10. LIGHT

1. Light

Light is a form of energy. More specifically, light is a general term commonly used to refer to the "visible spectrum", which is the range of wavelengths, (and their corresponding frequencies) that forms the visible part of the electro-magnetic spectrum. The ranges in wavelengths vary from 380 nm to 750 nm. Each wavelength corresponds to light of one particular colour so the "visible spectrum" range of wavelengths would look something like the block below if each wavelength appeared only once and they were all lined-up in order of increasing wavelength.

Check Out- CBSE Class 9 Science Notes

The term "visible spectrum" means the range of electro-magnetic energy that most people (i.e. those with "normal" vision) can see with the naked eye. This is just a small part of a much wider range of energies, many of which we cannot see but some of which are used in other ways, e.g. Radio Waves, Microwaves, Ultra Violet (UV) Light, Infra-Red (IR) Radiation, X-Rays, and other wavelengths such as those used in many different types of modern scanning equipment.

"White Light" is the way humans perceive and refer to our experience of receiving an approx. equal quantity of all the wavelengths (i.e. colours) in the visible spectrum. This explains why there are so many different "shades of white".

That is, when we see "white" we are receiving all the colours in approximately equal amounts - but only approximately.

The combination of wavelengths (colours) received by our eyes usually contains a bit more of some than of others, hence some "whites" can appear to be slightly "yellow", some slightly "blue", and so on.

Just as white is not a "spectral colour", neither is black or grey.

White is the way we perceive an approx. equal presence of all colours and black is the absence of light/colour such that all colours/wavelengths are (equally) lacking. Shades of grey also correspond to approximately the same amount of each colour, but in decreasing amounts along a scale from white (lots of "light" energy in the form of many different wavelengths, corresponding to different "colours", reaching the eye/brain) to black (no "light" energy, that is an imperceptibly small quantity of "light" energy in the form of many different wavelengths corresponding to different "colours" reaching the eye/brain).

1.2 Propagation of Light:

"Propagation" is a term used (in the context of light energy and also some other forms of energy, e.g. beams of X-rays, or sometimes other forms of energy that can be described as moving in "waves") to mean "movement" . "Propagation" is mentioned to introduce this frequently-used term but initially it is sufficient to describe how light "travels", which means the same thing.

Light generally travels through the air in straight lines, only changing direction when it passes from one type of substance (called a "medium") to another. For example, light changes direction slightly when it moves from air into water, or from air into glass, or vice-versa. This change in the direction of travel of light is due to refraction, which is explained later.

• Note that there are some situations in which light travels in curves rather than straight lines - as explained by the physics of diffraction and interference, but for the simple cases of describing image formation within the eye and the manifestation and correction of short-sight and long-sight, it is sufficient to think of rays of light traveling through any one medium, such as air or water, in a series of straight lines.

Light reaches objects from many different sources - both from large and powerful sources of illumination such as the sun or the main lights in a room, and also by reflection or scattering from all the surrounding objects.

When light reaches an object it can do one, or some combination of, the following:

To summarise:

A solid opaque object absorbs, scatters, or reflects light (or some combination of these) depending on its physical properties, including the properties of the material the object is made or formed from.

Aspects of objects that influence the onward path taken by light reaching their surfaces include:

• the physical state of the object (solid, liquid, gas),

• the substance it is formed from (wood, rock, glass etc.),

• the texture of its surface (rough, polished, carved, etc.),

• the thickness of the object/material (thin sheet of ice, or huge iceberg), and even

• its colour.

Other factors that affect how much light is absorbed, reflected, and scattered concern the light itself and how it arrived at the surface of the object, such as:

• the wavelength (colour) of the light, and

• the angle at which it reaches the surface.

Light also has other properties (e.g. polarisation states) that are more complicated to explain but are also relevant to some aspects of vision (e.g. explaining polarising sunglasses). These are omitted from these introductory pages.

Reflection of Light

When a ray of light falls on any surface, a part of the light is sent back to the same medium. This phenomenon where the incident light falling on a surface is sent back to the same medium is known as reflection.

There are two types of reflection of light:

• Regular reflection

• Irregular reflection

Laws of reflection of light:

If we know how light behaves when it is reflected we can use a mirror to change the direction in which the light is traveling. This happens when a mirror is placed at the entrance of a concealed drive to give warning of approaching traffic.

