

Permittivity is a property of a medium which determines the electric force between two charges situated in that medium. It is denoted by ε. Permittivity of vacuum or free space is minimum and it is denoted by εₒ. Permittivity of other medium are greater than εₒ. 

Relative Permittivity

The ratio (ε/εₒ) of the permittivity (ε) of a medium to the permittivity (εₒ) of free space is called relative permittivity (εᵣ ) of the given medium. 

Dielectric Constant (κ) 

Dielectric constant is defined as the ratio of the force between two charges placed some distance apart in free space to the force between the same two charges placed at same distance apart but in another medium. It is equal to relative permittivity. κ = εₒ. 

Dielctric constant for air = 1.00054

Dielctric constant for water = 80.

SUPERPOSITION OF ELECTROSTATIC FORCES

The principle of superposition states that when a number of charges are interacting, the total force on a given charge is the vector sum of the forces exerted on it due to all other charges. The force between two charges is not affected by the presence othe other charges. 

LECTURE 1: CLASS 10: LIFE PROCESSES

CLASS X   |    SCIENCE    |    LIFE PROCESSES

      Notes prepared by Subhankar Karmakar

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SCIENCE: CLASS X: CBSE (CLASS NOTES)

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A. CHARACTERISTICS OF LIVING THINGS

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The characteristics of living things:

• 1. Living things can move by themselves
• 2. Living things need food air and water
• 3. Living things can grow
• 4. Living things can respond to changes around them. They are sensitive.
• 5. Living things respire
• 6. Living things excrete
• 7. Living things can reproduce.  

B. LIFE PROCESSES

The basic functions performed by living organisms to maintain their life on this earth are called life processes. The basic life processes common to all the living organisms are:

• a. Nutrition and Respiration
• b. Transport and Excretion
• c. Control and Coordination
• d. Growth
• e. Movement
• f. Reproduction

C. NUTRITION

All the living organisms need energy to perform various life processes and they get it from the food they take. 

• Food: 

Food is an organic substance. The simplest food is glucose. 

Carbohydrates and fats are the nutrients which are used by an organism mainly as a source of energy whereas proteins and mineral salts are the nutrients used by an organism for the biosynthesis of its body constituents like skin blood etc. 

• Nutrition:

Nutrition is a process of intake of nutrients like carbohydrates fats proteins minerals vitamins and water by an organism as well as the utilisation of this nutrients by the organism.

• Nutrient:

A nutrient can be defined as a substance which an organism obtains from the surroundings and uses it as a source of energy or for the biosynthesis of its body constituents like tissues and organs. It may be organic or inorganic substance. 

D. MODES OF NUTRITION

Modes of Nutrition means methods of preparing food or obtaining food by an organism. There are mainly two modes of Nutrition. 

• 1. Autotrophic, and 
• 2. Heterotrophic

E. AUTOTROPHIC NUTRITION:  

• Autotrophic nutrition is that mode of nutrition in which an organism makes or synthesizes its own food from the simple inorganic materials like carbon dioxide and water present in the surroundings. 
• The green plants have an autotrophic mode of nutrition. Therefore, all the green plants are autotrophs. The autotrophic bacteria also obtain their food by the autotrophic mode of nutrition. Most of the bacteria are not autotrophic the organisms having autotrophic mode of nutrition are called autotrophic organisms or just autotrophs. 
• The autotrophic organisms or autotrophs contain the green pigment called chlorophyll which is capable of trapping sunlight energy. 

How does autotrophs prepare their food?

The autotrophic organisms contain the green pigment called chlorophyll which is capable of trapping sunlight energy. This trapped sunlight energy is utilised by the autotrophs to make food by combining organic materials like carbon dioxide and water present in the environment by the process of photosynthesis. Thus the autotrophs make their own food by photosynthesis. 

F. HETEROTROPHIC MODE OF NUTRITION

• Heterotrophic nutrition is that mode of nutrition in which an organism cannot make or synthesize its own food from simple inorganic materials like carbon dioxide and water and depends on other organisms for its food.
• All the animals have a heterotrophic mode of nutrition. Most bacteria and fungi also have heterotrophic mode of nutrition. The organisms having heterotrophic mode of nutrition are called heterotrophs. 
• Those organisms which cannot make their own food from inorganic substances like carbon dioxide and water and depend on other organisms for their food are called heterotrophs. The non green plants like yeast are also heterotrophs.

G. TYPES OF HETEROTROPHIC NUTRITION

A heterotrophic organism can obtain its food from other organisms in three ways. Therefore, there are three types of heterotrophic nutrition.

