Category: Physics Notes PPT

In physics, thermodynamics is the study of the effects of heat, energy and work on the system. Entropy is the measure of the thermal energy of a system per unit temperature.

 

It is the measure of unavailable energy in a closed thermodynamic system and is concerned with measuring the molecular disorder, or randomness, of the molecules inside the system. In simple terms, entropy is the degree of disorder or uncertainty in the system.

 

Enthalpy is a central factor in thermodynamics. It is the total heat contained in the system. This means if the energy is added, the enthalpy increases. 

 

If the energy is given off, then the enthalpy of the system decreases.

 

 

Enthalpy And Entropy In Thermodynamics

Enthalpy

In thermodynamics, 

H = U + PV

 

Where U is the internal energy 

P is the external pressure

V = Volume

H = Enthalpy; for example, consider a system that has molecules moving in random motion. These molecules have some attraction between them, and so they have potential energy.

 

Together these energies are made up of internal energy.

 

Here, the system is in a free state.

 

To establish the pressure and volume inside the system, some work is done. The energy used is actually the PV.

 

So,

 

Heat content = Internal energy = It comes from atoms and molecules or electrons at a quantum level as they are very small in range.

 

Here,  PV = is the energy required to establish a system at pressure P, volume V from empty space.

 

Hence, the total energy which is required in the whole process is called the enthalpy. 

 

The unit of H is KJ/mole.

 

The major drawback of H is that it is immeasurable, so we consider ΔH (enthalpy change).

 

Entropy 

The term entropy took birth from a spontaneous process (a process that happens itself or by a little push).

 

When the randomness of the system increases, the process is said to be spontaneous.

 

For example, you are sitting in the classroom according to your wish.

 

Your teacher makes you sit in your respective seats. In this way, randomness is created in the classroom because of external energy or a little push (by your teacher) applied to you. Such a process is spontaneous by nature.

 

The measure of such a disorganized motion of molecules is called the entropy (denoted by S).

 

When we consider nature, entropy keeps on increasing. Therefore, nature is spontaneous.

 

Relation Between Entropy And Enthalpy

Enthalpy is the sum total of all the energies, whereas entropy is the measure of the change in enthalpy/temperature.

 

Let’s understand by an example,

 

Suppose you have Rs. 100 with you. If someone gives you a Rs. 50 note, it will make a difference. 

 

If you have Rs. 1,00,00,000 with you and someone gives you Rs. 50, though the change is the same.

 

So, we need another term to measure the difference made by this 50 rupee note.

 

We can divide the change with the amount you initially had.

 

Like in the first case,

 

It is  50/100=0.5

 

While in the second case, it is

 

50/1,00,00,000=0.000005.

 

In thermodynamics, 

 

This ratio is called entropy i.eThe heat supplied (roughly the change in enthalpy, ΔH) divided by temperature (directly related to enthalpy).

 

Difference Between Enthalpy And Entropy

 

Spontaneity 

As we discussed above, there is a randomness in the molecules under the free gas expansion. 

 

∆H = -ve (heat is given off to the surroundings or exothermic), the stable system and hence spontaneous.

 

∆H = +ve  (heat added from surroundings), the entropy increases. 

 

∆S = +ve, randomness increases.

 

If  ∆S = -ve when water changes to ice, entropy decreases.

 

Here, due to variation, we couldn’t obtain perfect spontaneous reactions. 

 

So,

 

ΔG came as the perfect step to determine the spontaneity of reaction with a 100% guarantee.

 

G =  H – T S,

 

Where G is the Gibbs free energy.

 

If the reaction is carried out at ΔT=0 (T in kelvin), then

 

ΔG = ΔH – TΔS

 

This equation is called the Gibbs Helmholtz equation.

 

Where ∆G is the change in free energy.

 

For spontaneous reactions, ∆G is always <0.

 

Hence, Gibbs free energy is a thermodynamic potential that can be used to calculate the useful work done by a thermodynamic system at a constant temperature and pressure.  

Lens

Mirror

The Lens is a material made of glass or plastic bounded by two surfaces. It can either be curved at one side or both sides. 

The Mirror implies a glossy surface at one end and produces an Image of an object by reflection. 