An ordinary mirror is made by depositing a thin layer of silver on one side of a piece of glass and protecting it with paint. The silver - at the back of the glass - acts as the reflecting traffic.

From the below explanation we can understand the law of reflection of light.

Regular Reflection

Regular Reflection on a Smooth Surface

Regular reflection takes place when a ray of light is incident on a polished smooth surface like a mirror. Here the reflected ray of light moves only in a fixed direction.

Irregular Reflection or Diffused Reflection

Diffused Reflection on a Rough Surface

Irregular reflection or diffused reflection takes place when a ray of light is incident on a wall or wood, which is not smooth or polished. In this case, the different portions of the surface reflect the incident light in different directions. In such cases no definite image is formed, but the surface becomes visible. It is commonly known as scattering of light. Thus diffused reflection makes non-luminous objects visible.

Not all light, which hits an object, is reflected. Some of the incident light is absorbed. The brightness of an object depends on the intensity of the incident light and also on the reflectivity of the object.

If a surface allows the entire incident light to undergo regular reflection then it will become invisible.

Reflection of Light by a Plane Surface

The figure shows how a ray of light is reflected by a plane surface. Let MM' represent a reflecting surface. When a ray of light is incident on MM' in the direction IO it gets reflected along the direction OR. IO is the incident ray; O is the point of incidence and OR is the reflected ray.

Reflection of a Ray Light by a Plane Mirror

Let ON be the normal drawn perpendicular to the surface MM' at the point of incidence. The angle which the incident ray makes with the normal at the point of incidence is called the angle of incidence and is denoted by the letter 'i'. The angle that the reflected ray makes with the normal at the point of incidence is called the angle of reflection 'r'. Mirror is an example of a reflecting surface.

The Laws of Reflection

The reflection at any plane surface is found to obey the laws of reflection. The laws of reflection are:

• The incident ray, the reflected ray and the normal at the point of incidence lie in the same plane.

• The angle of incidence is equal to the angle of reflection.

Image

An image can be real or virtual. A real image is formed when the rays of light actually intersect after reflection. A virtual image is formed when the light rays after reflection do not actually intersect but appear to diverge from it (these rays of light intersect when produced backwards).

Virtual Image Formed by a Plane Mirror

In fig (i) we can see that the light beam from the point source O is a diverging beam. After reflection from the mirror it is still a diverging beam, which appears to come from I. The image formed by a plane mirror is virtual.

Formation of Image by a Plane Mirror - Ray Diagrams

The following rays are usually considered while constructing ray diagrams.

A Ray Diagram Showing the formation of an Image by a Plane Mirror

A ray of light incident on a plane mirror at 90^∘ gets reflected from the mirror along the same path.

A ray of light falling on a plane mirror at any angle gets reflected from the mirror such that the angle of incidence is equal to the angle of reflection.

• Image Formation When an Object is placed between Two Inclined Mirrors

The Angle of Inclination Between the Mirrors is 90^o.

• Place the mirrors MM' perpendicular to MM.

• An object O is kept in between these mirrors.

• OA and OB are the two rays, which are incident on the mirror MM.

• OA being normal to the surface retraces its path.

• OB makes an angle i with the normal N and gets reflected along BC according to the laws of reflection

• Extend the rays OA and BC backwards.

• They meet at O_1, which is the virtual image of O.

• OD and OE represent the rays which are incident on the mirror MM'.

• OD is perpendicular to the mirror MM' and hence gets reflected along the same path.

• OE is the incident ray and N₂ is the normal at the point of incidence and OE gets reflected along the path EF.

• Extend OD and EF backwards. They meet at O₂, which is the virtual image of O.

• The reflected ray BC gets internally reflected by the mirror MM' along CG.

• The ray DG appears to comes from O₃, which is the image of O_1,

• Similarly EF the reflected ray gets internally reflected by the mirror MM along FH.

• The ray FH appears to come from O₄, which is the image of O_2.

• The position of O₁ and O₂ coincide.

• Thus when the angle of inclination between the mirrors is 90⁰ we get three images.

Case III

Let us now calculate the number of images formed if the two mirrors are placed parallel to each other i.e., the angle of inclination between them is 0⁰.

