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10. Light-Reflection and Refraction

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Light makes things visible. The sun light helps us to see the objects during light.

How we able to see any object?

An object reflects light that falls on it. This reflected light, when received by our eyes, enables us to see things.

A ray of light: When light travels from its source of light, it looks like straight line, this line is called a ray of light. 

Shadow: When a beam of light pass through an opaque object and get reflected and it form a shadow of that opaque object. 

Diffraction of light : If an opaque object on the path of light becomes very small, light has a tendency to bend around it and not walk in a straight line – an effect known as the diffraction of light.

Reflection Of Light: 

When a ray of light falls on polished surface, it turns or reflects most of the light in the same medium from which it comes. This phenomenom is known as reflection of light. 

     

 

The laws of reflection of light:

(i)   The angle of incidence is equal to the angle of reflection, and
(ii)  The incident ray, the normal to the mirror at the point of incidence and the reflected ray, all lie in the same plane.

These laws of reflection are applicable to all types of reflecting surfaces
including spherical surfaces.

Some common wonderful phenomena

There occur some common wonderful phenomena due to reflection of light. These are followings;

Image formation by mirrors, the twinkling of stars, the beautiful colours of a rainbow, bending of light by a medium.

Type of Reflection:

1. Specular or regular reflection: Such type of reflection takes place from shiny or polished surface and incident rays remain parallel to each other after reflection.

                          

2. Diffused or irregular reflection: Such type of reflection takes place from

    rough surface and incident rays do not remain parallel to each other after 

   reflection. 

 

                    

Mirror : This is a shiny and more polished reflecting surface, which make the image of an object kept front of it. 

Types of Mirror: 

There are two types of mirror.

(A)  Plane Mirror : Its reflecting surface is straight and flat. 

                            

(B)  Spherical Mirror : It has curved reflecting surface. This curved reflecting surface can be curved inward or out outwart. 

On the basis of this curvature, spherical mirror are two types.

(i) Concave Mirror : Its reflecting surface is inward. 

 

                 

(ii) Convex Mirror : Its reflecting surface is outward.       

                  

                 

The Parts Of Spherical Mirror :

(i) Pole : The centre of reflecting surface of spherical mirror is called its pole. It is denoted by English letter P.

(ii) The Centre of Curvature : The reflecting surface of a spherical mirror forms a part of a sphere. This sphere has a centre. This point is called the centre of curvature of the spherical mirror.

(iii) The Radius of Curvature : The distance between Pole of the spherical mirror and the center of curvature is known as the radius of curvature. 

(iv) Principal Axis : The straight line passing through the pole and the centre of curvature of spherical mirror is known as principal axis.  

(v) Principal Focus : There is an another point F on principal axis lie between half of the pole and the center of curvature which is called the principal focus. Incident rays parallel to the principal axis intersect at principal focus after reflection in concave mirror and it seems to intersect in convex mirror. 

(vi) Focal Length : Distance between the pole and the principal focus of the mirror is called Focal Length. It is denoted by small 'f' of English alphabets. This distance is half of the radius of the curvature. 

(vii) Aperture : The reflecting surface of a spherical mirror is by and large spherical. The surface, then, has a circular outline. The diameter of the reflecting surface of spherical mirror is called its aperture.  

The Position, Nature and Size of Image: 

The position of object: The place where an object is placed.

The position of Image : The place where mirror forms the image of an

object.

The Size of Image : This is the size of image which tells that the image of object is formed either smaller or larger than the object. 

The nature of image : It is known by the nature of image that what type of image is formed by mirror like virtual and errect or real and inverted. 

There are two types of nature of images.

(i) Real and inverted : This types of images always form infront of mirror.

(ii) Virtual and errect : This types of images always form behind the mirror. 

Image Formation by Spherical Mirrors:

The formation of image in concave mirror is depended on the position of  an object. An object placed between the pole (P) and principal focus (F) form only virtual and errect image otherwise all others images are real  and inverted that kept any other places before the concave mirror. 

Some positions, natures and sizes of images formed by concave mirror.