A Mirror follows the laws of reflection.

The Lens is a transparent thick material that is shaped in such a manner that it bends the light passing through it. 

It can converge the light Rays onto a specific point or diverge it away from that point.

A Mirror is a reflector that is shiny from one side and reflects the light Rays coming from the object to make it appear as an Image to the other side.

The Lens is of two types viz: Concave Lens and convex Lens.

A Mirror is of three types viz: concave Mirror, plane Mirror, and convex Mirror

A Lens has two focal points namely F and 2F.

A plane Mirror has no focal point.

It forms an Image the same size as that of the object.

A concave Lens is a diverging Lens

A convex Lens is a converging Lens.

A concave Mirror is a converging Mirror A convex Mirror is a diverging Mirror.

Concave Lenses are used as an aid for people having Myopia or nearsightedness.

Convex Lenses are used as an aid for people having Hypermetropia or farsightedness.

Examples of Concave Mirror – shaving/make up Mirror

In streetlights and car headlights

Convex Mirror – Rearview Mirror in two and three-wheelers

The formula for the image formation by the lens is:

[frac{1}{v}-frac{1}{u}=frac{1}{f}]

Where,

v=the distance of image

u=the distance of object

f=focal length

The formula for the image formation by the lens is:

[frac{1}{v}+frac{1}{u}=frac{1}{f}]

Where,

v=the distance of image

u=the distance of object

f=focal length

Image formation for the object placed at infinity:

1. Concave Lens

2. Convex Lens

Sign conventions:

The Ray diagram for the object placed at infinity:

1. Concave Mirror

2. Convex Mirror

Image formation for the object placed at F

1. Concave Lens

2. Convex Lens

Image formation for the object placed at F

Image formation for the object placed between F (focus) and O (optical center)

Image formation for the object placed between F and C

Real-life example:

Whatever we observe around us is because of something called ‘Lens’. Eyes are natural Lenses that help us to read, write, watch movies, distinguish among various shades of a single color.

Real-life example:

Mirrors help us see our Image.

We use Mirrors at beauty salons, on vehicle headlights, torchlights, streetlamps, 

Intuition plays an important role in physics for learning mechanics.

If you have a strong intuition, it becomes easy for you to assimilate things.

If you are studying rotational mechanics, it becomes necessary for you to groom up your intuitive ability to understand things.

That’s why rotational mechanics is one of the toughest topics in mechanics.

Let’s understand the concept of torque interactively by using our intuition.

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If we apply a force on the fans of a fan, it starts rotating, however, on applying a force at its center, it remains unmoved. 

This is because no translational motion occurs at the center.

This center is the fixed point of a fan. On drawing a line through this point, we get an axis that keeps the fan rotating in a plane perpendicular to it.

So, this axis is the axis of rotation.

Let’s Consider Two Cases Here

Case 1: On applying a force towards the center, this force will pass through the axis, and no force will act on it.

Since the distance between the force F, and the distance ‘d’, is zero. That’s why the fan remains unmoved.

Case 2: Now, if we apply a force of the fans of this fan, the force won’t pass through the axis, because force F is at a distance ‘d’, from the axis of rotation.

Here, the rotation will occur.

So, the force acts at a perpendicular distance ‘d’, from the axis of rotation of the fan.

What is Torque?

The product of the force and the perpendicular distance is the ‘torque’. It is denoted by a Greek letter, tau, or て. Its formula is:

て = F x d

So, in case 1, The product, て is zero because the perpendicular distance between the axis and the force applied is zero.

In case 2, on applying a force at a distance ‘d’, from the axis, we got て = F x d; however, the magnitude of the force is the same in both the cases.

It means that the only application of force won’t rotate the fan; rather torque is responsible for its rotational motion.

Difference Between Torque and Power

Torque and horsepower are both ways of measuring force.

Torque measures force and power measures work i.e., force overtime.

We can imagine torque as a twisting or whirling force. So, if we apply a force on a body at some distance from its axis of rotation, a twisting force or torque supplied to make it rotate.

The same happens with a socket wrench while tightening down a bolt. We apply a force at a distance, and that supplies torque to that bolt to fasten down it.