• Place the mirrors MM and MM' parallel to each other.

• An object O is kept between these mirrors.

• OA and OO' represent the rays which are incident on the mirror MM.

• OO' being normal retraces its path.

• OA makes an angle i with the normal N₁ and gets reflected along AB according to the laws of reflection.

• Extend the rays AB and OM backwards.

• They meet at I₁, which is the virtual image of the object O.

• The reflected ray AB gets reflected by the mirror MM' and forms an image I_2.

• Similarly I₃, I₄ etc. are formed.

• The light from I₁, I₂, I₃, I₄ etc. gets reflected and forms their images.

In this manner, many images are formed but the intensity of the remote images goes on decreasing due to absorption of light energy at every successive reflection and thus we see only finite number of images even though infinite images will be formed.

Uses of Plane Mirrors

A plane mirror is used:

• as a looking glass to view ourselves

• by interior designers to create an illusion of depth

• to fold light as in a periscope and other optical instruments

• to make kaleidoscope, an interesting toy

Spherical Mirrors for Reflection

A mirror whose, polished, reflecting surface is a part of a hollow sphere of glass or plastic is called a spherical mirror.

In a spherical mirror, one of the two curved surfaces is coated with a thin layer of silver followed by a coating of red lead oxide paint. Thus, one side of the spherical mirror is opaque and the other side is a highly polished reflecting surface. In a diagram the opaque side of a mirror is always shown shaded.

In the diagrams given here, please remember that the opaque, non reflecting side is shaded grey. The reflecting side is black.

Depending upon the nature of the reflecting surface of a mirror, the spherical mirror is classified as:

• Concave mirror

• Convex mirror

Concave Mirror

Concave mirror is a spherical mirror whose reflecting surface is towards the center of the sphere of which the mirror is a part.

Convex Mirror

Convex mirror is a spherical mirror whose reflecting surface is away from the center of the sphere of which the mirror is a part.

Concave and Convex Mirror

Let us now define certain physical terms relating to spherical mirrors.

Center of Curvature

Center of Curvature is the center of the sphere of which the spherical mirror forms a part. It is denoted by the letter C.

Center of Curvature

Radius of Curvature

Radius of Curvature is the radius of the sphere of which the mirror is a part. It is represented by the letter R.

Radius of Curvature

Linear Aperture

Linear aperture is the distance between the extreme points (X and Y) on the periphery of the mirror.

XY is the Aperture

Pole

Pole is the midpoint of the aperture of the spherical mirror. It is represented by the letter P.

Midpoint of xy

Principal Axis

Principal axis is the straight line passing through the pole and the center of curvature of a spherical mirror.

Principal Axis

Normal

The normal at any point of the spherical mirror is the straight line obtained by joining that point with the center of the mirror. The normal at point A on the mirror is the line AC obtained by joining A to the center of curvature of the mirror. Normal at any point on a spherical mirror is equal to the radius of the sphere of which the mirror is a part.

Normal

Principal Focus or Focus

The rays of light parallel to the principal axis of a mirror after reflection, either pass through a point (in case of a concave mirror) or appear to diverge from a point (in the case of a convex mirror) on the principal axis and this point is referred to as the principal focus or focal point of the mirror.

The principal focus of a spherical mirror may be defined as a point on its principal axis where a beam of light parallel to the principal axis converges to or appears to diverge from after reflection from the spherical mirror.

Focal Length

Focal length is the distance between the pole and the focus of a mirror. It is represented by the letter f.

Characteristics of Focus of a Concave and a Convex Mirror

Note : A concave mirror is also known as a converging mirror as the parallel rays of light after getting reflected from the concave mirror converge at the focus.

A convex mirror is known as a diverging mirror as the parallel rays of light after reflection appear to come from a point, i.e., the rays diverge after reflection.

Relation between f and R

To show that f = R/2, where f is the focal length of a mirror and R its radius of curvature.

Case I Concave Mirror

To Show that f = R/2 for a Concave Mirror

Let a ray of light AB be incident, parallel to the principal axis, on a concave mirror. After reflection, the ray AB passes along BD, through the focus F. BC is normal to the concave mirror at B.

∠ABC = ∠CBD − (1)(According to the law of reflection ∠i=∠r)

We know that AB and PC are parallel to each other.