• The image of an object placed at infinity is real and inverted and very small like a point size and Image forms at Focus.
• The Image of an object placed far away from centre of curvature C forms real and inverted and very small image between Focus and centre of curvature.
• The Image of an object placed at Centre of curvature (C) forms real and inverted at C and equal in size of object. 
• The image of an object placed between centre of curvature and principal focus forms real and inverted, far aways from C and magnified. 
• The image of an object placed at principal focus forms real and inverted and very large to object at infinity. 
• The image is virtual and errect, larger than object and behind the mirror when object placed between P and F.  

Use Of Concave Mirror: 

(i)    Concave mirrors are commonly used in torches, search-lights and vehicles headlights to get powerful parallel beams of light.

(ii)    They are often used as shaving mirrors to see a larger image of the face.

(iii)   Concave mirrors are used to see large images of the teeth of patients by the dentists.

(iv)   Large concave mirrors are used to concentrate sunlight to produce  heat in solar furnaces.

Image Formation By Convex mirror: 

The image formed by convex mirror is always virtual and errect and smaller than the object. 

Use Of Convex Mirror: 

(i)   Convex mirrors are commonly used as rear-view (wing) mirrors in vehicles.

(ii)   It is used as reflector for street lighting purposes.

(iii)   Convex mirrors are useful for inspecting places difficult to get to.

(iv)   convex mirrors are also used for security situations.

Sign Convention for Reflection by Spherical Mirrors:

Reflection of light by spherical mirrors form a cartesian plane which is a

set of sign conventions called the New Cartesian sign Convention. 

These are as follows -  

• The pole (P) of the mirror is taken as the origin.
• The principal axis of the mirror is taken as the x-axis (X’X) of the
  coordinate system.
• The object is always placed to the left of the mirror. This implies
  that the light from the object falls on the mirror from the left-hand
  side.
• All distances parallel to the principal axis are measured from the
  pole of the mirror.
• All the distances measured to the right of the origin (along
  + x-axis) are taken as positive while those measured to the left of
  the origin (along – x-axis) are taken as negative.
• Distances measured perpendicular to and above the principal axis
  (along + y-axis) are taken as positive.
• Distances measured perpendicular to and below the principal axis
  (along –y-axis) are taken as negative.

Mirror Formula:

Uses of Mirror formula: 

Example 1: An object is placed 20 cm in front of a concave mirror of focal length 15 cm. Find the position of object, nature and size of image. 

Solution: 

Object-distance (u) = - 20 cm [ Distance of object is always negative (-) ]

focal length (f) = - 15 cm [Focal length in concave mirror is negative (-) ]

Image-Distance (v) = ? 

Using mirror formula; 

 

Example 2. An object of height 5 cm is placed 15 cm away from a convex mirror of focal length 15 cm. Find the position, nature and size of image formed. 

Solution: 

Object-distance (u) = -15 cm 

Focal length (f) = 15 cm       [ Focal length in convex mirror is positive (+) ]

Image-distance (v) = ? 

Using mirror formula: 

Position of image: 7.5 cm back of mirror

Nature of image: Vertual and irect 

Size: Half of the object (smaller). 

 

 

Chapter 10. Light-Reflection and Refraction

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Refraction of light: 

When a ray of light enters from one transparent medium to another transparent medium it changes its direction or it bends. This bending of light path is called refraction of light. 

The refraction of light only takes place through transparent materials like glass, air and water etc. 

There are two situation of this bending.

(i) When a ray of light enters from rarer medium to denser medium it bends towards the normal. 

(ii) When a ray of light enters from denser medium to rarer medium it bends away from normal. 

Cause of the refraction of light: The refraction of light occurs due to changing in speed of light it enter on transparent medium to another.  

The Law of refraction: 

The following are the laws of refraction of light:

(i) 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.

(ii) The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given colour and for the given pair of media. This law is also known as Snell’s law of refraction.

Snell's Law: The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given colour and for the given pair of media. This law is also known as Snell’s law of refraction.

Denser Medium: The medium which has greater refractive index is called dender medium. The particles of this medium is denser.

Rarer Medium: The medium which has smaller refractive index is called rarer medium. 

Refractive Index: The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given colour and for the given pair of media. This constant value is called refractive index of the second medium with respect to the first medium. 

