Light : Reflection and Refraction || Class 10th Science || CBSE Notes || Study World

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Introduction: Light is a form of energy which enables us to see objects from which it comes or from which it is reflected.

For examples: The Sun given out light , therefore we can see the sun.

Theory about the nature of Light: There are two theories about the nature of light.

(1) Wave Theory of Light

(2) Particle Theory of Light.

(1) Wave Theory of Light: According to wave theory light consists of electromagnetic waves which do not required a material medium for their propagation. The wavelength of visible light wave is very small ( being about 4 ✖ 10 ^{̶ 7}m to 8 ✖ 10 ^{̶ 7}m). Speed of light is about 3 ✖ 10 ^{̶ 8} meter per second in vacuum.

(2) Particle Theory of Light : According to particle theory light is composed of particles which travel in a straight line at very high speed. The elementary particle that define light is Photon. The modern theory of light called Quantum Theory of Light combines both the wave and particle models of light.

Reflection of Light

The process of sending back the light rays which falls on the surface of an object is called reflection of light. The reflection of light is as shown in figure.

when a beam of light AO falls on a mirror at point O , it sent back by the mirror in another direction OB , and we can say that mirror has reflected the beam of light falling on it .

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

👉 The rays of light which is send back by the mirror is called reflected rays.

👉 The line at right angle to the mirror surface at the point of incidence is called normal.

Laws of Reflection of Light

The reflection of light takes place according to two laws which are known as laws of reflection of light. the laws of reflection of light are given below:

First Law of Reflection: According to first law of reflection of light. The incident rays , refelected rays , and the normal at the point of incident all lies in the same plane.

Second Law of Reflection: According to second law of reflection of light; The angle of incidence is always equal to angle of reflection.

Object and Image:

Anything which gives out light rays either its own or reflected by it is called an object. e.g. a candle, a bulb etc.

Image is an optical appearance produced when light rays coming from an object are reflected from a mirror or reflected from a mirror or refracted through a lens.

Real Image and Virtual Image.

The image which can be obtained on a screen is called a real image. e.g. The image of actor in cinema hall on screen is real image, whereas the image which cannot be obtained on a screen is called virtual image.

A virtual image can be seen only by looking into the mirror.

Lateral Inversion:

When an object is placed in front of a plane mirror, then the right side of an object appears to becomes the left side of image. This change of side of an object and it s mirror image is called lateral inversion. The phenomenon of lateral inversion can be seen in the figure:

Characteristics of Image formed by the Plane Mirror :

Following are the characteristics of image formed by a plane mirror.

(1) The image formed in a plane mirror is virtual. It is not cannot be received on a screen.

(2) The image found in plane mirrors is erect. It is the same side up as object.

(3) The image formed by plane mirror is at the same distance behind the mirror as the object is in the front of the mirror.

(4) The image formed in a plane mirror is laterally inverted. ( or sideways reversed)

Use of Plane Mirror: Following are the uses of plane mirror:

(1) Plane mirror are used to see ourselves.

(2) Plane mirror fixed on the inside wall of certain shop (like jewellery shop) to make them look bigger.

(3) Plane mirror are fixed at blind turn of some busy roads so that drivers can see the vehicle coming from other side and prevent accidents.

(4) Plane mirror are used in making periscope.

Reflection of light from Curved Surface

Spherical Mirrors: A spherical mirror is that mirror whose reflecting surface is the part of hollow sphere of glass. The spherical mirror are of two types:

(1) Concave mirrors

(2) Convex mirrors.

(1) Concave mirrors: A concave mirror is that spherical mirror in which the refraction of light takes place at the concave surface ( or bent- in surface).

(2) Convex Mirror: A convex mirror is that spherical mirror in which the refraction of light takes place at the convex surface ( or bulging-out-surface). A convex mirror is as shown in figure.

