In this article, we shall study brief history of study of light, sources of light, andterminology of optics.

History of Study of Light:

• Light is a form of that energy which simulates our vision. Around 400 B.C., it was proposed that particles were emitted by eye when the object is seen.
• In 1660 The great British physician  Sir Issac Newton proposed Corpuscular theory to explain the propagation of light. He assumed the particle nature of light.
• In 1680, A Dutch (Holand) scientist and contemporary of Newton, Christan Huygens (1629 – 1695) proposed Wave theory of light.
• The rectilinear propagation of light is due to the fact that the wavelength of light may be much smaller than the dimensions of openings and obstacles casting sharp shadows. Due to Newton’s clout on scientists in that era, the Huygens’s wave theory of light remained in a dump for almost century. Newton’s theory was challenged on the basis of Huygens’s wave theory of light by Thomas Young (1773 – 1829) in 1801 using his Double slit experiment.
• These experiments clearly established that light coming from two coherent sources interfere and produce maxima and minima depending upon path difference between the two waves. This phenomenon is known as the interference of light.
• Augustin Jean Fresnel (1788 – 1827)  performed a series of experiments to study the diffraction of light and disapproved Newton’s theory and supported Huygens’s wave theory of light.
• The exact nature of light waves was not known, because only mechanical waves were known at that time. For the propagation of mechanical waves, the medium is required. But light waves were found to travel in a vacuum. Hence in 1860 Maxwell proposed that the light are electromagnetic waves and do not require any medium for propagation.
• In 1888 Hertz and in 1900 Hallwachs and Lenard observed that when light falls on the metal surface, electrons are ejected and that the kinetic energy of emitting electrons does not depend on the intensity of light used.  This observation is known as the photoelectric effect. This effect was explained by Albert Einstein in 1905 on the basis of the particle model of light.
• Now it is accepted by the scientific community of the world that light has a dual nature particle as well as wave. A particular nature either wave or particle depends on circumstances.

Phenomenon Associated With Light:

Rectilinear Propagation of Light:

Light travels in a straight lines unless it is reflected by a polished surface or the medium of propagation is changed.

Reflection of Light:

When light rays are incident on a polished  surface, they are sent back in the same medium such that the angle of incidence is equal to angle of reflection and the incident ray, the reflected ray and the normal at the point of incidence lie in same plane.

Refraction of Light:

When light ray traveling in one optically active medium enters another optically active medium then the light ray deviates from its path. This phenomenon is known as refraction of light.

Diffraction of Light:

When a light wave is obstructed by an obstacle, then the rays round the corner. This phenomenon is called diffraction of light.

Interference of Light:

Light coming from two coherent sources interfere and produce maxima and minima depending upon path difference between the two waves. Thus alternate bright and dark regions can be obtained on the screen kept in the path of the two waves. This phenomenon is known as interference of light.

Polarization of Light:

The electric field in a light wave vibrate in the direction perpendicular to the direction of propagation of the wave. But there are infinite directions which are perpendicular to the direction of propagation of the wave. Thus the wave can vibrate in any plane perpendicular to the direction of propagation of the wave. Such wave is called non polarised wave.

By certain arrangements the non-polarized light wave is made to vibrate in one and only one plane, then the light is called polarised light.

Scattering of Light:

When a parallel beam of light passes through a gas, a part of it appears in directions other than the incident direction. This phenomenon is known as scattering of light.

Spectrum of Light

Visible Spectra:

The part of the spectrum of light which is visible to the human eye is called visible spectra. The frequency of visible light varies from  3.8 x 10¹⁴ Hz to 7.8 x 10¹⁴ Hz. The corresponding wavelengths are 380 nm and 780 nm.

The colour sensation of the human eye is related to the wavelength of light. The light close to 780 nm appears red and light close to 380 nm appears violet. The human eye is more sensitive to yellow and green light.

Colour Wavelengths:  Red (620 – 780 nm) Orange (590 – 620 nm) Yellow (570 – 590 nm) Green (500 – 570 nm) Blue (450 – 500 nm) Violet (380 – 450 nm).

Non Visible Spectra:

Light waves having a wavelength above 780 nm or having a frequency less than 3.8 x 1014 Hz are said to be lying in the infrared region.

Light waves having a wavelength above 380 nm or having frequency more than 7.8 x 1014 Hz are said to be lying in the ultraviolet region.

