0

### Light – Reflection and Refraction

Reflection is one of the unique properties of light. It is the reflection of light, which enables us to see any object.

Reflection: The bouncing back of rays of light from a polished and shiny surface is called reflection or reflection of light. It is similar to bouncing back of a football after colliding with a wall or any hard surface.

Laws of Reflection of light:

• The angle of incidence and angle of reflection is equal.
• The incident ray, reflected ray and normal to the point of reflection lie in the same plane.

The angle of incidence is denoted by ‘i’ and angle of reflection is denoted by ‘r’. The law of reflection is applicable to all types of reflecting surface.

Mirror and Reflection of Light:

Mirror is a shiny polished object (glass) which reflects most of the rays of light falling upon it. One side of mirror is polished with suitable material to make the other side reflective.

Types of Image formed by mirrors:

Real Image: Image which is formed in front of the mirror and it can be obtained on a screen is called real image.

Virtual Image: Image which is formed behind the mirror and cannot be obtained on a screen is called virtual image.

##### Types of Mirror:

Plain Mirror: A mirror having a flat surface is called plane mirror.

Formation of image in plane mirror:

Fig: Image formation in plain mirror

• A plane mirror always forms virtual and erect image.
• The distance of image and that of object is equal from the mirror.
• The image formed by a plane mirror is laterally inverted.

Spherical Mirror
Mirrors having curved reflecting surface are called spherical mirrors. A spherical mirror is a part of a sphere.

Types of Spherical Mirror:
Concave Mirror: Spherical mirror with reflecting surface curved inwards is called concave mirror.
Convex Mirror: Spherical mirror with reflecting surface curved outwards is called convex mirror.

Important terms in the case of spherical mirror:

Fig: Concave Mirror

Pole: The centre of reflecting surface of a spherical mirror is known as Pole. Pole lies on the surface of spherical mirror. Pole is generally represented by ‘P’.

Centre of Curvature: The centre of sphere; of which the reflecting surface of a spherical mirror is a part; is called the centre of curvature of the spherical mirror. Centre of curvature is not a part of spherical mirror rather it lies outside the mirror. Centre of curvature is denoted by letter ‘C’.
In the case of concave mirror centre of curvature lies in front of the reflecting surface. On the other hand, centre of curvature lies behind the reflecting surface in the case of convex mirror.

Fig: Convex Mirror

Radius of Curvature: The radius of sphere; of which the reflecting surface of a spherical mirror is a part; is called the Radius of Curvature of the spherical mirror. The radius of curvature of a spherical mirror is denoted by letter ‘R’.

Similar to centre of curvature, radius of curvature lies in front of concave mirror and lies behind the convex mirror and is not a part of the mirror as it lies outside the mirror.

Aperture: The diameter of reflecting surface of a spherical mirror is called aperture.

Principal Axis: Imaginary line passing through the centre of curvature and pole of a spherical mirror is called the Principal Axis.

Focus or Principal Focus: Point on principal axis at which parallel rays; coming from infinity; converge after reflection is called the Focus or Principal Focus of the spherical mirror. Focus is represented by letter ‘F’.

Fig: Converging Mirror

In the case of a concave mirror, parallel rays; coming from infinity; converge after reflection in front of the mirror. Thus, the focus lies in front of a concave mirror.

Fig: Diverging Mirror

In the case of a convex mirror, parallel rays; coming from infinity; appear to be diverging from behind the mirror. Thus, the focus lies behind the convex mirror.

Focal length: The distance from pole to focus is called focal length. Focal length is denoted by letter ‘f’. Focal length is equal to half of the radius of curvature.

##### Reflection from spherical mirror:

Reflection of Rays parallel to Principal Axis:

In the case of concave mirror:  A Ray parallel to principal axis passes through the principal focus after reflection from a concave mirror.