Let’s consider a toolbox and one meter-long wrench, and if we fasten a bolt by applying one Newton of force, it means that we are applying one Newton-meter torque on it

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The same thing happens with the engine of our car.

Engine torque measures the amount of the force that an engine produces.

Let’s consider a piston, driving the crankshaft; we can see that where it is attached, turns around its axis just like the wrenches turned around the bolt.

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The combustion within the cylinder supplies the force in pressing down the piston, pushes the crankshaft.

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The force exerted on the crankpin is transferred to the shaft to get it spinning.

How is the Torque Determined?

The torque is determined by two factors, i.e: Torque = The product of the amount of force on the crankpin which comes from the piston, and the distance of that force from the center axis, or throws which vary by the crankshaft.

If the throw remains the same, we generate more force from the piston which means more displacement.

We can increase torque if the force from the piston remains the same. Therefore, we can increase the distance of the pin from the crankshaft center to increase the torque.

Difference Between Torque and Power in Cars

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Let’s consider a car moving at a certain speed ‘s’. If it moves at a high speed, it means an enormous force is supplied to make it move faster, which means fastly, the wheels are spinning.

Well, fastly the car moves, the more revolutions wheels make while spinning. So, horsepower is the torque multiplied by rpm (revolutions per minute) or the rate of work done.

So, how fast a wheel spins is the point where we get consistent with the force acting on the piston.

The faster the shaft spins by applying the same force at the same distance, the more power it will make. 

Let’s Understand this by an Example

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Car A has 300 Horsepower and has 100 N-m of torque.

Car B has 100 hp and 300 N-m of torque, which is 1/3 rd of the power and thrice the torque as that of in car B.

So, car A has more hp i.e, thrice to that of car B, and ⅓ of torque.

Which means car A moves faster as it has high acceleration.

The most common confusion in students is what’s the difference between EMF and voltage. To understand the difference between EMF and voltage, let us first understand what we mean by the terms EMF and voltage.

 

Electromotive force and voltage are often mistaken to be the same but there are differences between them. They are sometimes confused with electromagnetic fields as well. One can say that they are all related, but are not the same. Electromotive force and voltage are directly related to the generation of electromagnetic fields (EMF). Electromotive force is an invisible form of energy produced by the interaction of electric and magnetic fields which results in the movement of electrons from one point to another.

Electromotive Force (EMF) 

Electromotive force or also known as EMF is an energy input for charging through a battery cell. In other words, it creates and maintains a voltage in the active cell, by supplying energy in Joules to each unit of Coulomb charge. This is represented by “ε” and the unit of measurement is the same as voltage, which is Volt. 

EMF is the maximum potential difference between two points of the battery when no current flows from the source in the case of an open circuit. That is, it is caused by EMF and is affected by voltage or potential difference. A generator or battery is used to convert one energy into another. In these devices, one terminal is positively charged and the other is negatively charged. Therefore, an electromotive force is work done on a unit electric charge.

Voltage 

Voltage is the force that causes an electric charge to flow. This is the potential difference between two connections where one connection collects more electrons than the other. Voltage is defined as potential energy per charge. 

 

Voltage is measured in volt (V), which is the derivation unit of potential. A voltage drop is a drop in potential along the current path through a circuit. The higher the resistance of a component, the greater the voltage drop between connections. When electricity encounters resistance,  potential energy is lost because it is converted into another form of energy to do the work. For example,  electric potential energy is converted into thermal energy by a resistor.

 

Difference between EMF and Voltage 

Points to Remember 

1. EMF or electromotive force is the potential difference generated by one or more cells or a changing magnetic field in a solar cell, and voltage is the potential difference measured at any two points in the magnetic field. 

2. The SI unit and voltage of EMF  are the same (volt). 

3.  The magnitude of the EMF depends on the change in the magnetic field, and the voltage depends on the magnitude and resistance of the current. 

4. Voltage can be thought of as the difference between two electrical states in an electric field, but EMF is the force that causes the difference in electrical states.

What is  EMF?

1. EMF stands for electromotive force. EMF is the voltage at the terminals of the source in the absence of an electric current. 