• 1. Saprotrophic nutrition
• 2. Parasitic nutrition and 
• 3. Holozoic nutrition. 

• SAPROTROPHIC NUTRITION
• Saprotrophic nutrition is that nutrition in which an organism obtains its food from the organic matter of dead plants, dead animals and rotten bread etc. 

• The organisms having saprotrophic mode of nutrition are called saprophytes.
• Saprophytes are the organisms which obtain their food from like rotten leaves, dead and decaying animal bodies and other decaying organic matter like rotten bread.
• Examples. Fungi like bread moulds, mushrooms and yeast and many bacteria are saprophytes. 

• PARASITIC NUTRITION
• The parasitic nutrition is that nutrition in which an organism derives its food from the body of another living organism called its host without killing it. 
• The organism which obtains the food is called a parasite and the organisms from whose body food is obtained is called the host. A parasite is an organism plant or animal which feeds on another living organism known as host. 
• Example. Most of the disease causing organism are parasites. Parasitic mode of nutrition is observed in several fungi bacteria a few plants like Cuscuta and some animals like plasmodium and roundworms. 
• Malaria parasite: Plasmodium is known as  malaria parasite.

• HOLOZOIC NUTRITION
• The holozoic nutrition is that nutrition in which an organism takes the complex organic food materials into its body by the process of ingestion the ingested food is digested and then absorbed into the body cells of the organism. 
• The undigested and un absorbed part of the food is thrown out of the body of the organism by the process of egestion. 
• Examples. Man, cat, dog, cattle, deer, tiger, lion, and amoeba have the holozoic mode of nutrition.

LECTURE 2: CHAPTER 16: HUMAN EYE

HUMAN EYE:

Eye is one of our most important sense organs. The main parts of the human eye are:

Cornea, Iris, Pupil, Ciliary muscles, Eye lens, Retina, and Optic nerve. 

1. Our eye is shaped like a ball. It has a roughly spherical structure. 

2. Outer coat of eye is white.

3. The front part of the eye is called Cornea. Cornea is made of a transparent substance and it is bulging out. The light coming from an object enters the eye through Cornea. The main function of Cornea is to protect the eye. 

4. Just behind the Cornea, there is  Iris. Iris is the coloured part of the eye. The iris has a hole at its centre which is called pupil. 

5. The eye lens is a convex lens which is behind the pupil. 

6. The eye lens is held in position by ciliary muscles. It controls the eye lens. 

7. The retina is a screen on which the image is formed in the eye. The eye lens focuses the image of an object on the retina. 

8. The optic nerve carries the image formed on retina to the brain. 

WORKING OF THE EYE

1. Light from the object enter Pupil of the eye and fall on the eye lens.

2. The eye lens is a convex lens, so it converges the light rays and produces a real and inverted image of the object on the retina.

3. The retina has a large number of light sensitive cells. 

4. When the image of the object falls on the retina, then the light sensitive cells generate electric signals. 

5. The retina send this electrical signals to the brain through the optic nerve and we are able to see the object.

6. Although the image of an object formed on the retina is inverted but our brain interpret this image as that of an erect image. 

FUNCTION OF IRIS AND PUPIL

The iris automatically adjusts the size  of pupil according to the intensity of light received by the eye from the surroundings. 

RODS AND CONES

Rods are the rod-shaped cells present in the retina of an eye which are sensitive to dim light.

Cones are the cone shaped cells present in the retina of an eye which are sensitive to bright light. Cones also cause the sensation of colour of objects in our eyes. 

BLIND SPOT

Blind spot is a small area of the retina insensitive to light where the optic nerve leaves the eye.

PERSISTENCE OF VISION

The ability of an eye to continue to see the image of an object for a very short duration even after the image has disappeared from view is called persistence of vision. 

RANGE OF VISION OF A NORMAL HUMAN EYE

The farthest point from the eye at which an object can be seen clearly is known as the far point of the eye. The far point of a normal human eye is at infinity. 

The nearest point upto which the eye can see an object clearly without any strain is called near point of the eye. The near point of a normal human eye is at a distance of 25 cm from the eye. 

DEFECTS OF THE EYE

Myopia is the defect of eye due to which a person cannot see e the distant objects clearly though he can see e the nearby objects clearly.

Myopia is corrected by using spectacles containing concave lenses.

Hypermetropia is the defect of eye due to which a person cannot see the nearby objects clearly though he can see the distant objects clearly. 