Characteristics of Light:

• When a monochromatic light travels from one medium to another, its wavelength changes but its frequency remains constant.
• In the electromagnetic waves the angle between electric field vector and magnetic field vector is 90°.
• In the propagation of electromagnetic waves, the angle between the direction of propagation and the plane of polarisation is zero.
• In the propagation of electromagnetic waves, the angle between the plane of vibration and the plane of polarisation is 90°.
• The oscillating electric and magnetic vector of an electromagnetic wave are oriented along mutually perpendicular direction and are in phase.
• Electromagnetic waves transport energy, momentum, information.
• Electromagnetic waves do not carry any charge.Energy of visible light is low (few eV)

Sources of Light:

Sun is major source of light. Some artificial sources of light are as follows

Thermal Sources :

These sources light of all wavelengths in the visible region i.e. having wavelengths in the range from 390 nm to 760 nm. Example: incandescent Bulb, Gas Discharge Tubes. A gas discharge tube emits light of a few wavelengths band. Example: Neon tube gives a characteristic red light.

Luminescent Sources:

These sources emit light partly in the visible region and partly in the ultraviolet region. Example: Fluorescent tube.

Phenomenon of Luminescene:

The phenomenon of emission of light after absorbing some electromagnetic radiations is called luminescene.

Types of Luminescene: 

• Electroluminescence: It is a phenomenon of emission of light by electrical means.
• Chemiluminescence: It is a phenomenon of emission of light by chemical reactions.
• Bioluminescence: It is a phenomenon of emission of light by biochemical reactions.

Photometry:

The branch of physics which deals with the measurement of light energy or with the comparisons of illuminating power of the sources or with the comparisons of illumination of the surfaces is called photometry.

 Efficiency of Light Source:

When a source of light emits energy, the whole of the radiant energy does not lie in the visible region. A small amount of energy lies in the nonvisible region i.e. infrared and ultraviolet region.

The efficiency of a light source is defined as the ratio of output power in the visible region to the input electrical power.

Luminous flux is measured in lumen (lm) and input electric power is measured in watts (W), hence unit of efficiency of a light source is lumen per watt (lm W-1)

Terminology:

• Optical Medium: The medium capable of transmitting light is called an optical medium.
• Isotropic medium: The homogeneous medium, which has the same properties in all the directions is called an isotropic medium.
• Monochromatic light: A light having one single wavelength is called as monochromatic light (Mono means one and chroma means colour).
• Incident ray: The light ray, which is falling on reflecting or refracting surface is called the incident ray.
• Point of incidence: The point at which the incident ray cuts the reflecting or refracting surface is called the point of incidence.
• Normal: A perpendicular drawn to the surface at the point of incidence is called the normal.
• Angle of incidence: The angle made by the incident ray with the normal at the point of incidence is called the angle of incidence.

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In this article, we shall study the use of the phenomenon of polarization of light, principle, construction, and working of polaroids.

Double Refraction:

In the case of some crystals like calcite or quartz, a single ray of unpolarized light from a point source of light splits up into two refracted rays casting two images of the point object. This phenomenon is known as double refraction or birefringence. In this case, both the refracted rays are polarized in two mutually perpendicular planes.

Nicol’s Prism:

The phenomenon of double refraction is used to get polarized light from Nicol prism. This was constructed by William Nicol in 1828 A.D. In this method ordinary rays are eliminated by total internal reflection and only extraordinary rays are allowed to come out of the prism.

Construction:

A naturally occurring form of calcium carbonate is known as Calcite or Iceland spar. In Nicol’s prism, the length of the crystal is three times the breadth.  The ends are grounded until they make an angle of 68° and 112° to form a parallelogram. These crystals are cut into two halves and cemented together by means of Canada balsam.  This gives Nicol prism. Nicol’s prism can be used as a polarizer as well as an analyzer.

Polaroids:

Polaroid is a large sheet of synthetic material packed with tiny crystals of a dichroic substance oriented parallel to one another so that it transmits light only in one direction of the electric vector.

Doubly refracting crystals split the incident unpolarized light passing through them into O – light, and E – light which are plane-polarized in mutually perpendicular planes. Some such crystals have the property of absorbing the ordinary and extraordinary light unequally. This property is called dichroism and crystal possessing this property is called dichroic.  e.g. tourmaline. It absorbs O – light and transmits E – light.

Polaroids are artificially prepared dichroic substances. In 1852, W. H. Herapath discovered synthetic crystalline material iodosulphate of quinine known as herapathite which exhibits dichroism. In 1934 E.H. Land embedded tiny herapathite crystals in cellulose acetate with their optic axis parallel. The layers of the crystal were mounted between two glass sheets for protection. This acts as a sheet of the polarizer and called as polaroids. It can be used as a polarizer as well as an analyzer.

Uses of Polaroids:

• Light usually scatters in all directions; but when it’s reflected from flat surfaces, it tends to become polarized. This creates an annoying and sometimes dangerous intensity of reflected light that causes glare and reduces visibility. Polaroids are used in sunglasses to cut off the glare reflected by horizontal surfaces.
• Polaroids are used in glass windows of an airplane to control the intensity of light entering the airplane.
• Polaroid glasses are used to view three-dimensional pictures and movies.
• Polaroids are used as a filter in the photographic camera.
• They are used in the production and analysis of plane-polarized light.
• They are used to improve colour contrast in old oil paintings.
• They are used in calculators, watches, monitors of laptops which have LCD screens.

