XI-Physics CH-8

Physical Optics and Gravitational Waves

TOPIC 1Polarization of Light
SQ 8.1.1

With what does this chapter deal?
Answer
This chapter deals with two major areas of physics, namely polarization of transverse waves and gravitational waves.
SQ 8.1.2

With what does physical optics deal?
Answer
Physical optics with reference to polarization deals with the behaviour of light waves and their interaction with matter.
SQ 8.1.3

What is the plane of polarization?
Definition
The plane of polarization is the plane containing the direction of vibration of the particles of the medium and the direction of propagation of the wave.
SQ 8.1.4

Of what does a light wave produced by an oscillating charge consist?
Answer
It consists of a periodic variation of the electric field vector $\mathbf{E}$, accompanied by the magnetic field vector $\mathbf{B}$ at right angles to it.
SQ 8.1.5

What is unpolarized light?
Definition
Ordinary light has components of vibration in all possible planes. Such light is unpolarized.
SQ 8.1.6

What is polarized light?
Definition
If the vibrations of light are confined only in one plane, the light is said to be polarized.
SQ 8.1.7

Give examples of unpolarized light sources.
Examples
Sunlight, incandescent light bulbs, fluorescent light bulbs, and light from a candle or fire.
SQ 8.1.8

Define polarization.
Definition
Polarization is the process by which the electric and magnetic vibrations of light waves are restricted to a single plane of vibration.
SQ 8.1.9

Why does polarization not occur in sound waves?
Reason
Polarization is a property exhibited only by transverse waves such as light waves. It does not occur for longitudinal waves such as sound waves.
SQ 8.1.10

Name three methods by which unpolarized light can be polarized.
Methods
By passing light through a polarizing filter such as a polaroid sheet.
By using a polarizing beam splitter.
By employing certain optical crystals or materials, such as calcite and quartz.
SQ 8.1.11

How does a polarizing filter polarize light?
Working
When unpolarized light passes through the polarizing filter, only the electric field vector which is parallel to the axis of the filter can pass through it, while all other vectors are blocked.
Result
The resultant light then becomes polarized.
SQ 8.1.12

What is the basis of polarization?
Answer
The orientation of the electric field vector $\mathbf{E}$ of light waves in a specific direction is the basis of polarization.
TOPIC 2Types of Polarization
SQ 8.2.1

Define linear polarization.
Definition
When the electric field vector oscillates in a single plane, the light is said to be linearly polarized.
Example
Light passing through a polarizing filter, like sunglasses.
SQ 8.2.2

Define circular polarization.
Definition
When the electric field rotates circularly, either clockwise (right-handed) or counterclockwise (left-handed), the light is said to be circularly polarized.
Example
Light reflected off a Compact Disc or a Digital Versatile Disc.
SQ 8.2.3

Define elliptical polarization.
Definition
Elliptical polarization is a combination of linear and circular polarization, where the electric field vector traces an elliptical path.
Condition
The two components $E_x$ and $E_y$ are not equal, or they differ in phase by an arbitrary angle.
Example
Light passing through a stress plate or a waveplate.
SQ 8.2.4

Differentiate between linear and circular polarization.
Linear PolarizationCircular Polarization
The electric field vector oscillates in a single plane.The electric field vector rotates circularly.
Light through sunglasses is an example.Light reflected off a CD is an example.
TOPIC 3Production and Detection of Plane Polarized Light
SQ 8.3.1

Why is the light from an ordinary incandescent bulb unpolarized?
Reason
The light emitted by an ordinary incandescent bulb is unpolarized because its electrical vibrations are randomly oriented in space.
SQ 8.3.2

What are a polarizer and an analyzer?
Polarizer
The first sheet of polaroid on which unpolarized light is made incident, whose transmitted light is plane polarized.
Analyzer
A second sheet of polaroid placed after the polarizer to detect the polarized light.
SQ 8.3.3

What is observed when the axes of the two polaroids are parallel?
Answer
When the axes of the two polaroids are parallel, the light is transmitted through the second polaroid and is brightest.
SQ 8.3.4

What is observed when the analyzer is slowly rotated?
Answer
The light emerging from the second polaroid gets dimmer and dimmer and ultimately disappears when the axes become mutually perpendicular. The light reappears on further rotation.
SQ 8.3.5

What does the polaroid experiment prove?
Proof
This experiment proves that light waves are transverse waves.
Reason
If the light waves were longitudinal, they would never disappear even if the two polaroids were mutually perpendicular.
SQ 8.3.6

