Ray Optics

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😊....End of the Chapter….😊

                       
                            Ray  Optics 

INTRO

            In this chapter we learn about different natural phenomena which is due to the ray nature of light like Reflection, Refraction etc. As we know that we are able to see each things due to light and one of the nature of light is its ray nature which we see in this chapter.

LIGHT

                 Light is a form of energy which enables a person to see an objects.

RAY AND BEAM OF LIGHT

                                          The direction or path along which, light energy travels in a medium is called a ray of light. It is represented by a straight line on which arrow is marked.

Beam of light is group of rays of light.

                                                       

OBJECT
             Object is any matter which has identifiable boundary. In optics the ray of light is emerging from the objects as a convention to form there image.

TYPE OF OBJECTS

                                    On the basis of emission of Light the objects are of two types

a)  Luminous object 

                            The objects which emits there own light is called luminous object.

For Example.   Sun, Stars, Oil lamps, Candle etc.

b)  Non- Luminous object

                                       The object which do not emit there own light but become visible due to reflection of light falling on them are called non-luminous objects.

For example.     Earth, Moon, Chair, Table, Wood etc.

REFLECTION OF LIGHT

                                                When a ray of light after incidenting on a boundary separating two mediums come back into same medium then this phenomenon is called reflection of light.

LAWS OF REFLECTION

                                                 There are two laws of reflections

1.      The incident ray, reflected ray and the normal at the point of incident all three lie in the same plane.

2.      The incident angle and reflected angle are always equal.

TYPES OF REFLECTION

                                      There are two types of reflection on the basis of reflection plane.

1.  Regular reflection

                              If the reflecting surface is smooth then parallel coming incident rays also go back parallel to each other this type of reflection is called regular reflection.

2.  Irregular reflection

                              If reflecting surface is not smooth then parallel coming incident ray go back non parallel to each other this type of reflection is called irregular reflection.

IMAGE

            After reflection, refraction or diffraction when ray of light meet or seems to meet at a place then at that place an apparent reproduction of object is form which is called image.

TYPES OF IMAGE

                                    There are two types of image are there.

1. Real image

                  The image which is form due real meeting of ray of light after reflection, refraction or diffraction that image is called real image.

2. Virtual image

                     The image which from due to non real ( not really meet but seems to meet ) meeting of ray of light after reflection, refraction or diffraction that image is called virtual image.

MIRROR

                 If a smooth glass is polished in one side so that its other side get reflecting surface then that is called mirrors.

TYPES OF MIRROR

                                        The mirror are of different types but there are three main types of mirror in use.

1)  Plane mirror

                       Plane mirror is a mirror with flat reflecting surface.

2)  Spherical mirrors

                             If a part of glass cut from a spherical glass and mirror is formed the that mirror is called spherical mirror.

There are two type of spherical mirrors are there

a)  Concave spherical mirror

                                          The mirror which is cut from a sphere and polished on outer side so that reflecting surface appears at inside part that mirror is called concave spherical mirror.

It is also called converging mirror because it converge the light.

b)  Convex spherical mirror

                                         The mirror which is cut from a sphere and polished on inner side so that reflecting surface appears at outer part of the mirror that mirror is called convex spherical mirror. It is also called diverging mirror because it diverges the parallel coming rays.

3)  Parabolic mirrors

                                The parabolic mirror is like a parabola in the shape.

REFLECTION THROUGH PLANE MIRROR

                                                                                     The plane mirror is a smooth surface mirror so all the rays which strike to the mirror at an angle that go back to same angle after reflection.

IMAGE FORMATION BY PLANE MIRROR

                                                                                  The rays after reflection through plane mirror can never meet because of the smoothness of surface that’s why the plane mirror form image of following nature.

1) Image is always virtual.

2) Image is always erect.

3) Image is always form behind the mirror.

4) The size of image is always equal to the size of object.

5) The distance of image from mirror is always equal to the distance of object from mirror. That is the distance of object and image both are equal from the mirror.

TERMS RELATED TO SPHERICAL MIRRORS

1)  Centre of curvature

                                  The centre of sphere from which mirror is cut is called centere of curvature of the mirror. It represented by C.

2)  Radius of curvature

                               The radius of sphere from which mirror is cut is called the radius of curvature of the mirror. It represented by R.