Doppler Effect in Light:      

The apparent change in the frequency of the light observed by an observer, due to relative motion between the source of the light and the observer, is called the Doppler effect.

One major difference between Doppler Effect exhibited by sound and light is as follows: In the case of sound, the frequency change depends on whether the source is moving or the observer is moving even if their relative velocities are the same. In the case of light, the Doppler Effect depends only on the relative velocity of the source and the observer, irrespective of which of the two is moving. Hence the Doppler effect exhibited by light is symmetric.

Red Shift of Light:

When the source and observer move away from each other, the wavelength in the middle of the spectrum will be shifted towards red. This phenomenon is called a red shift due to Doppler effect. When the source and observer move away from each other, the observer observes the lower frequency than the actual frequency of the light (towards red).

Blue Shift of Light:

When the source and observer move towards each other, the wavelength in the middle of the spectrum will be shifted towards blue. This phenomenon is called a blue shift due to the Doppler Effect. When the source and observer move towards each other, the observer observes the higher frequency than the actual frequency of the light (towards blue).

Applications of Doppler Effect in Light:

• It is used to measure the speed of rotation of the sun.
• It is also used in the measurement of plasma temperature.
• Edwin Hubble (1889-1953) found a method to red shift and blue shift to study the relative motion of the stars and galaxies.
• It is used in tracking satellites.
• They are used in speed guns to measure speed of cricket and tennis ball.

Use of Doppler Effect of Light to Measure Speed of Rotation of the Sun:

A spectrum is an arrangement of electromagnetic radiation, which includes visible light, placed in order of wavelength. The spectrum of light tells us about the composition of an object such as a star, its temperature, its pressure, the abundance of elements in the star, its motion (velocity), etc.

We observe the spectrum from different regions. If the lines are shifted towards the red end (longer wavelengths) relative to a spectrum at rest than that part of the Sun is moving away from us; a blue shift tells us that region of the Sun is approaching us. The extent of the shift tells us the velocity.

The east and west edges of the sun are photographed. Each photograph contains absorption lines due to elements like vapourized ion in the sun and oxygen in the earth’s atmosphere. Then the two photographs are put together such that the oxygen lines coincide. We observe a relative displacement in the iron lines w.r.t. each other. One line corresponds to the edge of the sun approaches the earth while another line corresponds to the other edge of the sun that recedes from the earth.

The difference in spectral lines is used to measure the speed of rotation of the sun. It is nearly 2 km/s.

Use of Doppler Effect of Light to Measure Plasma Temperature:

Plasma is phase constituting very hot gases where the temperature is of the order of millions of degrees Celsius. Plasma state is obtained in thermonuclear fusion experiments. In this state, the gas molecules are moving towards or away from the observer at very high speeds. Due to the Doppler Effect, the wavelength observed of a particular spectral line is different from the actual wavelength.

One edge of the line corresponds to an apparently increased wavelength due to the molecules directly moving towards the observer while the other edge of the line corresponds to an apparently decreased wavelength due to the molecules directly moving away from the observer. The line is thus observed to be broadened. A diffraction grating is used to measure the breadth of the line. As we know the wavelength λ and speed of light v, the temperature of the gas can be obtained using the formula

Where R is the molar gas constant, T is the temperature of the gas, M is the molecular mass of the gas.

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In this article, we shall study the concept of polarization of light, Brewster’s law associated with it.

Ordinary Light:

Light waves are transverse in nature. The direction of its vibration is in the plane which is perpendicular to the direction of propagation of the wave. Thus wave can vibrate in any plane (infinite possibilities) which is perpendicular to the direction of propagation of the wave. Such a light wave is called unpolarized light.

Transverse Nature of Light Waves:

The following phenomena prove the transverse nature of light.

• The intensity of light at a place changes continuously.
• Light can be polarized.

When light waves are passed through two crystalline slits say A and B (These slits are the tourmaline plates cut parallel to the axis of crystal). Ordinary light (say from the sun) is incident on the crystal A.

When crystal A and crystal B are parallel to each other, the intensity of the light emerging from crystal A is constant at any orientation of A and passes through crystal B without any change.

Now crystal B is rotated w.r.t. crystal A, the intensity of emerging light from crystal B decreases and becomes zero when crystal B is at right angle w.r.t crystal A.

This experiment proves the transverse nature of the light waves. Crystal A is called polarizer and crystal B is called analyzer.

Plane Polarized Light:

When the transverse vibrations of the light wave are confined to a plane containing the direction of propagation, the light is said to be plane-polarized. The plane in which the vibration lie is called the plane of vibration. The plane perpendicular to the plane of vibration is called the plane of polarization and the light is said to be polarized in it. In this plane the vibrations of light are absent.

