Introduction

•Light is a form of  energy. Light needed to see things around us.

•Light enables us to see objects from which it comes or from which it is reflected.

•There are a number of common wonderful phenomena associated with light such as image formation by mirrors, the twinkling of stars, the beautiful colors of a rainbow, bending of light by a medium and so on. A study of the properties of light helps us to explore them.

•By observing the common optical phenomena around us, we may conclude that light seems to travel in straight lines. The fact that a small source of light casts a sharp shadow of an opaque object points to this straight-line path of light, usually indicated as a ray of light.

Laws of Reflection

Regular and irregular Reflection

Object and Image

• Object: Anything which gives out light rays (either its own or reflected by it ) is called an object.
• Image : It is an optical appearance produced when light rays coming from an object are reflected from a mirror (or refracted through a lens).

Real and Virtual Image

Real Image

1.A real image is formed due to the actual intersection of the reflected rays.

2.A real image can be obtained on a screen.

3. A real image is inverted with respected to the object

Virtual Image

1.A virtual image is formed when the reflected rays appear to meet when produced backwards.

2.A virtual image can not be obtained on a screen.

3.A virtual image is erect with respect to the object.

Formation of image in a Plane Mirror

Characteristics of the image formed by a Plane mirror

• Nature -Virtual & Erect
• Size – same size as the object
• Position – Same distance behind the mirror as the object in the front it
• Laterally inverted

When an object is placed in front of a plane mirror, then the right side of object appears to become the left side of the image; and the left side of object appears to become the right side of the image. This change of sides of an object and its mirror image is called lateral inversion.

Spherical Mirror

A reflecting surface which is a part of a sphere is called a spherical mirror.

Types of Spherical Mirror

• Concave Mirror: The concave mirror is made by silvering the outer (or bulging) surface of the piece of a hollow sphere such that the reflection takes place from the hollow (or concave) surface.
• Convex Mirror: The convex mirror is made by silvering the inner surface of the piece of a hollow sphere such that the reflection takes place from the outer (or bulging) surface.

Terms related to Spherical Mirror

• Centre of Curvature: The centre of curvature of a mirror is the centre of the sphere of which the mirror is a part of.
• Radius of Curvature:  The radius of sphere of which the spherical mirror is a part, is called the radius of curvature of the mirror.
• Principle axis: It is the straight line joining the pole of the mirror to its centre of curvature.
• Aperture: The portion of the mirror from which the reflection of light actually takes place is called the aperture of the mirror.
• Pole:The geometric centre of the spherical surface of the mirror is called the pole of the mirror.

Principal Focus and Focal length of a Concave Mirror

• The Principle focus of a concave mirror is a point on its principle axis to which all the light rays which are parallel and close to the axis, converge after reflection from the concave mirror.
• A concave mirror has a real focus.
• Since a concave mirror converges a parallel beam of light rays, it is called a converging mirror.
• The focal length of a concave mirror is the distance between its pole and principal focus.

Principal Focus and Focal length of a Convex Mirror

• The focus of a convex mirror is a point on the principal axis from which, the light rays incident parallel to the principal axis, appears to come, after reflection from the mirror.
• A convex mirror has a virtual focus.
• Since a convex mirror diverges a parallel beam of light rays, it is called a diverging mirror.
• The focal length of a convex mirror is the distance between its pole and principal focus.

Rules for obtaining images formed by Concave mirror

• A ray of light which is parallel to principal axis always pass through focus (meet at focus) or vice-versa.

• A ray of light passing through the focus of concave mirror becomes parallel to the principal axis after reflection.

A ray of light passing through the centre of curvature of a concave mirror is reflected back along the same path.

• A ray of light which is incident at the pole of a concave mirror is reflected back making the same angle with the principal axis.

Formation of Images by a Concave mirror

Case 1: When object is at infinity

Characteristics of image;

Nature of the image: real and inverted

Position of the image: at focus

Size of the image: Highly diminished

Case 2: When object is placed beyond centre of curvature

Characteristics of image;

Nature of the image: real and inverted

Position of the image: between F & C

Size of the image: Diminished

Case 3: When object is at centre of curvature

Characteristics of image;

Nature of the image: real and inverted

Position of the image: at C

Size of the image: Same size as object

Case 4: When object is between F & C

Characteristics of image;

Nature of the image: real and inverted

Position of the image: Beyond C

Size of the image: Enlarged

Case 5: When object is at Focus

Characteristics of image;

Nature of the image: real and inverted

Position of the image: at infinity

Size of the image: Enlarged

Case 6: When object is between Pole and Focus

Characteristics of image;

Nature of the image: virtual and erect

Position of the image: behind the mirror

Size of the image: Enlarged

Image formation by a concave mirror for different positions of the object

Uses of concave mirror

• Concave mirrors are used as a shaving mirrors to see a large image of the face.
• Concave mirrors are used by dentist to see the large images of the teeth of patients.
• Concave mirrors are used as reflectors in torches, vehicle head-lights and search lights to get powerful beams of light.
• Concave mirrors are used as doctor’s head-mirrors to focus light coming from a lamp on to the body parts of a patient (such as eye, ear, nose, throat, etc.) to be examined by the doctor.
• Concave dishes are used in TV dish antennas to receive TV signals from the distant communications satellites.
• Large concave mirrors are used in the field of solar energy to focus sun’s rays for heating solar furnaces.