Centre of Curvature, Radius of Curvature, Pole and Principal axis of Spherical Mirror

Centre of Curvature: The centre of curvature of a spherical mirror is the center of hollow sphere of glass of which the mirror is a part. It is represented by the letter C. In figure C is the centre of curvature.

The center of curvature of a spherical mirror is in front of it but the centre of curvature of a convex mirror is behind it.

Radius of Curvature: The radius of curvature of a spherical mirror is the radius of Hollow sphere of glass of which the mirror is a part. In figure the distance CP is the radius of curvature of the mirror. The radius of curvature is represented by letter R.

Pole: The centre of a spherical mirror is called its pole. In other worlds, the middle point of a spherical mirror is called its pole. In figure P is the pole of mirror.

Principal Axis: The straight line passing through the centre of curvature and pole of a spherical mirror is called its principal axis. In figure the line XY by passing through C and P is the principal axis of mirror.

Aperture: That portion of mirror from which the reflection of light actually takes place is called aperture of the mirror. In figure MM^̷ is the aperture of a mirror.

Relation between radius of Curvature and Focal Length of a Spherical Mirror

For a spherical mirror having small aperture the focus lies exactly mid-way between the pole and centre of curvature. So, the focal length of a spherical mirror is equal to half of its radius of curvature.

Mathematically:- If f is the focal length of a spherical mirror and R is its radius of curvature, then
f = R/ 2

Principal focus and Focal length of a Mirror

Principal Focus: The principal focus of a mirror is a point on its principal axis to which the light rays which are parallel and close to the axis converge or diverge after reflection from the mirror. The focal length of the mirror is denoted by letter f

while the focus of convex mirror is situated behind the mirror as shown in figure (a) and (b). A convex mirror has a virtual focus while concave mirror has real focus.

Focal length: The focal length of a mirror is the distance between its pole and principal focus. It is denoted by letter f

Rule for obtaining image formed by Mirrors

When object is placed in front of a concave mirror, images formed. The image formed at the point where at least two reflected rays intersect or appear to intersect.

Some of the rule for obtaining images formed by the mirror are as:

Rule 1: A Ray of light which is parallel to the principal Axis passing through its focus after reflection from the mirror ( for concave mirror)

Whereas it appear to come from the focus after reflection in case of convex mirror as shown in figure below:

Rule 2 : A Ray of light passing through the centre of (concave and convex) curvature is reflected back along the same path because it strike the mirror normally or perpendicular.

Rule 3: A Ray of light passing through the focus of mirror becomes parallel to the principal axis after reflection as shown in figure.

Rule 4 : A Ray of light which is incident at the pole of a mirror is reflected back making the same angle with the principal Axis as shown in figure.

Formation of different type of image by the concave mirror:

The type of image formed by the concave mirror depend on the position of the object in front of the mirror.

We will draw the ray diagram to show the concave image formed by a concave mirror for different position of an object. We will discuss it one by one.

Case 1: Image formed by a concave mirror when the object is placed between pole and focus of the mirror (object between P and F ).

When an object is placed between the pole(P) and focus(F) of the concave mirror, the image formed is :

(1) behind the mirror

(2) virtual and erect, and

(3) larger than the object (or magnified) as shown in figure

Case 2: When the object is placed at the focus of a concave mirror (object at F)

When an object is placed at the focus of the concave mirror,the image is formed is:

(1) at infinity

(2) real and inverted, and

(3) highly magnified (or highly enlarged)

Case 3: When the object is placed between focus and centre of curvature (object between F and C)

When the object is placed between the focus (F) and centre of curvature (C) of a concave mirror, the image formed is:

(1) beyond the centre of curvature. real and inverted, and

(2) larger than the object(or magnified)

👉Note: A real image is always inverted, and virtual image is always erect.

Case 4: When the object is placed at the centre of curvature of a concave mirror(object at C)

When an object is placed at the centre of curvature of a concave mirror, the image formed is

(1) at the centre of curvature(C).

(2) real and inverted, and some same size as the object.