Can a polarizer be used as an analyzer?
Answer
Yes. An analyzer is also a polarizer that is placed after a polarizer, so the same sheet of polaroid can serve either purpose depending on its position in the arrangement.
TOPIC 4Polarization of Light by the Method of Reflection
SQ 8.4.1

What did Malus discover in 1808?
Discovery
In 1808 Malus discovered that polarized light is obtained when ordinary light is reflected by a plane sheet of glass.
SQ 8.4.2

How is it shown that reflected light is plane polarized?
Method
If the reflected light is viewed through a polaroid which is slowly rotated about the line of vision, the light is practically extinguished at a certain orientation of the polaroid.
SQ 8.4.3

What is the most suitable angle of incidence for glass?
Answer
The most suitable angle of incidence is about $57^{\circ}$ for glass, for which the reflected ray becomes plane polarized.
SQ 8.4.4

Give an everyday example of partial polarization by reflection.
Example
Light reflected from the surface of a table becomes darker when viewed through a rotated polaroid, showing that it is partially plane polarized.
Light reflected from a smooth surface of water is partially polarized parallel to the surface.
SQ 8.4.5

Define the polarizing angle.
Definition
The particular angle of incidence on a transparent medium, when the reflected light is almost plane polarized, is called the polarizing angle.
SQ 8.4.6

What is the relation between the reflected and refracted beams at the polarizing angle?
Answer
At the polarizing angle the reflected and refracted beams are at right angles to each other, so
$$\theta_p+\theta_r=90^{\circ}$$
SQ 8.4.7

Derive Brewster’s law.
Derivation
From Snell’s law
$$n_1\sin\theta_p=n_2\sin\theta_r$$
and since
$$\theta_r=90^{\circ}-\theta_p$$
we get
$$n_1\sin\theta_p=n_2\cos\theta_p$$
Result
$$\tan\theta_p=\frac{n_2}{n_1}$$
SQ 8.4.8

Write Brewster’s law when the first medium is air.
Derivation
If medium 1 is air then
$$n_1=1$$
and
$$n_2=n$$
Result
$$\tan\theta_p=n$$
Thus the tangent of the angle of polarization is numerically equal to the refractive index of the medium.
SQ 8.4.9

What is the Brewster angle?
Definition
The angle $\theta_p$ for which the reflected ray and the refracted ray make an angle of $90^{\circ}$ between them is called the Brewster angle.
SQ 8.4.10

Light strikes glass of refractive index √3 at the polarizing angle. Find the polarizing angle.
Solution
Using
$$\tan\theta_p=n$$
Calculation
$$\theta_p=\tan^{-1}(\sqrt{3})$$
Result
$$\theta_p=60^{\circ}$$
SQ 8.4.11

For light incident on glass at a polarizing angle of 60°, find the angle of refraction.
Solution
Since
$$\theta_r=90^{\circ}-\theta_p$$
Calculation
$$\theta_r=90^{\circ}-60^{\circ}$$
Result
$$\theta_r=30^{\circ}$$
SQ 8.4.12

Find the refractive index of a medium if its polarizing angle is 54.5°.
Solution
Using
$$n=\tan\theta_p$$
Calculation
$$n=\tan54.5^{\circ}$$
Result
$$n=1.4$$
SQ 8.4.13

What are the applications of Brewster’s angle?
Applications
Brewster’s angle is used to produce plane polarized light by reflection, and to remove glare from reflecting surfaces such as water, glass and roads, as is done by polaroid sunglasses.
TOPIC 5Malus’s Law
SQ 8.5.1

State Malus’s law.
Statement
The intensity of plane polarized light after passing through an analyzer is directly proportional to the square of the cosine of the angle between the transmission axis of the analyzer and the polarizer.
Formula
$$I=I_0\cos^{2}\theta$$
SQ 8.5.2

What relation does Malus’s law give?
Answer
Malus’s law gives a mathematical relation between the intensity of light incident on the first polaroid (the polarizer) and the intensity of light obtained after passing it through the second polaroid (the analyzer).
SQ 8.5.3

What is the purpose of an analyzer?
Answer
An analyzer is used to further reduce the intensity of light, and also to adjust it by adjusting the angle of the analyzer with respect to the polarizer.
SQ 8.5.4

What are polaroids?
Definition
Certain transparent crystalline materials, like tourmaline and calcite crystals, are capable of confining vibrations of light waves in only one plane. Such materials are called polaroids, which have high directionality in crystal structure.
SQ 8.5.5

By which natural phenomena can light be polarized?
Answer
Light can also be polarized by natural phenomena like reflection, refraction and scattering.
SQ 8.5.6