Rules for obtaining images formed by Convex mirror

• A ray of light which is parallel to the principal axis of a convex mirror, appears to be coming from its focus after reflection from the mirror.

• A ray of light going towards the centre of curvature of a convex mirror is reflected back along the same path.

• A ray of light going towards the focus of a convex mirror becomes parallel to the principal axis after reflection.

• A ray of light which is incident at the pole of a convex mirror is reflected back making the same angle with principal axis.

Formation of Images by a Convex mirror

Case 1. When the object is at infinity

Characteristics of image;

Nature of the image: virtual and erect

Position of the image: At the focus F, behind the mirror

Size of the image: Diminished

Case2. Object is anywhere between P and infinity

Characteristics of image;

Nature of the image: virtual and erect

Position of the image: Between P and F, behind the mirror

Size of the image: Diminished

Image formation by a convex mirror for different positions of the object

Uses of concave 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 driver to see traffic behind him/her 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.
• Big convex mirrors are used as ‘shop security mirrors’

Sign Convention for reflection by Spherical mirror

According to the New Cartesian Sign Convention:

• All the distances are measured from pole of the mirror as origin.
• Distances measured in the same direction as that of incident light are taken as positive.
• Distances measured against the direction of incident light are taken as negative.
• Distances measured upward and perpendicular to the principal axis are as positive.
• Disatnces measured downward and perpendicular to the principal axis are taken as negative.
• The object is always placed on the left side of the mirror so that the direction of incident light is from left to right.

Mirror Formula

In a spherical mirror,

• the distance of the object from its pole is called the object distance (u).
• The distance of the image from the pole of the mirror is called the image distance (v).
• The distance of the principal focus from the pole is called the focal length (f).

There is a relationship between these three quantities given by the mirror formula which is expressed as

Magnification

• It is expressed as the ratio of the height of the image to the height of the
  object.
• It is usually represented by the letter m.

The magnification m is also related to the object distance (u) and
image distance (v). It can be expressed as:

Note

• A negative sign in the value of the magnification indicates that the image is real.
• A positive sign in the value of the magnification indicates that the image is virtual.

Refraction of Light

 The change in the direction of light when it passes from one medium to another obliquely, is called refraction of light.

• A medium in which the speed of light is more is known as optically rarer medium.
• A medium in which the speed of light is less, is known as optically rarer medium.

• When a ray light travels from a rarer medium to a denser medium, it bends towards the normal.

• When a ray of light travels from a denser medium to a rarer medium, it bends away from normal.

• The ray of light incident normally on the surface separating the two media, passes undeviated (i.e., such a ray suffers no bending at the surface).

Causes of refraction (or cause of change in direction)

When a ray of light passes from one medium to another medium, its direction (or path) changes because of change in speed of light in going from one medium to another. In passing from one medium to other, if light slows down, it bends towards the normal and if light speeds up, it bends aways from the normal .

Refraction through a rectangular glass slab

• PQRS is a rectangular glass slab. A light ray AO falls on the surface PQ. NOM is the normal to the surface PQ at the point of incidence O.
• At the surface PQ, the ray AO enters from air (rarer medium) to glass (denser medium), so it slows down and bends towards the normal NOM.
• It travels inside glass in a straight path along OB.
• At the surface RS, the ray OB suffers another refraction.
• N₁BM₁ is the normal to the surface RS at the point of incidence B.
• The ray OB now enters from glass (denser medium) to air (rarer medium), so it speeds up and bends away from the normal N₁BM₁.
• It travels along BC in air.
• The ray AO is called the incident ray, OB the refracted ray and BC the emergent ray.
• The ∠AON is the angle of incidence i, the ∠BOM is the angle of refraction r and the ∠CBM₁ is the angle of emergence e.
• Since refraction occurs at two parallel surfaces PQ and RS, therefore, ∠MOB = ∠N₁BO and ∠i = ∠e i.e., the angle of incidence i is equal to the angle of emergence e by the principle of reversibility of the path of a light ray.
• Thus, the emergent ray BC is parallel to the incident ray AO
  

Lateral displacement

The perpendicular distance between the original path of incident ray and the emergent ray coming out of the glass slab is called lateral displacement.

Laws of Refraction

• 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.
• 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. (This is true for angle 0 < i < $90^0$)

• This constant value is called the refractive index of the second medium with respect to the first.