2. The concept of EMF defines the amount of work required to separate the charge carriers in the source current, such that the force acting on the charges at the terminals of the source is not a direct consequence of the field. Emf is developed as a result of internal resistance.

3. The electromotive force (EMF) is defined as- The amount of work done in the energy transformation and the amount of electricity that passes through the electrical source or the generator.

4. EMF is measured in Volts and denoted by the symbol ε (or E).

 

What is Voltage?

• The voltage is defined as the amount of energy required to move a unit charge from one end to another end. Voltage is measured in Volts and denoted by the symbol V.

• The voltage is mainly developed between the two poles of the electric circuit i.e. it developed between the anode and cathode of the battery. 

• The positive terminal of the battery is known as the cathode and the negative terminal of the battery is known as the anode. The potential at the cathode of the source will be higher than the potential at the anode.

• When a potential difference or the voltage is developed across the passive elements is known as the voltage drop. (Passive elements-the electrical elements that do not generate power, such as resistors, capacitors, etc. which are used to dissipate, store charges)

• The voltage developed is a result of the electric field.

Difference Between EMF And Terminal Voltage

Now the major emf and voltage difference is, voltage or terminal voltage is too small in comparison with the emf. It implies that the Intensity of Emf developed will be always greater than the voltage as the voltage exists in a loaded circuit. Due to external resistance, there is always voltage drop or energy loss which will lead to varying intensity. But, emf is always constant.

 

Let us look at other voltage and EMF difference as listed below:

 

Difference Between Voltage and EMF

 

These are some major notable differences between the emf and terminal voltages. Though both are measured as potential differences, they are not the same.

 

Solved Examples

1. Consider an electrical circuit with a potential difference of 5V, a current of 0.9A, and the internal resistance of the battery is 0.7ohms. Calculate the EMF of the battery.

Ans:

Given,

Potential difference = V = 5V

Current in the circuit = I =0.9A

Internal resistance of the battery =r = 0.7

 

Now, Emf of the circuit is given by:

=> E=I(R+r)

Where,

R- External resistance of the electrical circuit.

r- Internal resistance of the given circuit

I- Current flowing through the circuit

 

On rearranging the above expression,

=> E=IR+Ir

 

We know that the product of current in the circuit and the external resistance is the potential difference across the resistance. Thus

=> E=V+Ir

 

Substituting given values in the equation,

=> E = 5 + (0.9 x 0.7) = 5.63 volts

 

Therefore, the EMF of the battery is given by 5.63V.

 

2. A battery provides a current of 1A through a 3ohm coil and 0.8A through a 5ohm coil. Calculate emf and the internal resistance of the battery.

Ans:

Given,

Let the emf of the battery be E and the internal resistance of the battery be r.

 

Now,

Emf of battery is given by:

E = I(R+r)

 

Where,

R- External resistance of the electrical circuit.

r- Internal resistance of the given circuit

I- Current flowing through the circuit

 

For 3 Ω coil: E = 1(3+r)……..(1)

For 5 Ω coil: E = 0.8(5+r)……….(2)

On solving (1) and (2) we get the value of the internal resistance of the battery, r = 5 Ω

Now emf of the battery is, E= 8V

 

Therefore, the emf and internal resistance of the battery are 8volts and 5ohms respectively.

 

Did You Know?

• Various types of batteries are available in the market and the emf of batteries will vary from each other. 12V emf batteries are the standard ones used for practical purposes.

• The emf of batteries is also determined by the type of chemical reaction involved. Lead-Acid batteries used in cars and other vehicles are the most common types.

• Though Emf stands for electromotive force, it is still the voltage developed in the circuit. Here force means energy per unit charge.

The electric dipole moment is the product of either of two charges (ignoring the sign) and the distance between them.

A dipole is an arrangement of two charges bearing the same magnitude but an opposite polarity separated by some distance. 

So, if there are two charges and we join the center of these two charges with an imaginary line and the distance between them is ‘2a’, then the dipole moment is: 

[vec{P} = q(2vec{a})]

Here,

p = electric dipole moment, and it has a direction, i.e., a vector quantity

q = charge

 

2a = dipole length (a vector quantity) = displacement of – q charge w.r.t. + q. 