• The refractive index can be linked to an important physical quantity, the relative speed of propagation of light in different media. It turns out that light propagates with different speeds in different media. Light travels the fastest in vacuum with the highest speed of 3×108 m s–1.
• In air, the speed of light is only marginally less, compared to that in vacuum.
• It reduces considerably in glass or water. The value of the refractive index for a given pair of media depends upon the speed of light in the two media.
• Refractive index with higher value of material has less speed of light through it.
• Refractive index with lower value of material has high speed of light through it.

Example: The refractive index of diamond is 2.42, it means the ratio of speed of light in air and speed of light in diamond is 2.42. Diamond has higher refractive index and when the light will pass through it, the speed of light will be less. The material media of higher refractive index reduce the speed of light than normal and the material media of lower refractive index increase the speed of light when pass through it. 

Absolute refractive index of some material media:

 An optically denser medium may not possess greater mass density. For example, kerosene having higher refractive index, is optically denser than water, although its mass density is less than water.

Optically Denser Medium: In comparing two media, the one with the larger refractive index is optically denser medium than the other.

Optically Rarer Medium: In comparing two media, the one with the lower refractive index is optically rarer medium than the other.

Refractive Index of Medium₂ with respect to Medium₁:

The refractive index of medium 2 with respect to medium 1 is given by the ratio of the speed of light in medium 1 and the speed of light in medium 2. This is usually represented by the symbol n₂₁.

Example: The speed of light in air is 3 x 10⁸ ms^-1 and the speed of light in water is 2.25 x 10⁸ ms^-1. Find the refractive index of water with respect to air.

Solution: Speed of light in air = 3 x 10⁸ ms^-1. 

Speed of light in water - 2.25 x 10⁸ ms^-1. 

Refractive Index of Water is 1.33 

Refractive Index of Medium₁ with respect to Medium₂:

The refractive index of medium1 with respect to medium 2 is represented as n₁₂. It is given by

Example: Speed of light in water is 2.25 x 10⁸ ms^-1 and the speed of light in Kerosene is 2.08×10⁸ ms^-1. Find the Refractive index of water with respect to Kerosene. 

Solution: Speed of light in water (V₁) = 2.25 x 10⁸ ms^-1. 

Speed of light in Kerosene (V₂) = 2.08 x 10⁸ ms^-1. 

Refractive Index of water = Speed of light in Kerosene (V₂)/Speed of light in water (V₁)

= 2.08 x 10⁸ ms^-1/2.25 x 10⁸ ms^-1

= 2.08/2.25 

= 0.924 

Refractive Index of water with respect to Kerosene = 0.924 

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Questions for Practice: 

Q1. What is refractive index? 

Q2. Write the law of refraction of light.

Q3. What are the two situation of bending the path of light during refraction of light.

Q4. The refractive index of diamond is 2.42. What is the meaning of this statement?

Q5. Light enters from air to glass having refractive index 1.50. What is the speed of light in the glass? The speed of light in vacuum is 3 × 10⁸ m s^–1.

Q6. Define Optically denser medium and Optically rarer medium. 

Q7. Write the Snell's law. 

Q8. The Refractive Index Of Kerosene Is 1.44 . Find The Speed Of Light In Kerosene.

Q9. You are given kerosene, turpentine and water. In which of these does the light travel fastest?

Q10. Give the examples of the medium having highest optical density.
Also give the example of the medium with lowest optical density.

 

Refraction by Spherical Lenses: 

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Lens: A piece of glass or other transparent material bound by two
surfaces, of which one or both surfaces are spherical, forms a lens. This means that a lens is bound by at least one spherical surface.

Category of Lens: There are two types of lens.

(i) Convex lens: A lens which spherical surfaces bulging outward, such a lens is called a double convex lens. It is simply called a convex lens. It converges light rays hence convex lenses are also called converging lenses.

Features of convex lens:

(i) It is thicker at the middle as compared to the edges.

(ii) Convex lens converges light rays. 

(ii) Concave Lens: A lens which is bounded by two spherical surfaces and curved inwards such lens is called concave lens. Concave lens is thicker at the edges than at the middle and it diverge light rays so it is called diverging lens. A double concave lens is simply called a concave lens.