Refractive Index and speed of light

• The extent of the change in direction of light that takes place in a given pair of media may be expressed in terms of the refractive index.
• The refractive index can also be written as the ratio of speed of light in two media.
• Let v₁ be the speed of light in medium 1 and v₂ be the speed of light in medium 2. 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.

• The refractive index of medium 1 with respect to medium 2 is represented as n₁₂.It is given by

• If medium 1 is vacuum or air, then the refractive index of medium 2 is considered with respect to vacuum. This is called the absolute refractive index of the medium. It is simply represented as n₂

• If c is the speed of light in air and v is the speed of light in the medium, then, the refractive index of the medium n_m is given by

• The absolute refractive index of a medium is simply called its refractive index.

Refraction by Spherical lenses

• The working of a lens is based on the refraction of light rays when they pass through it.
• A lens is a piece of transparent glass bound by two spherical surfaces.

There are two types of lenses: Convex lens and concave lens

• A convex lens is thick at the centre but thinner at the edges.

• A concave lens is thin at the middle but thicker at the edges.

Terms related to Lens

• Optical centre: The centre point of lens is known as its optical centre.
• Principal axis: The principal axis of a lens is a line passing through the optical centre of the lens and perpendicular to both the faces of the lens.

Principal focus and Focal length of a convex lens

• The principal focus of a convex lens is a point on its principal axis to which light rays parallel to the principal axis converge after passing through the lens.
• The focal length of a lens is the distance between optical centre and principal focus of the lens.

Principal focus and Focal length of a convex lens

The principal focus of a concave lens is a point on its principal axis from which light rays, originally parallel to the axis, appear to diverge after passing through the concave lens.

Rule for obtaining images formed by a convex lenses

• A ray of light which is parallel to the principal axis of a convex lens, passes through its focus after refraction through the lens.

• A ray of light passing through the optical centre of a convex lens goes straight after refraction through the lens.

• A ray of light passing through the focus of a convex lens becomes parallel to its principal axis after refraction through the lens.

Formation of different types of images by a convex lens

• Case 1: When object is at infinity

Characteristics of image;

Nature of the image: real and inverted

Position of the image: at focus

Size of the image: Highly diminished

• Case 2: When object is placed beyond 2F’

Characteristics of image;

Nature of the image: real and inverted

Position of the image: between F and 2F

Size of the image: Diminished

• Case 3: When object is at 2F’

Characteristics of image;

Nature of the image: real and inverted

Position of the image: at 2F

Size of the image: Same size as the object

• Case 4: When object is placed between F’ and 2F’

Characteristics of image;

Nature of the image: real and inverted

Position of the image: beyong 2F

Size of the image: Magnified

• Case 5: When object is palced at focus

Characteristics of image;

Nature of the image: real and inverted

Position of the image: at infinity

Size of the image: highly enlarged

• Case 6: When object is placed between optical centre and focus

Characteristics of image;

Nature of the image: Virtual and erect

Position of the image: behind the object (on the left side of lens)

Size of the image: enlarged

Uses of Convex lenses

• Convex lenses are used in spectacles to correct the defect of vision called hypermetropia (or long-sightedness).
• Convex lens is used for making a simple camera.
• Convex lens is used as a magnifying glass (or magnifying lens).
• Convex lenses are used in making microscopes, telescopes, and slide projectors (or film projectors).

Rules for obtainig image formed by Concave Lenses

• A ray of light which is parallel to the principal axis of a concave lens, appears to be coming from its focus after refraction through the lens.

• A ray of light passing hrough the optical centre of a concave lens goes straight after passing through the lens.

• 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 a Concave lens

• Case 1: When object at infinity

Characteristics of image;

Nature of the image: Virtual and erect

Position of the image: at focus

Size of the image: diminished

• Case 2: When object is placed anywhere between between optical centre and infinity

Characteristics of image;

Nature of the image: Virtual and erect

Position of the image: between optical centre and focus

Size of the image: diminished

Uses of Concave lenses

• Concave lenses are used in spectacles to correct the defect of vision called myopia (or short-sightedness).
• Concave lens is used as eye-lens in Galilean telescope.
• Concave lenses are used in combination with convex lenses to make high quality lens system for optical instrument.
• Concave lens is used in wide-angle spyhole in doors.

Sign Convention

According to the New Cartesian Sign Convention:

• All distances are measured from the optical centre of the lens.
• The object is always placed on the left side of the lens.
• The distances measured in the same direction as that of incident light are taken positive.
• The distances measured against the direction of incident light are taken as negative.
• The distances measured upward and perpendicular to the principal axis are taken as positive.
• The distances measured downward and perpendicular to the principal axis are taken as negative.

Lens Formula

Magnification

• It is expressed as the ratio of the height of the image to the height of the
  object.
• It is usually represented by the letter m.

The magnification m is also related to the object distance (u) and
image distance (v). It can be expressed as:

• A negative sign in the value of the magnification indicates that the image is real.
• A positive sign in the value of the magnification indicates that the image is virtual.

Power of a lens

• The power of a lens is a measure of the 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.