Physics

Light

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Light

Light is a form of energy which is propagated as electromagnetic waves. In the spectrum of electromagnetic waves it lies between ultra-violet and infra-red region and has wavelength between 3900 A to 7800 A.

Electromagnetic waves are transverse, hence light is transverse wave.
All the electromagnetic waves including light do not require medium to propagate.
Wave nature of light explains rectilinear propagation, reflection, refraction, interference, diffraction and polarisation of light.
The phenomena like photoelectric effect and Compton effect are not explained on the basis of wave nature of light. These phenomena are explained on the basis of quantum theory of light/particle nature of light as proposed by Einstein.
In quantum theory, light is regarded as a packet or bundle of energy called photon. Photon is associated with it an energy E where E = Jiv.
Clearly light behaves as wave and particle both. Thus light has dual nature.
Speed of light was first measured by Roemer (1678 AD). Speed of light is maximum in vacuum and air (3 x 10⁸ m/s) (and independent of density, temperature and pressure)

Refractive index:

R.I. of a medium is defined as the o of speed of light in vacuum to the speed of light in the medium.

$\mu = \frac{c}{v} = \frac{Speed.of.light.in.vacuum}{Speed.of.light.in.the.medium}$

Speed of light is different in different media. Velocity of light is large in a medium which has small refractive index.

Speed of light in different mediums

Medium	Speed of light (m/s)	Medium	Speed of light (m/s)
Vacuum	3 x 10⁸	Class	2 x 10⁸
Water	2.25 x 10⁸	Tementine oil	2.04 x 10⁸
Rock salt	1.96 x 10⁸	Nylon	1.96 x 10⁸

Light takes 8 minute 19 second (499 second) to reach from sun to earth.
The light reflected from moon takes 1.28 second to reach earth.

Luminous bodies:

Those object which emit light by themselves are called luminous bodies. e g.- sun, stars, electric bulb etc.

Non-luminous bodies:

Those objects which do not emit light by themselves but are visible by the light falling on them emitted by self luminous bodies are called non-luminous bodies.

A Material can be classified as:

1. Transparent:

The substances which allow most of the incident light to pass through them are called transparent, e.g. glass, water.

2. Translucent:

The substances which allow a part of incident light to pass through them are called translucent es e.g. oiled paper.

3. Opaque:

The substances which do not allow the incident light to pass through them are called opaque bodies, e.g., mirror, metal, wood etc.

Shadow: Shadow is the dark region on a screen when an opaque object is placed in the path of light. If is due to rectilinear propagation of light.

In case of point source, the shadow has s lapely defir.t d outline.

In case of extended source of light, the shadow has two distinct regions.

Umbra: The region in which no light reaches, (regic-of complete darkness)

Penumbra: The region in which partial light reaches.

Reflection of light:

Light moving in one medium when falls at the surface of another medium, part of light returns back to the same medium. This phenomenon of retumire back of light in the first medium at the interface of two media is known as reflection of light.

If the reflecting surface is smooth, reflection is regular In case of rough surface, reflection is irregular.

Laws of reflection

1. The incident ray, reflected ray and normal to the reflecting surface at the incident point all lie in the same plane.

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

Reflection from plane mirror

1. The image is virtual, laterally inverted.

2. The size of image is equal to that of object.

3. The distance of image from the mirror is equal to distance of object from the mirror.

4. If an object moves towards (or away from) a plane mirror with speed v, the image moves towards (or away) with a speed 2v relative to the object.

5. If a plane mirror is rotated by an angle θ, keeping the incident ray fixed, the reflected ray is rotated by an angle 2 θ.

6. To see his full image in a plane mirror, a person requires a mirror of at least half of his height.

7. If two plane mirrors are inclined to each other at an angle θ the number of images (n) of a point object formed are determined as follows:

(a) If $\frac{360}{\theta }$ is even integer, then $n = \frac{360}{\theta } - 1$

(b) If $\frac{360}{\theta }$ is odd integer, then $n = \frac{360}{\theta } - 1$ if the object is symmetrically placed, and $n = \frac{360}{\theta }$ if the object is not symmetrically placed.