Schematic Representation of Light:

Polarized light:

When the transverse vibrations of the light wave are confined to a plane containing the direction of propagation, the light is said to be plane-polarized.

Plane of vibration:

The plane in which the vibrations of polarized light takes place is called the plane of vibration.

Plane of polarization:

The plane perpendicular to the plane of vibration in which there are no vibrations of polarized light is called the plane of polarization.

Polarization:

The phenomenon of restriction of the vibrations of light waves in a particular plane perpendicular to the direction of propagation of wave motion is called polarization.

Polarizer:

The substances which bring about the plane polarization of light are called as polarisers. e.g. Tourmaline crystal, Nicol prism.

Unpolarized light:

Light waves are transverse in nature. The direction of a light in which the vibrations of the electric vectors are in all possible directions, which are perpendicular to the direction of propagation

Unpolarized light:

Light waves are transverse in nature. The direction of a light in which the vibrations of the electric vectors are in all possible directions, which are perpendicular to the direction of propagation of the wave is called unpolarized waves.

Plane of Incidence:

The plane containing the incident and reflected rays and normal to the surface is called the plane of incidence.

Diagram Showing Partial Polarization:

Malus showed that when a beam of unpolarized light is reflected from a nonmetallic surface, the reflected light is partially plane-polarized. The degree of polarization depends on the angle of incidence. The particular angle of incidence at which the reflected light is completely plane polarized is called the angle of polarization or polarizing angle. The vibrations of the reflected plane-polarized light are found to be perpendicular to the plane of incidence.

Distinguishing between Polarized Light and Unpolarized Light:

Brewster’s law:

The tangent of the polarizing angle is equal to the refractive index of the material of the surface from which reflection is taking place.

Mathematically,     μ = tan i_p

This polarizing angle is the characteristic of the medium.

i_p = angle of incidence and r = angle of refraction

Proof: 

Let us consider the unpolarized monochromatic light incident in the air at the polarizing angle i_p on the plane surface XY of the transparent medium of refractive index μ. Experimentally Brewster proved that ∠ SQR = 90°.

Brewster further proved that the polarizing angle is a function of a wavelength of the light. This law is not obeyed by polished metallic surfaces.

To prove that at the polarizing angle the reflected ray and refracted ray are mutually perpendicular.

i_p = angle of incidence and r = angle of refraction

Numerical Problems:

Example – 01:

Find the refractive index of glass if the angle of incidence at which the polarization of light reflected from the surface of the glass is 58°.

Given: the polarization angle = i_p = 58°

To Find: Refractive index of the medium = μ = ?

Solution:

μ = tan i_p = tan 58° = 1.6003

Ans: Refractive index of the medium is 1.6003

Example – 02:

In a glass plate of refractive index is 1.732 is to be used as a polarizer, what would be the polarizing angle and angle of refraction.

Given: Refractive index of the medium = μ = 1.732

To find: polarising angle = i_p = ?, angle of refraction = r =?

Solution:

μ = tan i_p = 1.732

∴  i_p = tan^-1(1.732) = 60°

By snell’s law

μ = sini/sinr

sin r = sini/μ = sin 60°/1.732 = 0.8660/1.732 = 0.5

∴  r = sin^-1(0.5) = 30°

Ans: Polarizing angle is 60° and angle of refraction is 30°

Example – 03:

A ray of light travelling through air, falls on the surface of a glass slab at an angle i. it is found that the angle between the reflected and refracted ray is 90°. If the speed of light in glass is 2 x 10⁸ m/s, find the angle of incidence. c = 3 x 10⁸ m/s.

Given:  angle between the reflected and refracted ray is 90°, speed of light in glass is = c_g = 2 x 10⁸, speed of light in air = c_a = 3 x 10⁸ m/s

To find: angle of incidence = i = ?

Solution:

The refractive index of glass is given by

μ_g = c_a/c_g = 3 x 10⁸ / 2 x 10⁸ = 1.5

Now the angle between the reflected and refracted ray is 90°

Hence the angle of incidence is equal to the angle of polarization.

μ = tan i_p = 1.5

∴  i_p = tan^-1(1.5) = 56°19′

Ans: Angle of polarization is 56°19′

Example – 04:

If the critical angle of the medium is sin^-1 (3/5), find the polarizing angle.

Given: Critical Angle = i_c = sin^-1 (3/5)

To Find: Polrizing angle = i_p = ?

Solution:

i_c = sin^-1 (3/5)

Sin i_c = 3/5

Refractive index = μ = 1/ Sin i_c = 5/3

μ = tan i_p = 5/3

∴  i_p = tan^-1(5/3) = 56°19′

Ans: Angle of polarization is 59°2′

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