Features of concave lens: 

(i) Concave lens is thicker at the edges than at the middle.

(ii) It diverge light rays

Parts of Spherical Lens:

(i) Centers of Curvature: A lens, either a convex lens or a concave lens, has two spherical surfaces. Each of these surfaces forms a part of a sphere. The centres of these spheres are called centres of curvature of the lens.

The centre of curvature of a lens is usually represented by the letter C.

Since there are two centres of curvature, we may represent them as C1
and C2.

(ii) Principal axis: An imaginary straight line passing through the two centres of curvature of a lens is called its principal axis.

(iii) Optical Centre: The central point of a lens is its optical centre. It is usually represented by the letter O.

(iv) Aperture: The effective diameter of the circular outline of a spherical lens is called its aperture.

(v) Thin lens with small aperture: Lenses whose aperture is much less than its radius of curvature. Such lenses are called thin lenses with small apertures.

(vi) Principal Focus of convex lens: A point on the principal axis on which light rays after refraction from the lens converge, this point is called principal focus of convex lens. 

(vii) Principal Focus of concave lens: Light rays after refraction from the lens, are appearing to diverge from a point on the principal axis. This point on the principal axis is called the principal focus of the concave lens. 

Letter F is usually used to represent principal focus. However, a lens has two principal foci. They are represented by F₁ and F₂. 

See the fig.

Image of sun on paper sheet by using lens: 

When we point a lens over a paper sheet for sometimes. The paper begins to burn producing smoke. It may even catch fire after a while. The light from the Sun constitutes parallel rays of light. These rays were converged by the lens at the sharp bright spot formed on the paper. In fact, the bright spot you got on the paper is a real image of the Sun. The concentration of the sunlight at a point generated heat. This caused the paper to burn.

(viii) Focal Length: The distance of the principal focus from the optical centre of a lens is called its focal length. The letter f is used to represent the focal length.

 

Image Formation by Lenses: 

Refracting the light from a lens after passing through an object the lens forms an image of the object. 

A. Nature of the Image: The image formed by a lens can either be real and inverted or be virtual and erect, these are called the nature of Image. 

Type of Nature of Images: 

(I) Real and Inverted : The image which can be shown on a screen is called real image and forming upside of an image down or in the opposite position is called inverted image. 

(II) Virtual and Erect: The image which can not be printed on a screen is called vertual image and Erect means upward in straight position. 

B. Position of the image: The place where the image forms is called the position of the image. Position is a vector quantity which may be negative or positive in magnitude. All positions in a lens is measured from optic centre. From where the light enters or the object is placed is measured as negative and where the light refracts is measured as positive. 

Position of the object: Where the object is placed is called the position of the object. It may be at infinity, beyond 2F1, between F1 and 2F1, at focus F1 and between F1 and optical centre. 

Position of the object always measured as negative because objects are placed where the light enters.  

C. Relative size of the image: There are various sizes of images formed by the lenses. It may be point size, highly diminished, diminished same size enlarged or highly enlarge. 

See the table: Nature, position and relative size of the image formed by a convex lens for various positions of the objects. 

Nature, position and relative size of the image formed by a concave lens for various positions of the objects. 

Image Formation in Lenses Using Ray Diagrams:

To understand the ray diagram we have to study the two rays;

(i) Ray passing through the object parallel to principal axis.

(ii) Ray passing through the object and optical centre. 

In convex lens: 

(i) A ray of light from the object, parallel to the principal axis, after refraction from a convex lens, passes through the principal focus on the other side of the lens. 

(ii) A ray of light passing through a principal focus, after refraction
from a convex lens, will emerge parallel to the principal axis.

(iii) A ray of light passing through the optical centre of a lens will
emerge without any deviation.

In Concave lens:

(i) A ray of light from the object, parallel to the principal axis, after
refraction from a concave lens, the ray appears to diverge from the principal focus located on the same side of the lens.

(ii) A ray of light appearing to meet at the principal focus of a concave lens, after refraction, will emerge parallel to the principal axis.

(iii) A ray of light passing through the optical centre of a lens will emerge without any deviation.

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