Fig: Rays parallel to principal axis

Similarly, all parallel rays to the principal axis pass through the principal focus after reflection from a concave mirror. Since, a concave mirror converge the parallel rays after reflection, thus a concave mirror is also known as converging mirror.

In the case of convex mirror: A ray parallel to principal axis appears to diverge from the principal focus after reflecting from the surface of a convex mirror.

Fig: Rays parallel to principal axis

Similarly, all rays parallel to the principal axis of a convex mirror appear to diverge or coming from principal focus after reflection from a convex mirror. Since, a convex mirror diverges the parallel rays after reflection, thus it is also known as diverging mirror.

##### Reflection of ray passing through the Principal Focus:

In the case of concave mirror: Ray passing through the principal focus goes parallel to principal axis after reflection in the case of concave mirror.

Fig: Ray passing through principal focus

In the case of convex mirror: A ray directed towards principal focus goes parallel to principal axis after reflecting from the surface of a convex mirror.

Fig: Ray through principal focus

##### Ray passing through the Centre of curvature:

In the case of concave mirror: Ray passing through the centre of curvature returns at the same path after reflecting from the surface of a concave mirror.

Fig: Ray passing through C

In the case of convex mirror: Ray appears to passing through or directed towards the centre of curvature goes parallel to the principal axis after reflecting from the surface of a convex mirror.

Fig: Ray passing through C

Ray incident obliquely to the principal axis: Ray obliquely to the principal axis goes obliquely after reflecting from the pole of the both concave and convex mirror and at the same angle.

Fig: Ray passing obliquely to principal axis

##### Image Formation by Concave Mirror

Formation of image depends upon the position of the object. There are six possibilities of the position of object in the case of concave mirror.

1. Object at infinity
2. Object between infinity and centre of curvature (C)
3. Object at centre of curvature (C)
4. Object between centre of curvature (C) and Principal focus (F)
5. Object at Principal Focus (F)
6. Object between Principal Focus (F) and Pole (P)

Object at infinity:
Since parallel rays coming from the object converge at principal focus, F of a concave mirror; after reflection. Hence, when the object is at infinity the image will form at F.

Fig: Object at Infinity

Properties of image:

• Point sized
• Highly diminished
• Real and inverted

Object between infinity and Centre of Curvature:
When object is placed between infinity and centre of curvature of a concave mirror the image is formed between centre of curvature (C) and focus (F).

Fig: Object Between Infinity and C

Properties of image:

• Diminished compared to object
• Real and inverted

Object at Centre of Curvature (C):
When the object is placed at centre of curvature (C) of a concave mirror, a real and inverted image is formed at the same position.

Fig: Object at C

Properties of image:

• Same size as object
• Real and inverted

Object between Centre of curvature (C) and Principal Focus (F):
When the object is placed between centre of curvature and principal focus of concave mirror, a real image is formed beyond the centre of curvature (C).

Fig: Object between C and F

Properties of image:

• Larger than object
• Real and inverted

Object at Principal Focus (F):
When the object is placed at principal focus (F) of a concave mirror, a highly enlarged image is formed at infinity.

Fig: Object at F

Properties of image:

• Highly enlarged
• Real and inverted

Object between Principal Focus (F) and Pole (P):

When the object is placed between principal focus and pole of a concave mirror, an enlarged, virtual and erect image is formed behind the mirror.

Fig: Object between F and P

Properties of image:

• Enlarged
• Virtual and erect
 Positions of Object and Image in Concave Mirror Position of Object Position of Image Size of Image Nature of Image At infinity At focus Point sized, highly diminished Real and inverted Between infinity and C Between F and C Dminished Real and inverted At C At C Same size Real and inverted Between C and F Beyond C Enlarged Real and inverted At F At infinity Highly enlarged Real and inverted Between F and P Behind mirror Enlarged Virtual and erect

##### Image Formation by Convex Mirror

There are only two possibilities of position of object in the case of a convex mirror, i.e. object at infinity and object between infinity and pole of a convex mirror.