Case 5: When the object is beyond the centre of curvature of a concave mirror (object beyond C)

When an object is placed at the centre of curvature (C) of a concave mirror, the image formed is:

(1) between the focus and centre of curvature

(2) real and inverted, and

(3) smaller than the object (or diminished)

Case 6: When the object is at infinity.

When an object is at infinity from a concave mirror, the image formed is

(1) at the focus (F).

(2) real and inverted, and

(3) much smaller than the object ( highly diminished).

Formation of image by a convex mirror

Case 1: When an object is placed anywhere between pole(P) and infinity in front of a convex mirror, then the image formed is:-

(1) behind the mirror between pole(P) and focus(F).

(2) virtual and erect.

(3) diminished (smaller then the object)

Case 2: When an object is at infinity from a convex mirror, then the image formed is:-

(1) behind the mirror at focus(F)

(2) virtual and erect, and

(3) highly diminished.(much smaller than the object).

Sign convention for Spherical Mirror

According to the new Cartesian sign convention:

(1) All the distance are there from pole of the mirror as origin.

(2) Distance measured in the same direction as that of incident light are taken as positive.

(3) Distance measured against the direction of incident light are taken as negative.

(4) Distance made upward and perpendicular to the principal axis are taken as positive.

(5) Distance measured downward and perpendicular to the principal Axis are taken as negative.

(6) The object is always placed on the left side of the mirror.

Mirror Formula

A formula which gives the relationship between image distance(v) object distance(u) and focal length (f) of the spherical mirror is known as mirror formula.The mirror formula can be written as:

where v= distance of image from mirror.

u = distance of object from mirror.

f = focal length of the mirror

The mirror formula has three value in it. If any two value or known, the third value can be calculated.

Linear Magnification Produced by Mirrors

The ratio of height of image to the height of object is known as linear magnification. i.e.

Where m=magnification

= Height of image

= Height of object.

The height of the object h₁ is always positive, the height h₂ of the image can be either positive or negative.

If the magnification has a plus (+) sign then the image is virtual and erect.

If the magnification has a minus (-) sign then the image is a real and inverted.

Sometime we do not know the height of object and image. In that case we will write another formula for calculating the magnification produced by a spherical mirror in term of object distance and image distance.

Then the linear magnification produced by a mirror is equal to the ratio of the image distance to the object distance with a minus ( ̶ ) sign.

Thus we have two formula for calculating the magnification.

Problem based on concave mirror

Find the size, nature and position of image formed when the when an object of size 1 cm is placed at a distance of 15 cm from a concave mirror of focal length 10 cm.

Solution: Given

(∵ it is concave mirror)

Now putting the this value in the mirror formula; we get

Thus the image is 30 cm to the left side of mirror (minus sign show that the image is in the left side)

Since the image is formed in front of a concave mirror. So its nature will be Real and Inverted.

Uses of Concave mirrors:

Following are the use of concave mirror:-

(1) Concave mirror is used as shaving mirror to see a large image of the face.

(2) Concave mirror is used as a head Mirror by the doctor to concentrate light coming from a lamp on the body part of the patient like ear, nose, throat etc.

(3) Concave mirror used as reflected in torches, vehicle head lights and search light to get a powerful beam of light.

(4) Concave mirror are used in the field of solar energy to focus sun’s rays for heating solar furnaces.

(5) Concave dishes are used in TV Dish antennas to receive TV signal from the Digital Communications satellites.

Uses of Convex Mirror

Following are the use of concave mirror:-

(1) Convex mirrors are used as rear view mirrors in vehicles like Car Cars, trucks and buses) to see the traffic at the rear side (or back side)

(2) Big Convex mirrors are used as Shop Security mirrors

(3) Big convex mirrors are used in blind curves on the roads to see the vehicle from opposite side.'

Refraction of Light: The change of direction of Light when it passes from one medium to another obliquely is called refraction of light .

In other words, the bending of light when it from one medium to another obliquely is called refraction of light. The refraction of light takes place at the boundary between the two media.