(c) If $\frac{360}{\theta }$ is a fraction then n is equal to integral part.

Focal length of a plane mirror is infinite.

Reflection from spherical mirror

Spherical mirrors are of two types - 1. Concave mirror and 2. Convex mirror

Position & nature of Image formed y a spherical mirror

Position of object	Position of image	Size image in comparison to Object	Nature of image
Concave mirror
At infinity	At Focus	Highly diminished	Real, inverted
Between infinity and centre of curvature	Between focus and centre of curvature	Diminished	Real, inverted
At centre of curvature	At centre of curvature	of same size	Real, inverted
Between focus and centre of curvature	Between centre of curvature and infinity	Enlarged	Real, inverted
At focus	At Infinity	Highly enlarged	Real, inverted
Between focus	Behind the mirror	Enlarged	Virtual, erect
Convex mirror
At infinity	At Focus	Highly diminished	Virtual, erect
Infront of mirro	Between pole and focus	Diminished	Virtual, erect

Note: Image formed by a convex mirror is always virtual, erect and diminished.

Uses of Concave mirror:

As a shaving glass.
As a reflector for the head lights of a vehicle, search light.
In opthalmoscope to examine eye, ear, nose by doctors.
In solar cookers.
In concentrating light at a given spot.

Uses of Convex mirror:

As a rear view mirror in vehicle because it provides the maximum rear field of view and image formed is always erect.
In sodium reflector lamp.

Refraction of light:

When a ray of light propagating in a medium enters the other medium, it deviates from its path. This phenomenon of change in the direction of propagation of light at the boundary when it passes from one medium to other medium is called refraction of light.

When a ray of light enters from rarer medium to denser medium (as from water to glass) it deviates towards the normal drawn on the boundary of two media at the incident point. Similarly in passing from denser to rarer medium, a ray deviates away from the normal. If light is incident normally on the boundary i.e. parallel to normal, it enters the second medium undeviated.

Laws of refraction:

1. Incident ray, refracted ray and normal drawn at incident point always lie in the same plane.

2. Snell's law: For a given colour of light, the ratio of sine of angle of incidence to the sine of angle of refraction is a constant,

i.e. $\frac{\sin i}{\sin r} = 1\mu _2$ (constant)

This constant $1\mu _2$ is called refractive index of second medium with respect to the first medium.

Absolute refractive index of a medium is defined as the ratio of speed of light in free space (vacuum) to that in the given medium,

i.e. absolute refractive index $({\mu}) = \frac{Speed.of.light.in.vacuum}{Speed.of.light.in.the.medium}$

The refractive index of a medium is different for different colours. The refractive index of a medium decreases with the increase in wavelength of light. Hence refractive index of a medium is maximum for violet colour of light and minimum for red colour of light.
The refractive index of a medium decreases with the increase in temperature. But this variation is very small. »- When a ray of light enters from one medium to other medium, its frequency and phase donot change but wavelength and velocity change.

Some illustrations of Refraction:

1. Bending of a linear object when it is partially dipeed in a liquid inclined to the surface of the liquid.

2. Twinkling of stars.

3. Oval shape of sun in the morning and evening.

4. An object in a denser medium when seen from a rarer medium appears to be at a smaller distance.

This is why (a) A fish in a pond when viewed from air appears to be at a smaller depth than actual depth (b) A coin at the base of a vessel filled with water appears raised (c) Water tank appears shallower when viewed from the top.

The refractive index is inversely proportional to wavelength. So shorter the wavelength, the less it refracts (deviates). Hence if a glass slab is placed over coloured letters, violet letters having the shortest wavelength will appear more raised than any other colour. Red colour being of the longest wavelength will appear less raised.

Critical angle:

In case of propagation of light from denser to rarer medium through a plane boundary, critical angle is the angle of incidence for which angle of refraction is 90°.

Total Internal Reflection:

if the light is propagating from the denser medium towards the rarer medium and angle of incidence is more than critical angle, then the light incident on the boundary is reflected back in the denser medium, obeying the laws of reflection. This phenomenon is called total internal reflection as total light energy is reflected, no part is absorbed or transmitted.