Object at infinity: When the object is at the infinity, a point sized image is formed at principal focus behind the convex mirror.

Fig: Object at infinity

Properties of image: Image is highly diminished, virtual and erect.

Object between infinity and pole: When the object is between infinity and pole of a convex mirror, a diminished, virtual and erect image is formed between pole and focus behind the mirror.

Fig: Object between infinity and P

Properties of image: Image is diminished, virtual and erect.

 Positions and Nature of Image in Convex Mirror Position of Object Position of Image Size of Image Nature of Image At infinity At F, behind mirror Highly diminished Virtual and erect Between infinity and P Between F and P, behind mirror Diminished Virtual and erect

• As reflector in electric torch, head lights of vehicle, search light, etc. The source of light is put at the focus of the reflector, which produces a strong parallel beam of light, which helps in clear visibility.
• As shaving mirror to produce larger image of face to facilitate better viewing during shaving.
• Concave mirror is used by dentists to see larger image of teeth of the patient. When a tooth is placed between focus and pole, the concave mirror produces a magnified image of the tooth.
• As reflector in solar furnace. By using concave mirror in solar furnace the concentrated rays of sunlight is obtained at focus which produces enormous amount of heat because of concentration.

Uses of Convex Mirror:

• Convex mirror is used in rear view mirror of vehicles; so that the driver can see the traffic coming from behind. The field of view is widest in case of a convex mirror, which enables it to show a wider area from behind.
• Convex mirror is used on hairpin bends on the road; so that the driver can see the traffic approaching from another side of the bend.
##### Sign Convention for Spherical Mirror:

Cartesian Sign Convention: In the case of spherical mirror all signs are taken from Pole of the spherical mirror, which is often called origin or origin point. This sign convention is known as New Cartesian Sign Convention.

Sign is taken as – (negative) from pole of a spherical mirror towards object along the principal axis. This means sign is always taken as – (negative) in front of a spherical mirror. For example; the distance of object is always taken as – (negative) in case of both types of spherical mirror, i.e. concave and convex mirrors.

• Sign is taken as + (positive) behind the spherical mirror. For example if an image is formed behind the mirror, the distance of image is taken as + (positive) from pole along the principal axis.
• The height of is taken as + (positive) above the principal axis and taken as – (negative) below the principal axis.

• Since, object is always placed in front of the mirror hence the sign of object is taken as negative.
• Since, the centre of curvature and focus lie in front of the concave mirror, so signs of radius of curvature and focal length are taken as negative in the case of concave mirror.
• When image is formed in front of the mirror, the distance of image is taken as – (negative) and when image is formed behind the mirror, the distance of image is taken as + (positive).
• Height of image is taken as positive in the case of erect image and taken as negative in the case of inverted image.

• Since, object is always placed in front of the mirror hence the sign of object is taken as negative.
• Since, the centre of curvature and focus lies behind the convex mirror, so sign of radius of curvature and focal length are taken as + (positive) in the case of convex mirror.
• In the case of convex mirror, image always formed behind the mirror, thus the distance of image is taken as positive.
• In the case of a convex mirror, always an erect image is formed, thus the height of image is taken as positive.

Mirror Formula:
Mirror formula shows the relation among distance of object, distance of image and focal length in case of spherical mirror. All distances are measured from pole of the mirror.

The distance of object is denoted by ‘u’
The distance of image is denoted by ‘v’
Focal length is denoted by f

By knowing any two, the third can be calculated using the mirror formula.

Magnification:

Magnification is the relative ratio of size of image formed by a spherical mirror to the size of object. Magnification is generally denoted by letter ‘m’.

Relation among magnification, distance of object and distance of image:

Where; m = magnification, h’ = height of image, h = height of object, v = image distance and u = object distance.

##### Refraction: Introduction

The change of direction of light because of change of medium is known as Refraction or Refraction of Light. The ray of light changes its direction or phenomenon of refraction takes place because of difference in speed in different media.