Hypermetropia is corrected by using spectacles containing convex lenses.

The medical condition in which the lens of eye of a person becomes progressively cloudy resulting in blurred vision is called cataract.

Cataract can be corrected with the help of surgery done on the eye. 

CARE OF THE EYES

1. Wash our eyes at least twice a day with clean water. 

2. We should not read or write in dim light.

3. We should not read by bringing the book too close to our eyes or too far from the eyes.

4. We should raise our eyes from time to time while reading, writing or watching television.

5. We should not rub the eyes with hands to prevent injury to the eyes.

6. In case of any problem we should consult an eye specialist.

7. We should take vitamin A regularly to keep our eyes healthy. 

NIGHT BLINDNESS

The inability of eyes to see properly in dim light during night is called night blindness. 

EYES OF OTHER ANIMALS

1. The eyes of a crab are quite small but they enable the crab to look all around. 

2. Butterflies have large eyes which appear to be made up of thousands of little eyes. They can see all around. 

3. Owl can see very well in the night, but not during the day. 

VISUALLY CHALLENGED PERSONS CAN READ AND WRITE

Those persons who are unable to see are known as visually challenged persons. 

Braille is a written language for the visually challenged persons in which characters like numbers and letters are represented by patterns of raised dots.

LECTURE - 1: CLASS VIII: LIGHT

CLASS VIII   |    SCIENCE    |    CHAPTER 16

     Notes prepared by Subhankar Karmakar

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• Luminous Objects: 

The objects their own light are called luminous objects. 

• Non Luminous Objects:

The objects which do not emit their own light are called non luminous objects. 

We can see the non luminous objectsbecause they reflects light into our eyes. Non luminous objects are also called illuminated objects. 

• Reflection of light

The process of sending back light rays which fall on the surface of an object, is called reflection of light.

• Incident Ray:

The ray of light which falls on the mirror surface is called incident ray. 

• Point of Incidence:

The point at which the incident ray strikes the mirror is called the point of incidence. 

• Reflected Ray:

The ray of light which is sent back by the mirror is called reflected ray.

• Normal at the point of incidence: 

The normal is a line drawn at right angles to the mirror surface at the point of incidence. It can be defined as a line which is perpendicular to the mirror surface at the point of incidence.

• Angle of incidence:

The angle between incident ray and normal is called the angle of incidence.

• Angle of reflection:

The Angle between reflected ray and normal is called the angle of reflection. 

• Laws of reflection of light:

There are two laws of reflection. They are as follows.

1. According to the first law of reflection, the incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane. 
2. According to the second law of reflection, the angle of reflection is always equal to the angle of incidence. 

• Special case: 

When a Ray of light falls normally or perpendicularly on the surface of a plane mirror the ray is reflected back along the same path.

• Regular reflection:

In regular reflection, a parallel beam of incident light is reflected as a parallel beam in one direction. Regular reflection of light occurs from smooth surface like that of a plane mirror or highly polished metal surfaces. 

• Diffuse reflection:

In diffuse reflection, a parallel beam of incident light is reflected in different directions. The diffuse reflection of light takes place from rough surfaces like that of paper, cardboard chalk, table, chair, walls and unpolished matter objects.

Both regular reflection as well as diffuse reflection obey laws of reflection.

Formation of image in a plane mirror:

Suppose a small object O is placed in front of a plane mirror MM'. 

1. We take two diverging incident rays OA and OB coming from the object O. These rays strike the mirror at point A and point B. 
2. Draw two normal AN and BN' at point A and point B. 
3. ∠OAN and ∠OBN' are two angles of incident. 
4. Draw ∠NAX = ∠OAN and ∠N'BY = ∠OBN'. Therefore, AX and BY will be the reflected rays respectively. 
5. Extend the rays XA and YB beyond the mirror and they intersect each other at point I.
6. I will be the image of the object O. 

LATERAL INVERSION

In an image formed by a plane mirror, the left side of object appears on the right side in the image whereas the right side of object appears on the left side in the image. This change of sides of an object and its mirror image is called lateral inversion. 

Characteristics of image formed by a plane mirror:

• 1. The image formed by a plane mirror is virtual or unreal.
• 2. The image formed by a plane mirror is behind the mirror. 
• 3. The image formed in a plane mirror is the same distance behind the mirror as the object is in front of it.
• 4. The image formed in a plane mirror is of the same size as the object. 
• 5. The image formed by a plane mirror is erect.
• 6. The image in a plane mirror is laterally inverted. 