Derive Malus’s law from the resolution of amplitude.
Derivation
When incident polarized light of amplitude $A_0$ strikes the analyzer at an angle $\theta$, it is resolved into $A_0\cos\theta$ and $A_0\sin\theta$. The component $A_0\sin\theta$ is absorbed.
Since only
$$A=A_0\cos\theta$$
passes through, and $I\propto A^{2}$,
Result
$$I=I_0\cos^{2}\theta$$
SQ 8.5.7

What happens when the angle between polarizer and analyzer is zero?
Answer
If
$$\theta=0^{\circ}$$
then
$$I=I_0$$
The intensity transmitted through the analyzer is equal to the initial light intensity that passes through the polarizer.
SQ 8.5.8

What happens when the angle between polarizer and analyzer is 90°?
Answer
If
$$\theta=90^{\circ}$$
then
$$I=0$$
The light is extinguished completely, so no light is allowed to pass through the analyzer.
SQ 8.5.9

Polarized light of 75 W m⁻² passes through an analyzer at 30°. Find the emerging intensity.
Solution
Using
$$I=I_0\cos^{2}\theta$$
Calculation
$$I=75\times(\cos30^{\circ})^{2}=75\times0.75$$
Result
$$I=56.25\,\mathrm{W\,m^{-2}}$$
SQ 8.5.10

Polarized light of amplitude 5 units passes through a polarizer at 60°. Find the emerging amplitude.
Solution
Using
$$A=A_0\cos\theta$$
Calculation
$$A=5\times\cos60^{\circ}=5\times0.5$$
Result
$$A=2.5\ \text{units}$$
SQ 8.5.11

Define optical activity.
Definition
Optical activity is the ability of a substance to rotate the plane of polarization of light passing through it. The rotation is detected with a polarizer or analyzer.
SQ 8.5.12

Give examples of optically active substances.
Examples
Quartz crystals, cinnabar, sugar water, insulin and collagen are optically active substances.
SQ 8.5.13

On what factors does the amount and direction of optical rotation depend?
Factors
The type of substance.
The concentration of the substance.
The distance the light travels through it.
The wavelength of light.
SQ 8.5.14

Why does optical activity occur?
Reason
Optical activity occurs due to the asymmetric shape of molecules in the substance, such as being helical. A few millimetres thickness of such crystals will rotate the plane of polarization by many degrees.
SQ 8.5.15

Give a practical use of optical activity.
Use
Certain organic substances such as sugar and tartaric acid show optical rotation when in solution. This property can be used to determine their concentration in the solutions.
SQ 8.5.16

Why is polarization important in optics and photonics?
Answer
Polarization is essential for applications like polarized sunglasses, Liquid Crystal Display screens, and optical communication systems.
SQ 8.5.17

How does polarization help in imaging and microscopy?
Answer
Polarization enhances image quality by reducing glare, that is unwanted light which interferes with vision, and by improving contrast, especially in microscopy and medical imaging.
SQ 8.5.18

Give the medical applications of polarization.
Applications
Polarization is used in cancer diagnosis, tissue imaging and laser surgery, leveraging its ability to distinguish between different tissue types.
SQ 8.5.19

How is polarization used in astronomy?
Answer
Polarization helps us to analyze cosmic phenomena, like the polarization of light from distant stars or the cosmic microwave background radiation.
SQ 8.5.20

How are polarizers used in sky photography?
Working
A camera used to photograph clouds is fitted with a polaroid, so the light coming from the sky is polarized.
Result
Polarizers reduce the glare and haze produced by scattering of light by small particles in the atmosphere, and enhance contrast by blocking excessive bright white light.
SQ 8.5.21

How are polarizers used in stress analysis of materials?
Working
When a material is stressed, its molecular structure changes, affecting the way it interacts with light, and interference patterns or fringes are formed.
Use
By shining polarized light through the transparent material, researchers can determine stress patterns, identify weaknesses or defects, and analyze optical properties.
SQ 8.5.22

What is photoelasticity?
Definition
The technique of analyzing the stress patterns of a material by shining polarized light through it is known as photoelasticity. It is widely used in engineering, materials science and quality control.
SQ 8.5.23

Why are polaroid sunglasses better than ordinary sunglasses?
Reason
Polaroid sunglasses are fitted with polarizing filters which block the partially polarized light reflected from surfaces such as roads and water.
Result
They therefore cut down glare, whereas ordinary sunglasses only reduce the overall brightness.
TOPIC 6Gravitational Waves
SQ 8.6.1

