## Light Reflection and Refraction

(CHAPTER   10)

(PART 1)

### CONTENT

#### TOPIC

1. INTRODUCTION
2. DIFFRACTION
4. REFLECTION OF LIGHT
5. SPHERICAL MIRRORS
6. TERMS ASSOCIATED WITH SPHERICAL MIRROR
7. IMAGE FORMATION IN SPHERIACL MIRROR
8. MIRROR FORMULA AND MAGNIFICATION
9. TEST FOR PRACTICE

### Introduction:-                                                              Can you see anything in a dark room? Your answer must be no. but when the room is lighted you can see everything. Why is this happening? This is due to the reflection of light.

The phenomenon like twinkling of stars, beautiful colours of rainbow, bending of light by a medium etc are associated with light.

When light ray from sun falls upon any object, it reflects the light rays. Hence we see the object .Likewise we can see through an opaque medium when light pass through it.

When an opaque object comes on the straight line path of light a sharp shadow of that object is formed. This clarifies the straight line motion of light. The straight-line motion of light is usually indicated by ray of light.

#### DIFFRACTION

• When a small opaque object comes on the straight line path of a light ray, then the light ray has a tendency to bend around it. This phenomenon of light is called diffraction.

Ex- bending of light near the windows and doors

• The straight line treatment of light fails to explain this property, hence light is treated as wave.

#### Dual nature of light:-

• Both the wave property and the particle property of light are independently fails to explain different phenomenon of light. That means the particle nature fails to explain phenomenon like diffraction while the particle nature fails to explain phenomenon like reflection and refraction.
• Hence light is treated both as wave and stream of particle. This is called dual nature of light.

When a light ray incident in an opaque object, it reflects from that object. This phenomenon of light is called as reflection of light.

#### REFLECTION OF LIGHT

• There are two laws of Reflection. These are :-
• The angle of incidence is equal to the angle of reflection, i.e ⦟i=⦟r and
• The incident ray, the normal

to the mirror at the point of incidence and the reflected ray, all lie in

the same plane.(see the pic 10.2)

• These laws of reflection are applicable also for spherical surface.
• Properties of images formed by Plane mirror:-
• The image always virtual and erect. The size of the image is
equal to that of the object.
• The image formed is as far behind the mirror
as the object is in front of it.
• Image is laterally inverted.

#### SPHERICAL MIRRORS:-

• The mirrors whose reflecting surfaces are spherical is called a spherical mirror.
• In such mirrors, the reflecting surfaces are considered as part of a sphere.
• The curved surface of a shining spoon could be considered as a curved
mirror. The most commonly used type of curved mirror is the spherical
mirror.
• There are TWO types of spherical mirrors.
• Convex mirror b) Concave mirror CONCAVE MIRROR:-
• The spherical mirror whose reflecting surface is curved, is called a concave mirror.
• In this, the reflecting surface faces towards the center of the sphere.

Ex– inward surface of a shining spoon.

• CONVEX MIRROR:-
• The spherical mirror whose reflecting surface is curved outwards, is called convex mirror.
• In this the reflecting surface faces opposite to the center of the sphere.

Ex-  bulged surface of a shining spoon

Some terms associated with spherical mirror;-

1. Pole(P):-  The center point  of the reflecting surface of a spherical mirror is called its pole. It lies on the surface of the mirror and represented by the letter P.(see pic 10.5)
2. Center of Curvature(C):- The reflecting surface of a spherical mirror is a part of a sphere.The  center of that sphere is called the center of curvature of that spherical mirror.It is a point which is not on the surface of the sphere.The point is denoted by C. (see pic 10.5).In concave mirror “C” is in-front of mirror, where in case of convex mirror the point is behind the mirror.
3. Radius of Curvature(R):- The radius of the sphere of which the
reflecting surface of a spherical mirror forms a part, is called the radius
of curvature of the mirror. It is represented by the letter “R. It is also defined as the line that touches point P and C.

Principal Axis:– The imaginary straight line that passes through the pole(P) and the centre of curvature(C) of a spherical mirror is called the principal axis. The principal axis is normal to the mirror at its pole.

• Focus:–  The definition of focus is different for concave and convex mirror.
• In the concave mirror, all the rays those fall parallel to the principal axis of spherical mirror after reflection(the reflected rays) meet or  intersects in a certain point on the principal axis. This point is called as Principal Focus of the concave mirror.
• In the convex mirror, all the rays those fall parallel to the principal axis after reflection(the reflected rays) appears to come from a certain point on the principal axis. This point is called as Principal  Focus of convex mirror.
1. Focal length:- The distance between the pole (P) and the principal focus (F) is called as focal length. It is denoted by f.

There is a relation between the focal length(f) and radius of curvature(R) in a spherical mirror of small apertures. The relation is

R=2f

i.e radius of curvature is two times of focal length

Image Formation by Spherical Mirrors:-

Some Rules for formation of images in Spherical mirror by ray diagram:-

1. When an extended object, of finite size, placed
in front of a spherical mirror. Each small portion of the extended object acts like a point source.
2. An infinite number of rays originate from each
of these points.
3. To construct the ray diagrams, in order to locate the
image of an object, an arbitrarily large number of rays emanating from a point consider.
4.  For the sake of clarity of the ray diagram, generally we consider only two rays.
5. Intersection of at least two reflected rays gives the position of image of the object.