3)  Pole

         The mid point of mirror is called the pole of the mirror.

4)  Principle axis

                    A straight line passing through the pole and centre of curvature of the mirror is called the principle axis.

5)  Focus

          The point at which paraxial rays ( that is rays parallel to principle axis and also close to principle axis ) meet after the reflection through mirror is called focus ( this definition is for concave mirror )

The point at which paraxial rays ( that is rays parallel to principle axis and also close to principle axis ) seems to emerging after reflection through mirror is called focus ( this definition is for convex mirror)

                                                                    OR

The point at which paraxial rays meet or seem as emerging after reflection through mirror is called focus of the mirror. It is represented by F.

6)  Focal length

                      The distance between focus and pole is called focal length. It is represented by f.

7)  Aperture

                   The effective Diameter of mirror is called the Aperture.

8)  Focal plane

                   A imaginary plane which passing through focus and perpendicular to principle axis is called focal plane.

REFLECTION THROUGH SPHERICAL MIRROR

                                                                                            The spherical mirror has a curve surface so when light fall on it some time it converges (in concave mirrors) , some time id diverges ( in convex mirror ) , and some times it go back to same path after reflection through spherical mirrors.

IMAGE FORMATION BY SPHERICAL MIRROR

                                                                                       The image formation in spherical mirrors is done by following rules which are also derived from basic reflection law ( incident angle = reflecting angle ). There are three basic rules are derived for the image formation in spherical mirrors.

RULES OF IMAGE FORMATION BY SPHERICAL MIRRORS

1) The rays which comes parallel to principle axis is always passes through focus after reflection.

2) The ray which come through focus is get parallel to principle axis after reflection.

3) The ray which come to centre of curvature is go back to same path after reflection.

IMAGE FORMATION BY CONCAVE MIRROR

a)  When object is at infinite ( at very large distance ).

Nature of image

Ø   Image is real

Ø  Image is like a point.

Ø  Image is formed at focus.

b)  When object is beyond the Centre of curvature .

Nature of image

Ø  Image is real.

Ø  Image is inverted.

Ø  Image is smaller than object.

Ø  Image is formed between focus and Centre.

c)  When object is present at Centre.

Nature of image

Ø  Image is real.

Ø  Image is Inverted.

Ø  Image is of same size of object.

Ø  Image is formed at the Centre.

d)   When object is in between focus and Centre.

Nature of image

Ø  Image is real.

Ø  Image is Inverted.

Ø  Image is larger than object.

Ø  Image is beyond the Centre.

e)  When object is present at focus.

Nature of image

Ø  Image is formed at infinite.

Ø  Image is very larger than object.

f)   When object is in between focus and pole.

Nature of image

Ø  Image is virtual.

Ø  Image is erect.

Ø  Image is larger than object.

Ø  Image is formed behind the mirror.

IMAGE FORMATION BY CONVEX MIRROR

                                                                                   Since in convex mirror there is no focus and Centre at the side of object that’s why all condition is same in the case of convex mirror.

Nature of image

Ø  Always virtual.

Ø  Always smaller than object.

Ø  Always erect.

RELATION BETWEEN FOCAL LENGTH AND RADIUS OF CURVATURE

R = 2 f

Proof

As shown in figure

Let a ray passes parallel to principal axis then it go through focus

SA = Incident ray

CA = Normal to concave mirror

AF = Reflected ray

CP = Principal axis

By the law of reflection

       Angle        i = r = Ɵ

Since SA is parallel to CP

So

       Angle  SAC = ACF = Ɵ

   

In Tringle ACF

               Angle     AFB is an exterior angle

So

      AFB = ACF + CAF

      AFB = Ɵ + Ɵ

      AFB = 2 Ɵ

In triangle ABC

  

    ( CB  = CP ) Approx

     ( For small Ɵ   tanƟ =  Ɵ )  ………………………………(i)

In tringle AFB

 

 ( Approx  FB = FP )

    ( For small Ɵ  tan2Ɵ = 2Ɵ ) ……………………….(ii)

From  (i) and (ii)
CP = 2 FP
R  = 2 f    ( CP = R  and FP = f )

MIRROR FORMULA

 

Proof

MAGNIFICATION