For total internal reflection,
1. Light must be propagating from denser to rarer medium
This is why if light goes from water to glass, total internal reflection will not take place.
2. Angle of incidence must exceeds the critical angle.

Illustrations of total internal reflection:

1. Sparkling of diamond

2. Mirage and looming.

3. Shining of air bubble in water.

4. Increase in duration of sun's visibility-The sun becomes visible even before sun rise and remains visible even after sunset due to total internal reflection of light.

5. Shining of a smoked ball or a metal ball on which lamp soot is deposited when dipped in water.

6. Optical Fibre: Optical fibre consists of thousands of strands of a very fine quality glass or quartz (of refractive index 1.7), each strand coated with a layer of material of lower refractive index (1.5). In it, light is propagated along the axis of fibre through multiple total internal reflection, even though the fibre is curved, without loss of energy.

Applications:

- For transmitting optical signals and the two dimensional pictures.
- For transmitting electrical signals by first converting them to light.
- For visualising the internal sites of the body by doctors in endoscopy.

Refraction of Light Through Lens

Lens is a section of transparent refractive material of two surfaces of definite geometrical shape of which one surface must be spherical. Lens is generally of two types:
1. Convex lens 2. Concave lens.
When a lens is thicker at the middle than at the edges, it is called a convex lens or a converging lens. When the lens is thicker at the edges than in the middle, it is called as concave lens or diverging lens.
Some terms regarding a lens.

$\textbf{O}$ – Optical Centre
$\mathbf{F_1}$ – First Focus
${\textbf{C}_{\textbf{1}}\textbf{C}_{\textbf{2}}}$ – Pricipal axis
$\textbf{F}_\textbf{2}$ – Second Focus

Power of a lens

Power of a lens is its capacity to deviate a ray. It is measured as the reciprocal of the focal length in meters, i.e $P = \frac{1}{f}$

SI Unit of power is dioptre (D).

The power of a convex lens is positive and that of a concave lens is negative.
If two lenses are placed in contact, then the power of combination is equal to the sum of powers of individual lenses.

Change in the power of a lens:

If a lens is dipped in a liquid, its focal length and power both change. This change depends upon the refractive indices of lens and the liquid. If a lens of refractive index μ is dipped in a liquid of refractive index μ, then the following three situations are possible

1. μ > μ' i.e. lens is dipped in a liquid of smaller refractive index like a lens of glass ( μ = 1.5) is dipped in water (μ = 1.33), then the focal length of the lens increases and the power of the lens decreases.

2. μ = μ' i.e. lens is dipped in a liquid of equal refractive index then the focal length of the lens becomes infinite i.e. its power becomes zero. The lens and the liquid behave as a single medium.

3. μ < μ' i.e. lens is dipped in a liquid of higher refractive index the focal length increases i.e. power decreases as well as the nature of the lens also changes i.e. convex lens behaves as concave lens and vice-versa. For example, an air bubble trapped in water or glass appears as convex but behaves as concave lens. Similarly a convex lens of glass (μ = 1.5) when dipped in carbon disulphide (μ = 1.68), it behaves as a concave lens.

Formation of Images by lenses

Position of Object	Position of Image	Size of Image	Nature of Image
Concave Lens
At infinity	At Focus	Highly diminished	Real, inverted
Beyond 2 F	Between F and 2F Diminished	Diminished	Real, inverted
At 2 F	At2F	Of same size	Real, inverted
Between F and 2F Beyond 2F	Beyond 2F	Enlarged	Real, inverted
At F	At infinity	Highly enlarged	Real, inverted
Between optical centre and F	The same side as in the object	Enlarged	Virtual and erect
Concave Lens
At infinity	At focus	Highly diminished	Virtual and erect
Between lens and infinity	Between lens and F on the same side	diminished	Virtual and erect

Dispersion of Light:

When a ray of white light (or a composite light) is passed through a prism, it gets splitted into its constituent colours. This phenomenon is called dispersion of light. The coloured pattern obtained on a screen after dispersion of light is called spectrum.