∴ ∠ABC = ∠BCP − (2)(Alternate angles)

From equations (1) and (2) we get

∠CBD = ∠BCP

Hence triangle BCF is isosceles

∴ BF = CF − (3)

If the aperture of the mirror is small then B will be very close to P.

∴ BF = PF − (4)

From equations (3) and (4) we conclude that

But by definition PF = f (focal length) and PC = R (radius of curvature)

Note: While Deriving the Relation we have considered only one of the incident rays

Case II Convex Mirror

Let a ray of light AB be incident, parallel to the principal axis, on a convex mirror. After reflection the ray AB appears to come from F. BC is the normal to the convex mirror at B.

∠ABN = ∠NBD − (1)(According to the law of reflection ∠i=∠r)

∠CBF = ∠NBD − (2)(Vertical angles)

∠BCF = ∠ABN − (Alternate angles)

∠BCF = ∠ABN = ∠NBD − (3) [from equation (1)]

From equations (2) and (3)

∠CBF = ∠BCF

Hence triangle BCF is isosceles

∴ BF = CF − (4)

If the aperture of the mirror is small then B will be very close to P.

∴ BF = PF − (5)

From the above relation we conclude that the radius of curvature of a mirror is twice its focal length.

Formation of Images by Spherical Mirrors

When an object is placed in front of a concave mirror, light rays from the object fall on the mirror and get reflected. The reflected rays produce an image at a point where they intersect or appear to intersect. Formation of an image by mirrors is usually shown by constructing ray diagrams. To construct a ray diagram, we need at least two rays whose paths after reflection from the mirror are known. These rays must be chosen according to our convenience. Any two of the rays can be considered to obtain the image.

• A ray of light parallel to the principal axis after reflection from a concave mirror passes through its focus.

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

• A ray of light passing through the center of curvature of a concave mirror retraces its path after reflection as the ray passing through the center of curvature acts as a normal to the spherical mirror.

• A ray of light which strikes the mirror at its pole gets reflected according to the law of reflection.

Formation of Images by a Concave Mirror

When an object is placed at infinity, the rays coming from it are parallel to each other. Let us consider two rays, one striking the mirror at its pole and the other passing through the center of curvature. The ray which is incident at the pole gets reflected according to the law of reflection and the second ray which passes through the center of curvature of the mirror retraces its path. These rays after reflection form an image at the focus. The image formed is real, inverted and diminished.

When the Object is Placed Beyond C

The two rays which are considered to obtain the image are:

• a ray passing through the center of curvature

• a ray parallel to the principal axis. The ray passing through the center of curvature retraces its path and the ray which is parallel to the principal axis passes through the focus after reflection. These rays after reflection meet at a point between C and F. The image is inverted, real and diminished

• When the Object is Placed at the Center of Curvature

Here we consider the two rays, one parallel to the principal axis and the other passing through the focus. The ray of light which is parallel to the principal axis passes through the focus after reflection. The other ray passing through the focus after reflection emerges parallel to the axis. After reflection these rays meet at the center of curvature to form an inverted image, which is real and of the same size as the object.

• When the Object is Between C and F

Here we consider a ray of light which is parallel to the principal axis and another ray passing through the focus. The ray which is parallel to the principal axis passes through the principal focus and the ray which passes through the focus after reflection emerges parallel to the principal axis. The reflected rays meet at a point beyond C and the image is real, inverted and magnified.

• When the Object is at the Focus

Here, we consider a ray of light which is parallel to the principal axis and another ray passing through the center of curvature. The ray which is parallel to the principal axis passes through the focus and the ray which passes through the center of curvature retraces its path. The reflected rays are parallel to each other, and would meet only at infinity i.e., the image is formed at infinity and it is a real, inverted, enlarged image of the object.

• When the Object is Between the Pole and the Focus

Here we consider a ray of light which is parallel to the incident ray and another ray which is passing through the center of curvature. The ray which is passing through the center of curvature retraces its path and the other ray which is parallel to the principal axis after reflection passes through the focus. These rays appear to meet behind the mirror when the reflected rays are extended backwards. The image is virtual, erect and magnified.

The following table gives the position, size and nature of the image formed in a concave mirror corresponding to different positions of the object and the use of concave mirror.

Case II Convex Mirror

The following rays are considered while constructing ray diagrams.