The angle between incident ray and normal (at the paint of incidence) is called the angle of incidence, and the angle between the refracted ray and the normal at the point of Incidence is called the angle of incident.

As we know that the angle of incidence always equal to angle of reflection but in case of refraction of light, the angle of incidence is not equal to angle of refraction.

Cause of Refraction: - As the speed of light is different in different media ( or substances)e.g. speed of light in air is 3 × 10⁸ m/s whereas that in glass is 2 × 10⁸ m/s.

The reflection of light is due to the change in the speed of light on going from one medium to another medium.

👉When a ray of light goes from air into glass it bends towards the normal.

👉While when a ray of light goes into air, it bends away from the normal.

Law of Refraction of Light.

The refraction of light on going from one medium to another takes place according to two laws which are known as laws of refraction of light. These are given below:

(1) According to the first law of Reflection of light : The incident ray, the refracted ray and the normal at the point of incidence all lies in the same plane.

(2) According to 2^nd law of Refraction of light:

The ratio of angle of incidence to the angle of refraction is constant for a given pair of media. (such as air and glass or air and water)

i.e. Sine of angle of incidence / Sine of angle of Refraction = Constant

or Sin i / Sin r = Constant

The Constant Sin i / Sin r is called the refractive index of the medium in which light goes from air.

i.e. Refractive index, n = Sin i ÷ Sin r

Where Sin i = Sine of angle of incidence.

Sin r = Sine of angle of refraction.

Numerical Problem :- A beam of light passes from air into a Substance X. If the angle of incidence be 72 and the angle of refraction be 40, Calculate the refractive index of substance X (Given Sin 72⁰ = 0.95 and Sin 40⁰ = 0.642)

Solutions :-

We know that

Refractive Index = Sine angle of incidence ÷ Sine of angle of refraction.

Thus , the refractive index of substance X is 1.48

Lens

A lens is a piece of transparent glass bound by two spherical surfaces. There are two types of lens;

(1) Convex lens

(2) Concave Lens

(1) Convex Lens: A convex lens is thick at the centre but thinner at the edges as shown in figure below:

(2) Concave Lens: A concave lens is thin in the middle but thicker at the edge as shown in figure above.

Principal Focus and Focal Length of a lens

Principal Focus: - It is s point on the principal axis of lens to which light rays parallel to the principal axis converge (in case of convex lens) or diverge (in case of concave lens) after passing through the lens.

A lens has two foci. The two foci are at equal distance from the optical centre, one on either side. The two foci are usually denoted by letter F and F^./ . Convex lens has real focus while that of concave lens has virtual focus.

Focal Length: The focal length of a lens is the distance between optical centre and principal focus of the lens. In the figure above CF and CF^/ are the focal length.

Rule for obtaining Image formed by Convex Lens

Rule 1: A ray of light which h is parallel to the principal axis of a convex lens, passes through its focus after refraction through the lens. This is shown in the figure given below:

Rule 2: A ray of light passing through the optical centre of a convex lens goes straight after refraction through the lens. It does not deviated.

Rule 3: A ray of light passing through the focus of a convex lens become parallel to its principal axis after refraction through the lens.

Formation of different types of Image by the Convex Lens.

The types of image formed by the convex lens depends on the position of the object in front of the lens. We can place the object at different position (or distance) from a convex lens to get different types of image. We will consider all these position one by one.