Electric Field due to Electric Dipole 

The study of electric dipoles is important for an electrical phenomenon in the matter. We know that a matter contains atoms and molecules, and each has positively charged and negatively charged nuclei. If the center of the mass of the positive nuclei coincides with the negative nuclei, it possesses an internal or permanent dipole moment. 

In the absence of an electric field, the dipole moments are randomly oriented such that the net dipole moment of the system becomes zero. 

When an electric field is supplied to the system of charges inside the matter, the polar molecules align themselves in the direction of the electric field, and some net dipole moment develops, and the matter is said to be polarized. 

So, the field of an electric dipole is the space around the dipole which can be experienced by the effect of an electric dipole, so let’s discuss the electric field due to the dipole. 

Electric Field due to Dipole at any Point.

Let’s take an arrangement for charges viz: electric dipole, and consider any point on the dipole. 

Let there be a system of two charges bearing + q and – q charges separated by some distance ‘2a’, and how to calculate the electric field of a dipole. 

Since the distance between the center of the dipole length and the point P is ‘r’ and the angle made by the line joining P to the center of the dipole is θ. 

We know that the electric field due to dipole is: 

On Axial Line of Electric Dipole

[vec{|E|} = frac{vec{|P|}}{4pi epsilon_{o}} . frac{2r}{(r^{2}-a^{2})^{2}}]

If the dipole length is short, then 2a<

so the formula becomes:

[vec{|E|} = frac{vec{|P|}}{4pi epsilon_{o}} . frac{2}{r^{3}}]

On Equatorial Line of Electric Dipole

The formula for the equatorial line of electric dipole is:

[vec{|E|} = frac{vec{|P|}}{4pi epsilon_{o}} . frac{2r}{(r^{2}+a^{2})^{2}}]

If the dipole is short, the formula becomes:

[vec{|E|} = frac{vec{|P|}}{4pi epsilon_{o}} . frac{2}{r^{3}}]

Let ‘O’ be the center of the dipole and consider point ‘P’ lying on the axial line of the dipole, which is at distance ‘r’ from the center ‘O’ such that OP = r.

p [costheta] is along [A_{1} B_{1}] and p [sintheta] is along [A_{1} B_{1} perp A_{2} B_{2}].

So, the electric field intensity will be:

[|vec{E_{1}}| = frac{2pcostheta}{4pi epsilon_{o}} .frac{1}{r^{3}}]

Let it be represented by [vec{KL}] along  with [vec{OK}], and the field intensity at k will be:

[|vec{E_{2}}| = frac{2psintheta}{4pi epsilon_{o}} .frac{1}{r^{3}}]

Let it be represented by [vec{KM}] parallel to [B_{2} A_{2}],

and perpendicular to [vec{KL}]. 

Complete the rectangle KLNM, and join [vec{KN}].

Now, applying the 2nd law of vector addition, [vec{KN}] represents the resultant electric field,

which is given by:

KN = [sqrt{KL^{2} + KM^{2}}]

   = [sqrt{E_1^2 +E_2^2}]

   = [sqrt{(frac{2pcostheta}{4pi epsilon_{o}} .frac{1}{r^{3}})^{2} + (frac{2psintheta}{4pi epsilon_{o}} .frac{1}{r^{3}})^{2}}]

   = [frac{P}{4pi epsilon_{o}r^{3}}sqrt{4cos^{2}theta + sin^{2}theta}]

[vec{|E|} = frac{P}{4pi epsilon_{o}r^{3}}sqrt{3cos^{2}theta + 1}]……(3)

So, we get the electric field of a dipole in eq(3)

Also, let LKN = [beta], then [triangle]KLN is:

[tanbeta = frac{LN}{KL} = frac{KM}{KL}]

= [(frac{psintheta}{4pi epsilon_{o}} .frac{1}{r^{3}})^{2} times frac{4pi epsilon_{o}}{2pcostheta}.frac{1}{r^{3}}]

[tanbeta = frac{1}{2} tantheta] …..(4)

Now, here we will consider two cases viz: Field along the axial line of the dipole and the second one for the field along the equatorial line of the dipole.