• A ray of light traveling parallel to the principal axis after reflection from a convex mirror appear to come from its focus behind the mirror.

• A ray of light traveling towards the center of curvature behind the mirror hits the mirror at 90^o and is reflected back along its path.

• A convex mirror always gives a virtual image irrespective of the position of the object.

Formation of Image in a Convex Mirror

The image is

• Formed between the pole and the focus

• Erect

• Diminished

• Virtual

When the Object is at Infinity

The image is

• Formed at the focus

• Extremely diminished

• Virtual

• Erect

Mirror Formula (Concave Mirror)

Mirror formula is the relationship between object distance (u), image distance (v) and focal length.

Sign Convention for Spherical Mirrors

The following sign convention is used for measuring various distances in the ray diagrams of spherical mirrors:

• All distances are measured from the pole of the mirror.

• Distances measured in the direction of the incident ray are positive and the distances measured in the direction opposite to that of the incident rays are negative.

• Distances measured above the principal axis are positive and that measured below the principal axis are negative.

Table Showing the Sign Convention

Derivation

An object AB at a distance u from the pole of a concave mirror. The image A₁B₁ is formed at a distance v from the mirror. The position of the image is obtained by drawing a ray diagram.

Consider the ΔA₁CB₁ and ΔACB

∠A₁CB₁ = ∠ACB − (Vertically opposite angles)

∠AB₁C = ∠ABC − (Right angles)

∠B₁A₁C = ∠BAC

[when two angles of ΔA₁CB₁ and ΔACB are equal then the third angle ∠B₁A₁C = ∠BAC

 ∴ ΔA₁CB₁and ΔACB are similar

BC = PC − PB

B₁C = PB₁ − PC

FB₁ = PB₁ − PF

But PC=R, PB=u, PB₁ = v, PF = f

By sign convention

PC = -R, PB = -u, PF = -f and PB₁ = -v

uv − uf − Rv + Rf = Rf − vf

uv − uf − Rv = Rf − Rf − vf

uv − uf − Rv =  − vf

R = 2f

uv − uf − 2fv =  − vf

uv − uf = 2fv − fv

uv − uf = fv − (4)

Equation (5) gives the mirror formula

Mirror Formula (Convex Mirror)

Let AB be an object placed on the principal axis of a convex mirror of focal length f. u is the distance between the object and the mirror and v is the distance between the image and the mirror.

In ΔABC and ΔA₁B₁C

∠ABC=∠A₁B₁C (Right angles)

∠ACB = ∠A₁CB₁

∠CAB = ∠CA₁B (Common angle)

∴ ΔABC is similar to ΔA₁B₁C

But DE = AB and when the aperture is very small EF = PF.

∴ Equation (2) becomes

[PF= f, PB₁ = v, PB = u, PC = 2f]

f(2f−v) = (f−v)(2f−u)

2f² − vf = 2f² − uf − 2fv + uv

2f² − vf − 2f² + uf + 2fv − uv = 0

uf + fv − uv = 0 − (4)

Dividing both sides of the equation (4) by uvf we get

Magnification

The ratio of the height of the image to the height of the object is called the linear magnification. It is denoted by the letter m. While deriving the mirror formula it has been proved that D ACB and D A₁CB₁ are similar and so also D FB₁A₁ and D FED are similar.

Where h₁ is the height of the image and h_o is the height of the object

For a real image u and v are negative and the magnification is negative. Negative magnification means the image is inverted. On the other hand for a virtual image u is negative and v is positive and hence the magnification is positive, i.e., the image is erect.

Uses of Concave Mirror

The use of a concave mirror depends upon the distance of the object from the mirror. Some of the uses are listed below.

Concave mirrors are used for the following purposes:

• as reflectors in the head lights of cars, search lights etc. to obtain parallel beam of light. For this, the source of light is placed at the focus of the concave reflector.

• by dentists to focus light on the tooth to be examined.

• as shaving mirrors and as make up mirrors to get an enlarged erect image of the face.

• to concentrate solar radiations in solar heating devices.

Uses of Convex Mirror

Convex mirrors are used for the following purposes:

• rear-view mirror in an automobile. This convex mirror gives the driver a clear view of the traffic approaching from behind.

• vigilance mirrors in departmental stores.