Case 1: Image formed by the convex lens when the object is placed between optical centre and focus:-

When the object is placed within the focus and optical centre of a convex lens, then the image formed is:

(a) behind the object

(b) virtual and erect

Case 2: When the object is placed at the focus of a convex lens. (object at F^/) :

When an object is placed at the focus of a convex lens , the image formed is :

(a) At infinity

(b) Real and inverted

Case 3: When the object is between F^/ and 2F^/

When the object is between F^/ and 2F^/in front of a convex lens, the image formed is:

(a) Beyond 2f

(b) Real and inverted

Case 4: When the object is at 2F^/

When an object is placed at a distance 2f in front of a convex lens, then the image formed is:

(a) at a distance 2f on the other side of the lens

(b) real and inverted

Case 5: When the object is beyond 2F^/

When the object is placed beyond 2F in front of a convex lens, then the image formed is

(a) between f and 2f on the other side of lens

(b) real and inverted

Case 6: When the object is at infinity:

When the object is at infinity from a convex lens, then the image formed is:

(a) at the focus

(b) real and inverted, and

Uses of Convex lens::

(1) Convex lens are used in spectacles to correct the defect of vision is called hypermetropia.

(2) Convex lens is used for making a simple camera.

(3) Convex lens is used for making magnifying glass.

(4) Convex lenses are used in making microscope.

Sign Convention for Spherical Lenses

According to the New Cartesian Sign Convention:

(1) All the distance is measured from the optical centre of the lens.

(2) The distance measured in the same direction as that of incident light are taken as positive.

(3) The distance measured against the direction of incident light is taken as negative.

(4) The distance measured upward and perpendicular to the principal axis is taken as positive.

(5) The distance measured downward and perpendicular is taken as negative.

Lens Formula

A formula which give the relationship between image distance (v) , object distance (u) and focal length (f) of a lens is known as the lens formula. The lens formula can be written as:

Magnification Produced by Lenses: The linear magnification is the ratio of the height of the image to the height of the object. i.e.

Where m = magnification

h₁= height of image

h₂ = height of object

the linear magnification of the lenses is equal to the ratio of image distance to the object distance.

i.e.

Where m = magnification

h₁= image distance

h₂ = object distance.

Rules for obtaining Image formed by the Concave Lenses

Rule 1: A ray of light which is parallel to the principal axis of a concave lens, appears to coming from its focus after refraction from the lens.

Rule 2: A ray of light passing through the optical centre of a concave lens goes straight after passing through the lens.

Rule 3: A ray of light going towards the focus of a concave lens, become parallel to its principal axis after refraction through the lens.

Formation of Image by Concave Lens.

There are only two cases for the formation of image by concave lens.

Case 1; When an object is placed anywhere between optical centre C and infinity in front of a concave lens, the image formed is:

(a) between optical centre and focus

(b) virtual and erect

Case 2: When an object is at infinity from a concave lens, the image formed is

(a) at focus (f)

(b) virtual and erect and

Uses of concave Lenses

(1) Concave Lenses are used in spectacles to correct the defect of vision called myopia.

(2) Concave lens is used as eye lens in Galilean telescope.

(3) Concave lens s used in wide angle spy hole in doors.

(4) Concave lens are used in combination with convex lens to make high quality lens system for optical instruments.

Power of a Lens

The power of a lens is a measure of degree of convergence or divergence of light rays falling on it.

The power of a lens is defined as the reciprocal of its focal length in meters.

Where P = Power of the lens

F = focal length of the lens (in meter)

Since the power is inversely proportional to its focal length, therefore a lens of short focal length has more power whereas a lens of long focal length has less power.

The unit of power of lens is dioptre. One dioptre is the power of a lens whose focal length is 1 metre.

Power of Combination of Lenses: If a number of lenses are placed in close contact, then the power of the combination of lenses is equal to the algebraic sum of power of individuals lenses.

Thus if two lenses of power P₁ and P₂ are placed in contact with each other, then their resultant power P is given by :

P = P₁ + P₂

For example, if a convex lens of power + 4D and a concave lens of power - 10D are placed in contact with each other, then their resultant power will be.

P = P₁ + P₂

= + 4 + (- 10) = 4 – 10 = - 6 D

Thus the resultant power is – 6 Dioptre.

In general , if the number of thin lenses having power P₁, P₂ , P₃, .............. etc are placed in close contact with one another, then their resultant power P is given by P = P₁+ P₂ + P_3
+ ..............

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