The light travels at faster speed in rare medium and at slower speed in denser medium. The nature of media is taken as relative. For example air is a rarer medium than water or glass.

When ray of light enters from a rarer medium into a denser medium, it bends towards normal at the point of incidence. On the contrary, when ray of light enters into a rarer medium from a denser medium it bends away from the normal.

Ray emerging after the denser medium goes in the same direction and parallel to the incident ray.

The angle between incident ray and normal is called Angle of Incidence and it is denoted as ‘i’. The angle between refracted ray and normal is called the Angle of Refraction. Angle of refraction is denoted by ‘r’.

Fig: Refraction of Light

Laws of Refraction:

1. The incident ray, refracted ray and normal to the interface of given two transparent media, all lie in same plane.
2. The ratio of sine of angle of incidence and sine of angle of refraction is always constant for the light of given colour and for the pair of given media.

The Second Law of Refraction is also known as Snell’s Law of Refraction.

The constant is called refractive index of the second medium in relation to the first medium. Refractive Index:

A ray of light changes its direction when it enters from one medium to another medium. This happens because speed of light is different in different media. For example; the speed of light is 3 x 108 m/s (2.99×108 m/s) in vacuum and it is 2.98 x 108 m/s in air.
Refractive Index is the extent of change of direction of light in a given pair of media. The refractive index is a relative value of speed of light in the given pair of media. Thus, to calculate the refractive Index the speed of light in two media is taken.

Let the speed of light in medium 1 is v1 and in medium 2 is v2
Therefore; refractive index of medium 2 with respect to medium 1 (n21)

Above expression gives the refractive index of medium 2 with respect to medium 1. This is generally denoted by n21.

Similarly, the refractive index of medium 1 with respect to medium 2 is denoted by n12.

Absolute Refractive Index:When one medium is taken as vacuum and speed of light is taken in it, then the refractive index of second medium with respect to vacuum is called Absolute Refractive Index and it is generally denoted by n2.

The speed of light in vacuum is slightly faster than in air. Let speed of light in air is ‘c’ and the speed of light in given medium is ‘v’. Therefore, refractive index of the given medium:

Since, Refractive Index is the relative value of the speed of light of a medium with respect to the speed of light in vacuum, thus light will travel faster in the medium having lower value of refractive index.

Optical Density: Medium having greater value of refractive index is called optically denser medium, this means light will travel at slower speed in optically denser medium compared to in an optically rarer medium.

##### Spherical Lens

Lens is an optical device which converges or diverges the rays of light before transmitting. A lens has similar shape to lentils and genus of lentil is called Lens, thus a lens got its name after the shape and name of genus of lentils. A lens is made by combining at least one part of sphere made of transparent material, generally glass.

Spherical Lens: Most of the lenses are made by the combination of parts of transparent sphere. Concave and Convex lens are most commonly use spherical lens.
Convex lens is the most commonly used lens in our day to day life.

Convex lens:
A lens having two spherical surface bulging outwards is called Convex Lens. It is also known as biconvex lens because of two spherical surface bulging outwards.

Fig: Spherical Lens

Concave lens:

A lens having two spherical surface bulging inwards is called Concave Lens. It is also known as biconcave lens because of two spherical surface bulging inwards.

Important terms for spherical lens:

Fig: Convex Lens

Centre of curvature: The centre of sphere of part of which a lens is formed is called the centre of curvature of the lens. Since concave and convex lenses are formed by the combination of two parts of spheres, therefore they have two centres of curvature.

One centre of curvature is usually denoted by C1 and second is denoted by C2.

Focus: Point at which parallel rays of light converge in a concave lens and parallel rays of light diverge from the point is called Focus or Principal Focus of the lens.

Fig: Converging Lens

Fig: Diverging Lens

Similar to centres of curvature; convex and concave lenses have two Foci. These are represented as F1 and F2.

Principal Axis: Imaginary line that passes through the centres of curvature of a lens is called Principal Focus.