The dispersion of light is due to different deviation suffered by different colours of light. The deviation is maximum for violet colour and minimum for red colour of light. The different colours appeared in the spectrum are on the following order, violet, indigo, blue, green, yellow, Orange and red. (VIBGYOR)
The dispersion of light is due to different velocities of light of different colours in a medium. As a result, the refractive index of a medium is different for different colours of light.
The velocity of light in a medium is maximum for that colour for which the refractive index is minimum. Clearly, the velocity of violet colour of light is minimum in a medium and retroactive index of that medium is maximum for violet colour. Similarly, the velocity of light in a medium is maximum for red colour and refractive index of that medium is minimum for red colour.

Rainbow:

Rainbow is the coloured display in the form of an arc of a circle hanging in the sky observed during or after a little drizzle appearing on the opposite side of sun. Rainbow is formed due to dispersion and refraction of sun light by the suspended water droplets.

Rainbow is of two types:

1. Primary rainbow 2. Secondary rainbow

Primary rainbow

Primary rainbow is formed due to two refractions and one total internal reflection of light falling on the raindrops. In the primary rainbow, the red colour is on the convex side and violet on the concave side. Primary rainbow has an angular width of 2° at an average angle of elevation of 41°.

Secondary rainbow

Secondary rainbow is formed due to two refractions and two internal reflections of light falling on rain drops. The order of colour on the secondary rainbow is in the reverse order and has an angular width of 3.5° at an average elevation of 52.75°. Secondary rainbow is less intense than primary rainbow.

Theory of Colours:

Colour is the sensation perceived by the cones in the eye due to light.

Primary Colours:

The spectral colours blue, green and red are called primary colours because all the colours can be produced by mixing these in proper proportion.

Blue + Red + Green = White

Secondary Colours:

The colour produced by mixing any two primary colours is called a secondary colour. There are three secondary colours yellow, magenta and cyan as

Green + Red = Yellow Red + Blue = Magenta Blue + Green = Cyan

When the three secondary colours are mixed, white colour is produced

Yellow + Magenta + Cyan = White

Complementary Colours:

Any two colours when added produce white light, are said to be complementary colours. Clearly a secondary colour and the remaining primary colour are complementary colours. Red and cyan, blue and yellow and green and magenta are complementary of eachother.

The different colours and their mixtures are shown by the colour triangle.
In coloured television, the three primary colours are used.

Colour of bodies:

The colour of a body is the colour of light which it reflects or transmits. An object is white, if it reflects all the components of white light and it is black if it absorbs all the light incident over it. This is why a red rose appears red when viewed in white or red light but appears black when viewed in blue or green light.

How a body will appear in light of different colour can be understood by the following table

Name of Object	In white light	In red light	In green light	In Yellow light	In blue light
White paper	White	Red	Green	Yellow	Blue
Red paper	Red	Red	Black	Black	Black
Green paper	Green	Black	Green	Black	Black
Yellow paper	Yellow	Black	Black	Yellow	Black
Blue paper	Blue	Black	Black	Black	Blue

Spectrum of colour in Compact Disc (CD) is due to reflection of white light from ridges in the metal.

Scattering of light:

When light waves fall on small bodies such as dust particles, water particles in suspension, suspended particles in colloidal solution, they are thrown out in all directions. This phenomenon is called scattering of light.

Scattering of light is maximum in case of violet colour and minimum in case of red colour of light.

Blue colour of sky is due to scattering of light.
The brilliant red colour of rising and setting sun is due to scattering of light.

Interference of light:

When two light waves of exactly the same frequency and a constant phase difference travel in same direction and superimpose then the resultant intensity in the region of superposition is different from the sum of intensity of individual waves. This modification in the intensity of light in the region of superposition is called interference of light. Interference is of two types-

1. Constructive interference 2. Destructive interference

Constructive interference:

At some points, where the two waves meet is same phase, resultant intensity is maximum. Such interference is called constructive interference.

Destructive interference:

At some points, where the two waves meet in opposite phase, resultant intensity is minimum. Such interference is called destructive interference.