• Multiple reflection:

A reflected ray can be reflected again and again. This property of light is extensively used in optical instruments. 

We shall discuss two optical instruments here. 

1. Periscope and 2. Kaleidoscope

• Periscope:

A Periscope is a long, tubular device through which a person can see objects that are out of their direct line of sight. It works on the reflection of light from two plane mirrors are parallel to one another. 

Usefulness: A Periscope gives us a higher view than normal. By using a periscope, we can see the objects on the other side of which cannot be seen by us directly. 

Construction: A Periscope consists of a long tube T having two plane mirrors M₁ and M₂ fitted at its two ends. The two plane mirrors are fitted in such a way that they are parallel to one another and their reflecting surfaces face each other. Each plane mirror makes an angle of 45° with the side of the tube. There are two holes in the Periscope tube, one hole is in front of the top mirror M₁ and the agar hole is in front of the bottom mirror M₂. 

Working of a Periscope:

Light ray from the object enters the Periscope through the upper hole and gets reflected by the top mirror vertically downwards. This reflected ray again strikes the bottom mirror  of the Periscope and reflected again along a horizontal direction and enters the eyes of the viewer. Thus the object can be seen behind an obstacle. 

Some of the uses of Periscope:

• 1. A Periscope is used to see over the heads of a crowd. 
• 2. A Periscope is used by soldiers sitting in a trench or bunker to observe the enemy activities outside over the ground. 
• 3. Epidiascope is used by a navy officer sitting in a submarine to see ships over the surface of water in the sea even though the submarine itself may be submerged under water. 

• Multiple images:

When two plane mirrors are kept inclined at an angle , they can form multiple images of an object. The image of object formed in one plane mirror acts as object for the other plane mirror. It has been found that if two plane mirrors are inclined at an angle x, then the number of images formed in them is given by the formula : 

No. of images formed = (360°/x) - 1

If an object is placed between two parallel plane mirrors facing each other, then theoretically, an infinite number of images should be formed. 

• Kaleidoscope:

The Kaleidoscope is an instrument or toy containing inclined plane mirrors which produce multiple reflections of coloured glass pieces and create beautiful patterns. 

The coloured glass pieces act as objects and the inclined plane mirrors form multiple images of these glass pieces by repeated reflections, which look like beautiful patterns. 

The coloured glass pieces act as objects and the inclined plane mirrors form multiple images of these glass pieces by repeated reflections, which look like beautiful patterns. 

(a pattern produced by kaleidoscope)

• Dispersion of light:

The splitting up of white light into seven colours on passing through a transparent medium like a glass prism is called dispersion of light. 

The formation of spectrum shows that white sunlight is made up of seven colours. The seven colours of the spectrum of white light are: Violet, Indigo, Blue, Green, Yellow, Orange and Red. 

• Sunlight - White or Coloured

The sunlight is referred to as white light. The white sunlight actually consists of seven colours. The fact that white sunlight consists of lights of seven different colours can be shown by using a glass prism as follows. 

Rainbow in sky is a natural phenomenon showing the dispersion of sunlight. 

NUMERICALS ON SIMPLE HARMONIC MOTION

1. A simple harmonic motion is represented by by    x = 10 sin (20t + 0.5), 

Write down its amplitude, angular frequency, frequency, time period and initial phase if displacement is measured in in metres and time in seconds. 

2. A body oscillates with SHM according to the equation, 

x = (5.0 m) cos [(2π rad/s)t + π/4]

At t = 1.5 s, calculate (a) displacement, (b) speed and (c) acceleration of the body. 

3. The equation of a simple harmonic motion is given by , 

y = 6 sin 10π t + 8 cos 10π t, where y is in cm, and t in seconds. Determine the amplitude, period and initial phase. 

4. A body oscillates with SHM according to the equation :

x(t) = 5 cos (2 πt + π/4)

Where t is in second, and x in metres. Calculate, 

(a) displacement at t = 0

(b) time period, (c) initial velocity

5. A spring of force constant  800 N/m has an extension of 5 cm. What is the work done in increasing the extension from 5 to 15 cm?

6. A body executes SHM of time period 8 s. If its mass be 0.1 kg, its velocity 1 second after it passes through its mean position be 4 m/s, find its (i) kinetic energy (ii) potential energy and (iii) total energy. 

7. A particle is executing SHM of amplitude A. At what displacement from the mean position, is the energy half kinetic and half potential?

8. What is the length of a second pendulum? 

(A second pendulum is a pendulum with a time period of 2 s). 

LECTURE 1: CLASS 12: ATOMS