Optical centre: The central point of a lens is called its Optical Centre. A ray passes through optical centre of a lens without any deviation.

Radius of curvature: The distance between optical centre and centre of curvature is called the radius of curvature, which is generally denoted by R.

Focal Length: The distance between optical centre and principal focus is called focal length of a lens. Focal length of a lens is half of the radius of curvature.

This is the cause that the centre of curvature is generally denoted by 2F for a lens instead of C.

Focus: Point at which parallel rays of light converge in a concave lens and parallel rays of light diverge from the point is called Focus or Principal Focus of the lens.

Fig: Converging Lens

Fig: Diverging Lens

Similar to centres of curvature; convex and concave lenses have two Foci. These are represented as F1 and F2.

Principal Axis: Imaginary line that passes through the centres of curvature of a lens is called Principal Focus.

Optical centre: The central point of a lens is called its Optical Centre. A ray passes through optical centre of a lens without any deviation.

Radius of curvature: The distance between optical centre and centre of curvature is called the radius of curvature, which is generally denoted by R.

Focal Length: The distance between optical centre and principal focus is called focal length of a lens. Focal length of a lens is half of the radius of curvature.

This is the cause that the centre of curvature is generally denoted by 2F for a lens instead of C.

##### Refraction through Lens

Refraction of parallel ray:

A parallel ray converges at focus of a convex lens and diverges from the focus of a concave lens.

Fig: Ray parallel to principal axis

Fig: Ray parallel to principal axis

Refraction of ray passing through the Principal focus:

A ray passing through principal focus emerges parallel to the principal axis after refraction from a convex lens.

Fig: Ray passing through focus

Fig: Ray passing through focus

A ray passing through the principal focus emerges parallel to the principal axis after diverging from a concave lens.

Ray passing through the optical centre of lens:

Ray passing through the optical centre of convex and concave lens emerges in same direction without any deviation.

Fig: Ray passing through O

Fig: Ray passing through O

Converging lens: A convex lens is known as converging lens because parallel rays converge at its focus.

Fig: Converging Lens

Diverging lens: A concave lens is known as diverging lens because parallel rays appear to diverge from the focus; after refraction.

Fig: Diverging Lens

##### Image Formation by Convex Lens

There are six possibilities of position of object in the case of convex lens:

1. Object at infinity
2. Object beyond centre of curvature, C
3. Object at centre of curvature, C
4. Object between centre of curvature, C and principal focus, F
5. Object at principal focus, F
6. Object between principal focus, F and optical centre, O

Object at infinity:

Convex lens converge parallel rays coming from objet at infinity and a highly diminished – point sized, real and inverted image is formed at principal focus F2.

Fig: Object at Infinity

Properties of Image: Image is highly diminished, real and inverted.

Object beyond centre of curvature, C1 or 2F1:

A diminished, real and inverted image is formed between principal focus, F2 and centre of curvature, C2 at the opposite side when an object is placed beyond C1 of a convex lens.

Fig: Object Beyond 2F

Properties of Image: Image is diminished, real and inverted.

Object at centre of curvature, C1 or 2F1:

A same sized, real and inverted image is formed at centre of curvature, C2 when object is placed at centre of curvature, C1 of a convex lens.

Fig: Object at 2F

Properties of Image: Image is same size as object, real and inverted.

Object between centre of curvature, C1 and principal focus, F1:

An enlarged, real and inverted image is formed beyond centre of curvature, C2 when an object is placed between centre of curvature, C1 and principal focus, F1 of a convex lens.

Fig: Object between 2F and F

Properties of Image: Image is enlarged, real and inverted.

Object at principal focus, F1:
An infinitely large, real and inverted image is formed at infinity when object is placed at principal focus, F1 of a convex lens.

Fig: Object at F

Properties of Image: Image is highly enlarged, real and inverted.