Diffraction of light:

When light waves fall on a small sized obstacle or a small aperture whose dimension is comparable to the wavelength of light, then there is a departure from the rectilinear propagation and light energy enters into the region of geometrical shadow. The spreading of light energy beyond the limit prescribed by rectilinear propagation of light is called diffraction of light. In other words, diffraction is the process by which a beam of light or other systems of wave is spread out as a result of passing through a narrow opening or across an edge.

Polarisation of light:

Polarisation is the only phenomenon which proves that light is a transverse wave Light is an electromagnetic wave in which electric and magnetic field vectors vibrate perpendicular to each other and also perpendicular to the direction of propagation. In ordinary light, the vibrations of electric field vector are in every plane perpendicular to the direction of propagation of wave. Polarisation is the phenomenon of restricting the vibrations of a light in a particular direction in a plane perpendicular to the direction of propagation of wave.

The visible effect of light is only due to electric field vector.

Human Eye

Human eye basically consists of a convex lens. This lens forms real and inverted image of an object on retina.

There are two kinds of vision cells in the retina. They are called rods and cones on account of their peculiar shape. Rods decides the intensity of light where as cones distinguish colour of light.
Least distance of distinct vision is 25 cm.

Defects of human eye and the remedies:

1. Myopia or short sightedness:

A person suffering from myopia can see the near objects clearly while far objects are not clear.

Causes:
i. Elongation of eye ball along the axis.

ii. Shortening of focal length of eye lens.

iii. Over stretching of ciliary muscles beyond the elastic limit.

Remedy: Diverging (concave) lens is used.

2. Hyperopia or hypermetropia or longsightedness:

A person suffering from hypermetropia can see the distant objects clearly but not the near objects.

Causes:

1. Shortening of eye ball along the axis.

2. Increase in the focal length of eye lens.

3. Stiffening of ciliary muscles.

Remedy: A converging (convex) lens is used.

3. Presbyopia:

This defect is generally found in elderly person. Due to stiffening of ciliary muscles, eye looses much of its accommodating power. As a result distinct as well as nearby objects can not be seen.

For its remedy two separate lens or a bifocal lens is used.

4. Astigmatism:

This defect arises due to difference in the radii of curvature of cornea in the different planes. As a result point in one plane of an object appears in focus while those in other plane are out of focus. For its remedy cylindrical lens is used.

Simple microscope:

This is simply a convex lens of small focal length. The object to be enlarged is placed within the focus of lens.

Magnifying power of a simple microscope is given as $M = 1 + \frac{F}{f}$ Where D = 25 cm, f = focal length of lens.

Compound microscope:

It consists of two convex lenses coaxially fitted in a hollow tube. The lens facing the object is called objective and the lens towards the eye is called eye piece.

The aperture of objective is smaller than that of eye piece.
Both the lenses are of smaller focal lengths. This increases the magnifying power of instrument.

Electron Microscope

Electron microscope uses the beam of accelerated electrons as a source of illumination. As the wavelength of electrons is shorter than that of visible light, the electron microscope has a higher resolving power.

Telescope

Telescopes are used to view distant objects which are not visible to naked eye. Telescope can be divided as astronomical telescope, terrestrial telescope and Galilean telescope.

Astronomical telescope consists of two convex lenses placed coaxially in a hollow tube. The lens facing the object is called objective and the lens towards the eye is called eye piece. Final image is inverted.
The objective has large aperture so that the rays from the object can be easily collected.
The focal length of objective is larger than that of eye piece.
Terrestrial Telescope is similar to astronomical telescope with one additional convex lens in between the objective and eye piece. The role of this lens is to invert the image formed by the objective so that the final image is erect, s* Galilean telescope consists of two lenses. The objective is convex and eye piece is concave. The final image is erect.
Optical telescope was invented by Hans Lippershey. But Galileo Galilei was first to use it systematically to study the night sky.

Movie (Film) or Slide Projector:

It projects magnified image of an object on a screen. The object (inverted) is placed between F and 2F of a projection lens (a convex lens) so that its real, inverted, magnified image is formed between 2F and infinity on the other side ie. the image is erect.