Some Golden Rules :-

If ray parallel to principal axis falls on the reflecting surface of a concave mirror, after reflection, the reflected ray will pass through the focus. But in case of convex mirror the reflected rays seems to diverge or come out from the focus.(see pic. 10.8)

ii. When a ray pass through the principal focus of concave mirror or a ray which is directed towards the principal focus of convex mirror, after reflection, will emerge parallel to the principal axis.(see pic 10.9)

iii. A ray pass through the centre of curvature of a concave mirror or directed towards the centre of curvature of a convex mirror, after reflection, will reflected back along the same path.(see pic 10.10)

iv. If a ray falls obliquely (means making some angle) to the principal axis, towards the point P(i.e pole of the mirror) of a concave or a convex mirror, it will be reflected obliquely(as the same angle of incidence). (see pic 10.11)

Understanding image formation in spherical mirrors:-

1. In Concave Mirror:-There are six cases for formation of image in a concave mirror .These are noted below.

Case 1 :-

Position of the object at infinity (see pic 10.12 a)

• always parallel rays comes from a object at infinity. As per golden rule (i) the reflected rays pass through the focus as seen in pic 10.12.
• hence the position of image is at focus as the two reflected rays meet each other at that point.

The size of the image is “highly diminished or point size and nature of the        image is “Real and inverted”.

Case 2:-

Position of the objectnear the Centre of Curvature (C) (see pic 10.12 b)

We are free to choose any two rays to construct the ray diagrams. But for making it easy We always take an incident ray parallel to the principal axis and another incident ray passes through the nearest point of the object (among the points C,F,P).

•   Hence, by drawing the ray diagram we get the position of the image is “between F and C” and nature of the image is “real and inverted.” And the size of the image is diminished.

Case 3:- (see pic 10.12 c)

Position of the objectat the centre of curvature or C

Position of the image at C

Nature of the image real and inverted

size of the image same as the object

Case 4:- (see pic 10.12 d)

Position of the objectbetween C and F

Position of the image beyond C

Nature of the image – real and inverted

size of the image enlarged

Case 5:- (see pic 10.12 e)

Position of the objectat principal focus F

Position of the image – at infinity

Nature of the image-  real and inverted

size of the image- highly enlarged

Case 6:- (see pic 10.12 f)

Position of the object- between P and F

Position of the image- behind the mirror

Nature of the image- virtual and erect

size of the image–  enlarged

B) In convex mirror :-

• In case of convex mirror there are only two positions of object. Because there is no known point at the left side of pole of a convex mirror.

Case 1 :-[pic 10.13 a]

Position of the object at infinity

Position of the image- at focus F behind the mirror

Nature of the image- virtual and erect

size of the image–  highly diminished or point sized

Case 2 :-

Position of the object between infinity and pole P

Position of the image- between P and F behind the mirror

Nature of the image- virtual and erect

size of the image- diminished

Uses of  Spherical Mirror:-

1. Use of concave mirror-Commonly used in torches, search-lights and as the vehicles head light to get powerful parallel beams. Also used as shaving mirror to see a large image of the face.Dentists use concave mirror to see the large image of the teeth of the patients. Large concave mirrors are also used to concentrate sunlight to produce heat in solar furnaces.
2. Use of convex mirror-Convex mirrors are commonly used as rear-view (wing) mirrors in vehicles. These mirrors are fitted on the sides of the vehicle, enabling the used to see traffic behind the driver to facilitate safe driving. Convex mirrors are preferred because they
always give an erect, though diminished, image. Also, they have a wider field of view as they are curved outwards. Thus, convex mirrors enable the driver to view much larger area than would be possible with a plane mirror.

Sign convention for reflection in spherical mirror :

New Cartesian sign convention:

• The set of sign convention followed during dealing with reflection in spherical mirror is called New Cartesian sign convention.

According to this system pole (P) of the mirror is taken as origin.

• The principal axis is taken as X  axis. The conventions for this are –
• The object is always placed at the left hand side of the mirror so that light from object falls on the left side of the mirror.
• All The distance parallel to the principal axis are measured from pole.
• All the distance measured to the right of the origin (i.e pole P) are taken as +ve(positive) and the distance measured to the left of the pole is taken as –ve (negative).

Ex (from pic 10.14)- the sign of distance of AB and A’B’ from the mirror is taken as -ve as they are in the left side of the pole.

• Distance measured perpendicular to and above the principal axis are taken as +ve.

Ex (from pic 10.14) – the sign of AB is taken as +ve. i.e “+AB”

• Distance measured perpendicular to and below the principal axis is taken as –ve.

Ex (from pic 10.14)- the sign of A’B’ is taken as negative

(-ve) i.e “ -A’B’ ”

MIRROR FORMULA AND MAGNIFICATION :

Mirror Formula ;

The relation between the object distance (u), image distance (v) and focal length (f) of a spherical mirror is called as the mirror formula.

Mathematically,

• Focal length of concave mirror is always taken as –ve (as it is in-front of the reflecting surface) and focal length of the convex mirror is taken as +ve (as it is behind the reflecting surface).

Magnification :

The relative extent to which the image of an object is magnified with respect to the object size in a spherical mirror is called as magnification produced by a spherical mirror.

• Generally, it is expressed as the ratio of height of image to the height of object. It is usually represented by the letter “m”.
• If “h” is the height of the object and “ h’ ” is the height of the image, then the magnification m produced by a spherical mirror is given by
• Magnification can be expressed in the terms of object distance (u) and image distance (v).mathematically,
• Hence, magnification (m) =
• The height of the object is taken as +ve as it is above the principal axis.
• The height of image is taken as –ve for real image (as real image is always inverted) while it is taken as +ve for virtual image (as virtual image is always erect).
• If the value of “m” is –ve then the image is real. But if the value of “m” is +ve then the image is virtual.
• Magnification has no unit as it is a proportion of same physical quantity that is height.

Categories: General 