Between principal focus, F1 and optical centre, O:

A virtual, erect and enlarged image is formed at the same side of lens, when an object is placed between principal focus, F1 and optical centre, O of a convex lens.

Fig: Object between F and O

Properties of Image: Image is enlarged, virtual and erect.

##### Image Formation by Concave Lens

There are only two possibilities of position of object in the case of a concave lens:

1. Object is at infinity
2. Object is between optical centre, O and infinity

Object is at infinity:
A highly diminished point sized, virtual and erect image is formed when object is at infinity by a concave lens at principal focus F1.

Fig: Object at Infinity

Properties of Image: Image is point sized, highly diminished, virtual and erect.

Object is between optical centre, O and infinity:
A diminished, virtual and erect image is formed between principal focus F1 and optical centre, O; when object is placed between optical centre and infinity of a concave lens.

Fig: Object between Infinity and O

Properties of Image: Image is diminished, virtual and erect.

Sign convention for lens:

Sign convention for lens is similar to that of spherical mirror. Signs are taken left of the optical centre as negative, right of the optical centre as positive, above of the principal axis as positive and below of the principal axis as negative.

Fig: Sign Convention

The new sign convention is known as New Cartesian Sign Convention. In this sign is taken negative towards left and taken as positive towards right at X-axis from origin.

The sign is taken as positive (+) above the origin point at Y-axis; and below the origin point as negative (-) at Y-axis.

##### Lens Formula and Magnification:

The relation between distance of object, distance of image and focal length for a lens is called lens formula.

Where, v is the distance of image, u is the distance of object, and f is the focal length of lens. Distance of object and image is measure from the optical centre of the lens. The sign for distance is given as per convention.

The lens formula is valid for all situations for spherical lens. By knowing any of the two the third can be calculated.

Magnification:
The ratio of height of image and that of object or ratio of distance of image and distance of object gives magnification. It is generally denoted by ‘m’.

The positive (+) sign of magnification shows that image is erect and virtual while a negative (-) sign of magnification shows that image is real and inverted.

Power of lens:

A convex lens with short focal length converges the light rays with greater degree nearer to principal focus and a concave lens with short focal length diverges the light rays with greater degree nearer to principal focus.

The degree of divergence or convergence of ray of light by a lens is expressed in terms of the power of lens. Degree of convergence and divergence depends upon the focal length of a lens. The power of a lens is denoted by ‘P’. The power of a lens is reciprocal of the focal length.

The SI unit of Power of lens is dioptre and it is denoted by ‘D’.

Power of a lens is expressed in dioptre when the focal length is expressed in metre. Thus, a lens having 1 metre of focal length has power equal to 1 dipotre.

Therefore, 1 D = 1 m−1
A convex lens has power in positive and a concave lens has power in negative.

Power of optical instruments having multiple lenses:
If there is more than one lens used, then total power of lenses is equal to the sum of power of all individual lenses.

Example: If there are three lenses used in an optical device having powers equal to 1 D, 2D and 3D respectively,

Therefore, the total power of the optical device = 1D + 2D + 3D = 6D

Some common phenomena of Refraction:

• Bending of pencil when placed in a glass with water: When a pencil or stick is kept in a beaker or a glass filled with water, the stick appears slightly bent. This happens because the light; entering from air (rarer medium) into water (denser medium); bends towards normal to the incident which makes the appearance of pencil or stick as bent.
• Position of fish in the water of pond: The ray coming from fish in the pond bends away from the normal to the incident. We see the emergent ray which makes the appearance of fish slightly above its position.
• Formation of rainbow: Rainbow is formed just after the rain. When ray of light travels from droplets of rain, it is scattered into its constituent seven colours and forms a rainbow in the sky.
• Visibility of sun slightly before the time of sunrise: When the rays coming from the sun enter into atmosphere (which is denser medium than vacuum), they bend away from normal to the incidence because of refraction. Since we see the refracted rays coming from the sun, that’s why the sun becomes visible slightly ahead of the time of sunrise.