Define a gravitational wave.
Definition
A gravitational wave is a stretching and compressing of space-time, and can be observed by measuring the change in length between two objects.
SQ 8.6.2

What are gravitational waves described as?
Description
Gravitational waves are ripples in the fabric of space-time, produced by violent cosmic events like colliding black holes or neutron stars, that travel at the speed of light carrying information about their source.
SQ 8.6.3

Give a simple example to understand gravitational waves.
Example
If we throw a stone into a pond, the stone creates ripples on the water surface, which represents space-time. These ripples travel outward, carrying information about the stone, which represents the cosmic event.
SQ 8.6.4

What is a binary system in the context of gravitational waves?
Definition
A binary system is a system consisting of two compact objects, such as black holes, neutron stars or white dwarfs, which are orbiting each other and emitting gravitational waves.
SQ 8.6.5

What are continuous gravitational waves?
Definition
When a single massive object spins with a constant rate, such as a neutron star, continuous gravitational waves are produced with a constant frequency and amplitude.
Source
White dwarf binary systems produce continuous gravitational waves.
SQ 8.6.6

What are compact binary inspiral gravitational waves?
Definition
They are produced by a binary system such as binary neutron stars, binary black holes, or a neutron star and black hole orbiting each other.
Characteristic
In this type there is a gradual increase in frequency and amplitude of the waves.
SQ 8.6.7

What are burst gravitational waves?
Definition
Burst gravitational waves are produced by violent events like supernovas, gamma-ray bursts or cosmic strings.
SQ 8.6.8

What are stochastic gravitational waves?
Definition
Stochastic gravitational waves are weak, random signals produced by the superposition of many weak gravitational wave sources, such as distant binary systems.
Property
These waves are the most difficult to detect.
SQ 8.6.9

Which observatories detect gravitational waves?
Answer
Gravitational waves can be detected by observatories like LIGO, the Laser Interferometer Gravitational wave Observatory in the USA, and Virgo, a large scale gravitational wave observatory in Cascina, Italy.
SQ 8.6.10

What information do gravitational waves from binaries carry?
Answer
The waves carry information about the system’s mass, spin and merger dynamics, offering insights into these extreme cosmic objects, and they move with the speed of light.
SQ 8.6.11

What is a merger in the context of binary systems?
Definition
A merger is the collision and union of two massive objects resulting in one more massive single object. Mergers are among the most intense cosmic events.
SQ 8.6.12

How do gravitational waves propagate through the universe?
Answer
As the masses orbit and accelerate, their gravitational intensity fluctuates, generating waves that radiate outward in all directions. These waves are not bound by the binary system’s gravity and travel freely through spacetime at the speed of light, weakening in intensity with distance.
SQ 8.6.13

On which properties of a system do the characteristics of gravitational waves depend?
Properties
The masses of the objects.
The orbital period and frequency.
The eccentricity of the orbit.
SQ 8.6.14

Define eccentricity and give its values for different orbits.
Definition
Eccentricity is a measure of the amount by which an object deviates from a perfect circle.
Values
$$e=0$$
is a circular orbit, $0<e<1$ is an elliptical orbit,
$$e=1$$
is a parabolic trajectory and $e>1$ is a hyperbolic trajectory.
SQ 8.6.15

What is space-time distortion?
Definition
Gravitational waves passing through a body with mass can cause the body to experience periodic stretching and compressing, also known as space-time distortion.
SQ 8.6.16

What are tidal forces?
Definition
The effect of periodic stretching and compressing caused by a gravitational wave is known as tidal forces, and it is a result of the wave’s oscillating nature.
SQ 8.6.17

How are tidal forces formed?
Formation
As the gravitational wave passes through a body, it causes the spacetime around the body to oscillate, leading to a periodic stretching and compressing of the body in the direction perpendicular to the wave’s propagation.
Analogy
This effect is similar to how the tides on Earth are caused by the gravitational pull of the Moon and Sun.
SQ 8.6.18

On what does the amount of stretching and compressing depend?
Answer
The amount of stretching and compressing depends on the strength of the gravitational wave, as well as on the mass and size of the body. This effect is an important prediction of Einstein’s general theory of relativity.
SQ 8.6.19

What is the amplitude of gravitational waves passing through the Earth?
Answer
The amplitude of these waves is extremely small, typically of the order of $10^{-18}$ to $10^{-21}\,\mathrm{m}$. Therefore the distortion is incredibly tiny and requires extremely sensitive instruments to detect.
SQ 8.6.20

What is the importance of gravitational waves despite their small amplitude?
Answer
Gravitational waves offer a unique window into the universe, allowing us to study strong-field gravity, to test general relativity, and to explore the universe in ways previously impossible.
SQ 8.6.21

Does every accelerating object produce gravitational waves?
Answer
Yes. Every physical object that accelerates produces gravitational waves, including vehicles and airplanes. However, the masses and accelerations of objects on the Earth are too small to make gravitational waves big enough to be detected.
SQ 8.6.22

Gravitational waves have a wavelength of 4000 km. Find their frequency.
Solution
Since
$$v=c=f\lambda$$
therefore
$$f=\dfrac{c}{\lambda}$$
Calculation
$$f=\frac{3\times10^{8}}{4\times10^{6}}$$
Result
$$f=75\,\mathrm{Hz}$$
SQ 8.6.23

A binary system emits gravitational waves of frequency 10⁻⁴ Hz. Find their wavelength.
Solution
Since
$$\lambda=\dfrac{c}{f}$$
Calculation
$$\lambda=\frac{3\times10^{8}}{10^{-4}}$$
Result
$$\lambda=3\times10^{12}\,\mathrm{m}$$
TOPIC 7Interferometer
SQ 8.7.1

What are the main differences between LIGO and a conventional interferometer?
Differences
LIGO is $1000$ times larger than a conventional device.
LIGO uses a LASER, whereas a conventional interferometer has a normal light source.
SQ 8.7.2

What is the function of the laser in a gravitational wave interferometer?
Answer
The laser produces a stable and high intensity beam of light.
SQ 8.7.3

What is the function of the power recycling mirror?
Answer
The power recycling mirror continually reflects laser light that has already travelled through the instrument back into the interferometer, and hence the term recycling is used.
SQ 8.7.4

What is the function of the beam splitter and the mirrors?
Beam Splitter
It divides the laser beam into two perpendicular beams.
Mirrors
They reflect the beams, creating two perpendicular arms.
SQ 8.7.5

What is the purpose of the Fabry-Perot cavity?
Answer
The Fabry-Perot cavity consists of two mirrors facing each other. The purpose of the cavity is to enhance the path length.
SQ 8.7.6

What is the function of the photodetectors and arm cavities?
Photodetectors
They measure the returning beams, detecting tiny phase shifts if any.
Arm Cavities
They enhance the laser light, increasing sensitivity.
SQ 8.7.7

Explain the working of a gravitational wave interferometer.
Working
A laser beam is split into two perpendicular beams, each travelling down two identical arms. The beams bounce off mirrors at the ends of each arm and return to the starting point, where they are recombined.
Detection
If a gravitational wave passes through, it causes a tiny disturbance in the distances between the mirrors, resulting in a phase shift between the two beams.
SQ 8.7.8

How is the gravitational wave finally detected?
Answer
When the beams recombine they create an interference pattern, which is measured by a photodetector. The tiny phase shift caused by the gravitational wave alters the interference pattern, allowing the detector to sense the wave’s presence.
SQ 8.7.9

When were gravitational waves first observed and from what source?
Answer
On 14 September 2015 the universe’s gravitational waves were observed for the first time. They came from a collision between two black holes and took $1.3$ billion years to arrive at the LIGO detector in the USA.
SQ 8.7.10

Who received the Nobel Prize for the observation of gravitational waves?
Answer
Rainer Weiss, Barry C. Barish and Kip S. Thorne received the Nobel Prize in 2017 for their work on the observation of gravitational waves.
SQ 8.7.11

Which Pakistani scientist was a member of the gravitational wave team?
Answer
Dr. Nergis Mavalvala, a Pakistani-American astrophysicist and a professor at the Massachusetts Institute of Technology, was one of the team members.
SQ 8.7.12

Describe the Virgo detector.
Description
Virgo is another facility for measuring gravitational waves, working under the European Gravitational Observatory at Cascina near Pisa, Italy.
Comparison
Virgo is also an interferometer with two arms of $3\,\mathrm{km}$, whereas LIGO has $4\,\mathrm{km}$ arms. Its first detection was in 2017.
SQ 8.7.13

After what is the Virgo observatory named?
Answer
The Virgo Observatory is named after the Virgo constellation, which is visible in the night sky during the months of March, April and May. The Virgo cluster is a group of about $1500$ galaxies about $50$ million light years away.
SQ 8.7.14

What is a light year and what is its approximate value?
Definition
One light year is the distance which light travels in one year.
Value
$$1\,\mathrm{LY}=9.5\ \text{billion km}$$