1. When Point K Lies Along the Axial Line of Dipole.At this moment, θ = 0° = Cos 0° = 1Now, equation (3) becomes:

[vec{|E|} = frac{P}{4pi epsilon_{o}r^{3}}sqrt{3cos^{2}0^{0} + 1}]

           [ = frac{2P}{4pi epsilon_{o}r^{3}}]

          

And, [tanbeta = frac{1}{2} tan 0^{0}]

[=beta = 0^{0}]

This shows that the electric field intensity is along the axial line of the electric dipole.

2. When the point K lies on the equatorial line of the dipole.At this moment, θ = 90° = Cos 90° = 0 From eq (3), we get:

[frac{P}{4pi epsilon_{o}r^{3}}sqrt{3cos^{2}90^{0} + 1}]

[vec{|E|} = frac{P}{epsilon_{o}r^{3}}]

And, [tan 90^{0} = frac{1}{2}tantheta]

[= frac{1}{2}tan 90^{0} = infty]

[= beta = tan 90^{0}]

Here, the angle 90° shows that the direction of the resultant electric field intensity is perpendicular to the equatorial line, and therefore, parallel to the axial line of a dipole.

Dipole electric field is a part of physics and it is discussed in detail in Chapter 1 electric charges and fields of the NCERT book of Class 12. It is considered an extremely important concept as it is prescribed by the Central board of secondary education that is the CBSE. It carries significant weightage in the Class 12 board examination and therefore it is advisable for students to study this chapter and this concept called Dipole electric field in depth.

To make the learning process easier and fun the ’s team of expert teachers who have done extensive research and have years of experience in the concerned field have curated the study material that is based on the CBSE curriculum. This article on dipole electric fields is written in an extremely simplified manner as the objective of writing this is to help students understand and get a good hold of the concept of electric charges and fields.

Along with the study material teachers have also provided students with practice questions with their solutions so that students can keep in check their progress and can get to know about their strengths and weaknesses.

The study notes on the dipole electric field can be easily accessed by visiting ’s website. ’s team has provided the study material in a PDF format which makes it even more convenient for students as it can be for free and can be used anywhere especially in an offline environment.

This chapter mainly deals with electrostatics which is basically the study of forces, fields, and potentials
that arise from static charge.

Fun Fact-

The concept of electricity was first discovered by Thales of Miletus, Greece, around 600 BC when he delved into how amber when rubbed with wool or silk cloth attracts light objects. The term electricity originated from the greek word called elektron which means amber. During that time various metals were discovered which when dropped could attract light objects like straws, bits of paper, or hair.

Key Concepts Needed to Understand Dipole Electric Field are-

1.1 ELECTRIC CHARGE

1.2 CONDUCTORS AND INSULATORS

1.3 CHARGING BY INDUCTION

1.4 BASIC PROPERTIES OF ELECTRIC CHARGE

1.4.1 Additivity of charges

1.4.2 Charge is conserved

1.4.3 Quantisation of charge

1.5 COULOMB’S LAW

1.6 FORCES BETWEEN MULTIPLE CHARGES

1.7 ELECTRIC FIELD

1.7.1 Electric field due to a system of charges

1.7.2 Physical significance of electric field

1.8 ELECTRIC FIELD LINES

1.9 ELECTRIC FLUX

1.10 ELECTRIC DIPOLE

1.10.1 The field of an electric dipole

1.10.2 Physical significance of dipoles

1.11 DIPOLE IN A UNIFORM EXTERNAL FIELD

1.12 CONTINUOUS CHARGE DISTRIBUTION

1.13 GAUSS’S LAW

1.14 APPLICATIONS OF GAUSS’S LAW

1.14.1 Field due to an infinitely long straight uniformly charged wire

1.14.2 Field due to a uniformly charged infinite plane sheet

1.14.3 Field due to a uniformly charged thin spherical shell

The double refraction of light is the phenomenon of birefringence. It is an optical property in which a single ray of unpolarized light enters an anisotropic medium and splits into two rays, each travelling in a different direction. We can think of double refraction as the end which divides into two roads. Here, the end is the anisotropic medium, the person travelling is the unpolarized light, while the two roads are the two rays, each travelling their paths. 

Birefringence is characterized by crystallographic materials with different recurrence indicators concerning different crystallographic directions. Birefringence occurs when light passes through transparent objects, ordered by molecules, indicating a differential difference in reception at refractive indices.

In this article, we will understand the definition of double refraction, explain the phenomenon of double refraction in depth.

Types of Birefringence and its measurement

• Intrinsic Birefringence: The anisotropy in crystals causes this sort of birefringence. Birefringence is caused by the atomic arrangement of the crystal. Calcite, tourmaline, and other minerals are examples.

• Stress-Induced Pressure-induced birefringence: This sort of birefringence is caused by applying pressure to the property. Glass and polymers, for example, exhibit a combination of strain birefringence.

Changes in the spacing of light waves can be used to determine birefringence. Polarimetry is the name for this measurement procedure. The birefringence of lipid bilayers is measured using a technique known as dual-polarization interferometry. 

Explain Double Refraction

We observe that in double refraction light is unpolarized and it divides into two rays when passed through the doubly refracting crystal that deviates the rays into different directions.

We can also observe the Double refraction of light by comparing two materials, viz: glass and calcite.  If a mark is drawn upon a sheet of paper with a pencil and then covered with a piece of glass, only one image is visible; but if the same paper is covered with a piece of calcite, and the crystal is adjusted in a specific direction, then two marks are visible.

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The figure above shows the phenomenon of double refraction via calcite crystal. An incident ray is seen to split into two rays, the first is the ordinary ray CO and another is the extraordinary ray, i.e., CE on entering the crystal face at point C. 

Explain the Phenomenon of Double Refraction

The optic axis of a Calcite crystal (doubly refracting crystal) is defined by the symmetry of the crystal lattice. In calcite compounds or CaCO₃, the CO₃ (Carbon trioxide) forms a triangular cluster and the optic axis lies perpendicular to this.  When light enters along with the optic axis of the crystal, nothing happens and the light comes out unpolarized. However, when the light enters at a certain angle to the optic axis, the asymmetry of the lattice splits the ray into two with mutually orthogonal polarizations, as shown in the below diagram of Birefringence in a calcite crystal. 

From the below figure, we see that one ray is the Ordinary ray, for which Snell’s law holds, while the other is the Extraordinary ray that does not obey Snell’s law.

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Observation

On observing an object through the above crystal, we see a double image of the object. While analysis through the Polaroid sheet shows that these images have axes of polarization perpendicular to each other; therefore, rotating the Polaroid makes the images alternately disappear. 

Things get interesting when you place a second crystal just on the top of the first. Now, you have four images instead of two, but when you rotate it, the second crystal functions as an analyzer for the first one, and you get two images again.

Double Refraction of Light

In double refraction of light, the ordinary ray and the extraordinary ray are polarized in planes oscillating at right angles to each other. Furthermore, the refractive index, i.e a number that determines the angle of bending specific for each material medium of the ordinary ray is observed to be constant in all directions.

The refractive index of the extraordinary ray changes according to the direction taken because it has both parallel and perpendicular components to the crystal’s optic axis.  It’s because the speed of light waves in a medium that is equal to their speed in a vaccum is divided by the index of refraction for that wavelength, an extraordinary ray can move both faster and slower than an ordinary ray.

Do You Know?

All transparent crystals like calcite crystals except those of the cubic system that is normally optically isotropic possess the phenomenon of double refraction: in addition to calcite, some well-known examples are sugar crystals, ice, mica, quartz, and tourmaline. 

• Other materials may become birefringent under special circumstances. Now, let’s consider some examples for the same:

• Solutions of long-chain molecules exhibit double refraction when they flow, and this principle is called streaming birefringence.

• Plastic materials formed of long-chain polymer molecules can also become doubly refractive when compressed or stretched. This phenomenon is called photoelasticity. 

• There are some isotropic materials like glass that also exhibit birefringence when placed in a magnetic field or electric field or when exposed to external stress.
  

Enhancing Knowledge!

The effect of birefringence was first described by the Danish scientist named Rasmus Bartholin in 1669.

Birefringence Applications

Birefringence finds use in the following applications: