Category: Physics Notes PPT

The magnetic field created by a constant electric field is described by the Biot Savart Law equation. According to this law, the magnitude, length, direction, and proximity of the electric current is related to the magnetic field. Also, this law is consistent with both Gauss’s theorem and Ampere’s circuital law. As Coulomb’s law is fundamental for electrostatics, similarly, Biot Savart Law is also fundamental for magnetostatics. In 1820 two French physicists Jean Baptiste Biot and Felix Savart created the Biot Savart Law statement, which derived the mathematical formula for magnetic flux density at a point due to a nearby current-carrying conductor. Witnessing the deflection of the magnetic compass needle, these scientists concluded that the current particle projects a magnetic field into the space surrounding it.

The mathematical expression was derived through observation and calculations, which showed the magnetic flux density. This flux density dB is proportional to the length of the current I, element dl, the sine of angle θ between the direction of the current and the vector joining a given point of a magnetic field and the current element. It is inversely proportional to the square of the distance of the given point from the current element r.

Biot Savart Law Derivation

The biot savart law formula can be given as

[dB alphafrac{Idlsintheta}{r^{2}}]

Or

[dB=kfrac{Idlsintheta}{r^{2}}]

Where, k is constant, depending upon the magnetic properties of the medium and system of the units employed. In the SI system of the unit,

[k = frac {mu_0 mu_r}{4pi}]

The final Biot-Savart law derivation is expressed as,

[db = frac {mu_0 mu_r}{4pi}times frac{Idlsintheta}{r^{2}}]

Consider a long wire carrying current I and at a point p in space. The wire is represented in the picture below by red color. Also, consider an infinitely small length of the wire dl at a distance r from the point P as shown in the diagram. Here, r is the distance vector, which makes the angle θ with the direction of the current in the minute portion of the wire.

Imagining the condition, you can understand that the magnetic field density at point P due to the minute length dl of the wire is proportional to the current carried by this portion of the wire. As the current through the minute length of the wire is similar to the current carried by the whole wire itself, we can express it as:

dB ∝ I

It is also natural to think that the magnetic field density at point P due to the minute length dl of wire is inversely proportional to the square of the straight distance from Point P to the center of dl. Mathematically it can be expressed as:

dB ∝ [frac{1}{r^{2}}]

Also, the magnetic field density at the point P due to the minute portion of the wire is proportional to the actual length of the minute length dl of wire. θ is the angle between distance vector r and direction of current through this minute portion of the wire, the component dl of the wire facing perpendicular to the point P is dlsinθ. 

Hence, dB ∝ dl sinθ

Now, merging these three statements, we can write,

[dB alpha kfrac{I.dl.sintheta}{r^{2}}]

The formula for Biot-savart law can be stated here as follows:

Now, introducing the value of constant k (which we have already mentioned at the starting of this derivation) in the above formula, we get,

[dB = frac{kl.dl.sintheta}{r^{2}}]

[ K = frac{mu_{0}mu_{r}}{4pi}]

Here, μ0 is the absolute permeability of air or vacuum used in the expression of constant k, and its value is 4π10-7 Wb/ A-m in the SI system of units. μr in the expression of constant k is the relative permeability of the medium. 

Now, flux density (B) at point P due to the total length of the current-carrying conductor or wire can be expressed as,

[B = int dB = dB= intfrac{mu_{0}mu_{r}}{4pi}timesfrac{kl.dl.sintheta}{r^{2}}]

[= frac{mu_{0}mu_{r}}{4pi}I intfrac{sintheta. dl}{r^{2}}]

If D is the perpendicular distance of point P from the wire, then

r sinθ = D or r =[frac{D}{sintheta}]

Now, the formula of flux density B at point P can be rewritten as,

[B = frac {Imu_0 mu_r}{4pi}int frac{sintheta}{r^{2}}dl = frac {Imu_0 mu_r}{4pi}intfrac{sin^{3}theta}{D^{2}}dl]

Again, [frac{l}{D}] = cotθ

 ⇒l = D cotθ

Therefore, dl = -Dcosec2θdθ

Finally, the expression of B comes as,

[B = frac {Imu_0 mu_r}{4pi}int frac{sin^{3}theta}{D^{2}} [-Dcosec^{2}theta dtheta]

=[-frac {Imu_0 mu_r}{4pi D}int sin^{3}cosec^{2}theta dtheta]

=[-frac {Imu_0 mu_r}{4pi D}int sintheta dtheta]

This angle θ is dependent upon the length of the wire and position of point P. Say for a certain partial length of the wire, angle θ, as indicated in the figure above, varies from  θ1 to θ2. Hence, magnetic flux density at the point P due to the total length of the conductor is,

[B = -frac {Imu_0 mu_r}{4pi D}int_{theta 1}^{theta 2}sintheta dtheta]

= [-frac {Imu_0 mu_r}{4pi D}[-costheta]_theta1^theta2]

= [frac {Imu_0 mu_r}{4pi D} [costheta_{1}- costheta_{2}]]

Let’s consider the wire is infinitely long, then θ will change from 0 to π that is  θ1 = 0 to  θ2 = π.

Placing these two values in the above final expression of Biot Savart law, we get,

[B = frac {Imu_0 mu_r}{4pi D}[cos0 – cospi =  frac {Imu_0 mu_r}{4pi D} 1-(-1)]

[B = frac{mu_{0}mu_{r}I}{2pi D}]

Applications of Biot Savart Law 

The applications of Biot Savart Law are mentioned below. 

• The Biot Savart Law is used to calculate magnetic responses at the molecular and atomic levels. 

• The Biot Savart Law is used in aerodynamic theory while calculating velocity generated by vortex lines. 

Importance of Biot Savart Law 

The Biot Savart Law is important for the following reasons: 

Bremsstrahlung is the electromagnetic radiation emitted in the form of photons when a charged particle is decelerated upon striking against another charged particle. This radiation gives a continuous X-ray spectrum. This is also known as “braking radiation”. These charged particles are mainly electrons and atomic nuclei of metals.  Let us now study bremsstrahlung radiation, its causes, and effects.

In the classical explanation of bremsstrahlung radiation, the quantum effects are neglected and a comparatively simpler approach was considered by Larmor. Bremsstrahlung has its uses in radiation safety equipment and astrophysics. Bremsstrahlung radiation is often considered to be secondary radiation.

Bremsstrahlung Radiation

Bremsstrahlung radiation is a type of electromagnetic radiation emitted when a charged particle upon getting deflected by another charged particle is decelerated. These charged particles are mainly electrons or atomic nuclei. The particles in motion upon clashing lose kinetic energy. The lost energy is emitted as radiation in the form of photons. Thus the law of conservation of energy is also satisfied. This is known as the bremsstrahlung radiation. This bremsstrahlung radiation gives a continuous spectrum. The peak intensities tend to shift towards higher frequencies with the increase in the energy of the decelerated charged articles. This is the bremsstrahlung radiation definition. Bremsstrahlung radiation is of two types namely inner bremsstrahlung and outer bremsstrahlung radiation. We’ll be discussing this later in this article.

Causes of Bremsstrahlung Radiation

Bremsstrahlung can be defined as a process by which some of the energy of the celestial rays is scattered into the atmosphere of Earth. The chromosphere emits solar x-rays in the form of bremsstrahlung radiation. This is generated by fast-moving electrons. However internal bremsstrahlung takes place in case of radioactive disintegration. During beta decay which involves the emission of electrons and positrons, the clash between these charged particles results in the emission of bremsstrahlung radiation. It is mainly caused by the acceleration and deceleration of charged particles such as atomic nuclei and electrons. If the particles emit bremsstrahlung radiation while being accelerated by an external magnetic field it is also known as synchrotron radiation.

Bremsstrahlung X- Rays 

The bremsstrahlung x-rays are emitted when electrons get decelerated when fired against a metal target. These charged particles emit bremsstrahlung radiation in the form of photons or bremsstrahlung x-rays. The continuous spectrum formed due to the bombardment of electrons lies in the x-ray region of the electromagnetic spectrum. The energy peaks of the x-ray spectrum tend to shift towards higher frequencies with the increase in energy of the electrons. Often the bombarding electrons also eject electrons from the inner atomic shells of the target metal. The vacancies are quickly filled by dropping electrons from the higher atomic shells. As a result, bremsstrahlung x-rays are emitted.

Inner and Outer Bremsstrahlung 

Inner bremsstrahlung and outer bremsstrahlung are the two types of bremsstrahlung radiations.The inner bremsstrahlung is also known as internal bremsstrahlung is caused by the electrons emitted from a radioactive decaying nucleus. This is a feature of beta decay in the nuclei. However, the outer bremsstrahlung is caused when electrons emitted from a separated nucleus are bombarded on other nuclei. The bremsstrahlung decreases constantly with the increase in the energy of the beta particles in the case of electrons and positrons which are emitted by the electron-nuclei pair in case of beta decay. The bremsstrahlung is emitted in case of electron capture without emission of any charged particle. Electron capture requires the energy of a neutrino. The bremsstrahlung radiation is the result of the acceleration of the captured electrons. These types of radiations often have the same frequencies as gamma radiation. These radiations do not exhibit any spectral lines of the gamma radiation and hence can not be considered as gamma decay. 

Did You Know? 

Capillarity meaning is very simple to understand in terms of hydrodynamics. Capillarity is an invisible force that works against the force of gravity. It pushes a liquid up in a tube or a narrow pipe. This rising of liquid is the capillary action. We call such liquid capillary water because the water follows the principle of capillarity.

In this article, we will learn how to do the capillary definition, discuss the capillary action definition, explain capillary action, understand the capillary water meaning, define capillary action, and understand the capillary action in detail.

Capillarity is the ability of a liquid to move through a second liquid due to attraction, and is one of the fundamental physical properties of all fluids. It can be defined as the rate at which liquids move across a surface (wetted or not) or between two surfaces.

Define Capillary Action

Capillary action is the force or an effort made to push the liquid by fighting the gravitational force of attraction. Also, after a certain amount of time, the liquid falls. This fall occurs when the liquid faces a surface tension.

()

For measuring the temperature of our body, we use a clinical thermometer. Generally, a digital thermometer takes 60 seconds to determine the temperature. So, there is another thermometer, which is a mercury thermometer, which displays the temperature in the form of mercury rise. The division at which the mercury rise stops is the ultimate body temperature. So, here, the mercury rise is the capillary action. Here, we also notice that after some time, the mercury falls. So, the rise and fall of mercury is also a capillary action.

In this text, we included the topic ‘surface tension,’ do you know what surface tension is? So, let’s understand this terminology:

Surface Tension

In Physics, the tension on the surface of the film of a liquid occurs because of the attraction of the surface particles by the bulk of the liquid that tries to minimise the surface area of the liquid drop, and this phenomenon is called surface tension. When the surface of the liquid is very strong, the surface tension is applicable and the liquid can hold weight.

In simple words, the definition of surface tension in capillary action definition is as follows:

Surface tension is the ability of liquid surfaces to shrink into the minimum possible surface area. Surface tension allows insects like water striders to swim and slide on a water surface without becoming even partly dipped.

Capillary Water Meaning

Now, we will understand the capillarity water meaning and explain capillary action with the help of real-life applications:

1. When we pour the kerosene oil in a lantern and the melted wax in a candle, the capillary action forms in the cotton wick and burns.

2. The coffee powder gets dissolved in water easily because water immediately wets the fine granules of coffee by the action of capillarity.

3. The water poured into the grassland rises in the uncountable capillaries formed in the stems (Xylem) of plants and trees and reaches the leaves. 

4. The tip or the nib of a pen splits to provide capillary action for the ink to rise, which helps us to write on the paper.

5. After taking a bath, we use a towel. The action of a towel in soaking up moisture from the body is due to the capillary action; also known as capillary water.

Capillary Action Formula Derivation

The ascent of a liquid column in a capillary tube is given by the following equation:

h = 2Scosθ/rρg − r/3

Now, let’s do the capillary action formula derivation:

If the capillary is very narrow, then we have:

h = 2Scosθ/rρg

Where,

h =  height of the capillary tube

r is the radius of the capillary tube,

ρ is the density of the liquid or water,

θ = angle of contact

Here, the angle of contact is the angle between the tangent drawn to the liquid surface at a certain point of contact of liquid and solid inside the liquid.

The angle of contact relies on the nature of both solid and liquid. For the concave meniscus of liquid, the angle of contact will be acute, while for the convex meniscus of liquid, it will be obtuse.

S = surface tension of the liquid/fluid/water

Point To Note:

At equilibrium, the height (h) does not depend on the shape of the capillary when the radius of the meniscus remains unchanged. Due to this reason,  the vertical height (h) of a liquid column in capillaries of different sizes and shapes also remains the same.

Now, let’s consider a few cases to see if the liquid rises, falls, or remains unchanged:

• If θ < 90°, which means cos θ is positive, so ‘h’ is also positive, i.e. liquid rises in a capillary tube.

• If θ > 90°, which means cos θ is negative, so ‘h’ is negative, i.e. liquid falls in a capillary tube.

• The rise of liquid in a capillary tube agrees and totally follows the law of conservation of energy.

Do You Know?

We see that at the liquid–air interfaces, surface tension always results from the greater attraction or cohesion of liquid molecules to each other than to the molecules in the air or adhesion. 

A simple pendulum is the example of bodies executing simple harmonic motion.

A pendulum consisting of a point mass body (bob) suspended by a weightless, inextensible and flexible string from rigid support about which it is free to move back and forth is called an ideal simple pendulum.

In an equilibrium position, the center of gravity of the bob lies vertically below the point of suspension.Here, O is called the equilibrium or the mean position or the point of oscillation of the simple pendulum. 

The distance between the point of suspension and the point of oscillation is called the effective length of a pendulum.

The Expression for the Period of Oscillation

Let the mass of bob = m

L = length of the simple pendulum

O1P = s

When the bob is displaced from its mean position by an angle Ө, the forces acting on it at P are:

1. Weight (mg) of the bob.

2. Tension T in the string along with OP.

Now, resolving mg into two rectangular components, we get:

1. mg CosӨ acts along with PA, opposite to T.

2. mg SinӨ acts along with PB, tangent to the arc O1P, and directed towards O1.

 If the string neither slackens nor breaks, then:

                                      T = mg CosӨ 

The force mg SinӨ tends to bring the bob to its mean position, so the restoring force will be:

                                       F = – mg SinӨ

Here, a negative sign shows that the pendulum shows the property similar to that of inertia. It tries to come back to its mean position.

Since Ө is very small, so, Sin Ө becomes equal to Ө = Arc (O1P)/L = s/L 

F = – mg Ө = – mgs/L…(1)

From eq(2),  we come to know that Force, F α displacement (s).

This F is directed towards the mean position O.

If the pendulum is left after stretching it, it starts executing an S.H.M.

So, in S.H.M., the restoring force, F = – ks..(2)

Combining (1) and (2), we get:

Spring factor, k = mg/L

Here, inertia factor = mass of bob = m 

Now, time period = 2π √inertia factor/spring factor = 2π√m/mg/L.               

So, we get the formula for a period as;                           

So, T is α √L and √1/g

Now, let’s understand how we can change the period of a pendulum.

Changing the Period of a Pendulum

Equation (3), states that T α √L, which means T increases with an increase in the effective length L.

Case 1: If the effective length L of the pendulum is very large which is comparable to the radius of the earth R, then T can be shown as:

                                    T = 2π√R/(1+R/L)g

Case 2: Now, if this length increases to the length greater than R or reaches to infinity

 (L → ∞), then the period becomes:

                                    T = 2π√R/g 

Putting R = 6.4 𝑥 10⁶m, and g = 9.8 ms^-2,

                                   T =  2π√6.4 𝑥 10⁶/9.8 = 84.6 minutes.

Case 3: If this length = R, then,

                                   T = 2π√R/2g = 2π√6.4 𝑥 10⁶/2 x 9.8

                                      = 60 minutes

This is how we keep on changing the period of a pendulum.

So, how can you increase the period of a pendulum?

Let’s look at these cases:

Case 4: T α √1/g

When the value of g decreases, the value of T increases with the decrease in the value of g by taking the pendulum in hilly areas. 

However, the pendulum clock slows down.

Case 5: With the rise in temperature of the pendulum, the effective length of a pendulum increases, along with the period.

                           T/T’ = √L/L’ = (1 + αӨ/2) 

% increase in time period = 50 αӨ.

Case 6: If the pendulum is made to oscillate in a fluid of density ρ0, where ρ0 < ρ, then, 

                       T/T’ = √g/g’ = √ρ/ρ – ρ0 > 1 (as ρ > ρ0)

So, the period increases with a decrease in g.

This is how you can increase the period of a pendulum.

Pendulum Swing Experiment

Aim: To change the period of a pendulum

Apparatus Required

1. Weights

2. Stopwatch/Timer

3. Tape

4. Scale

5. Straw

6. Table

Procedure

1. Tie a weight (of mg) to a thread and then tie the thread to a straw on a table such that around half of an inch hangs over the edge.

2. Tape the other end of the thread with the table in such a way that the length from the straw’s end to the middle of the weight is 6 inches.

3. Let the pendulum settle.

4. Now, pull the bob about one inch and leave it gently. Make sure to make the pendulum swing in a fixed arc.

5. When you take the bob at one end as soon as you leave, start the stopwatch to count the number of swings made by the pendulum.

6. Increase the length of the pendulum to 7 inches and the weight of the bobs, and

7. Repeat the above procedure.

Result

The number of swings divided by the time taken gives you the period of a pendulum.

Repeat the trials and record the results.

Put some drops of water on one side on a slanting surface and some drops of honey on the other. Come back and observe the flow of both the liquids. You would note that the slowness of water was very quick whereas honey was not that easily movable. In this case, honey is considered to be Viscous. 

So, viscosity is defined as the ratio of the force required to make adjacent layers of the liquid move over each other.

Figure .1 (a) shows an ideal or superfluid with no friction however, practically there is always some friction in the fluids as shown in the figure. 1(b).

Let’s take an example,

As you can see in the figure.2 above, there is a variation in each horizontal layer of the liquid that is happening due to the presence of some internal friction (viscosity) between the layers of the fluid passing via two plates.

The concept has significant importance for competitive exams like JEE and NEET. So the faculty at has holistically covered the topic keeping in mind the need of every student. So in this article, we shall be learning about – 

Table of Content

• Introduction

• What is the viscous gradient?

• What is the Coefficient of Viscosity?

• SI Unit of Coefficient of Viscosity

• Unit of Coefficient of Viscosity

• Coefficient of Viscosity Unit and Dimension

• The viscosity of Water in SI Units

• Do You Know?

• Benefits of studying with  

• Frequently asked questions

What is a Viscous Gradient?

The viscous gradient is the difference in the velocity between the adjacent layer of the fluid. If more force is applied by the upper layer to move forward the more will be the viscous gradient. It is represented by v/x, where v is the velocity difference and x will be the difference of distance between the two layers. So, the higher the value of v/x, the more will be the viscous gradient. 

Coefficient of Viscosity

The ratio of the shearing stress to the velocity gradient of the fluid is called the coefficient of viscosity η.

Hence the coefficient of viscosity is given by,

         

η  = F . d / A .ⅴ

Where F is the tangential force required to maintain a unit velocity gradient between two parallel layers of liquid of unit area.

ⅴ is the velocity.

A is the area

d is the distance between the two layers of liquid skidding over each other.

The difference in the stream of velocity between the adjacent layers of the fluid is measured in the velocity gradient.

The viscosity of gas is less than the liquid viscosity.

SI Unit of Coefficient of Viscosity

Every liquid has its specific viscosity and the measure of this attribute is called the coefficient of viscosity.

The coefficient of viscosity η is defined as the tangential force F required to maintain a unit velocity gradient between two parallel layers of liquid of unit area A.

The SI unit of η is Newton-second per square meter (Ns. m^-2) or

Pascal-seconds (Pa .s)

Hence the coefficient of viscosity is a measure of the resistance of the fluid to deformation at a given rate due to internal friction.

Unit of Coefficient of Viscosity

The centimetre-gram-second or CGS unit of coefficient of viscosity,  η is 

dyne-sec/ cm² which is equal to Poise.

Where one poise is exactly 0.1 Pa·s.

The meter-kilogram-second or MKS unit is: Kilogram per meter per second or

Kg m^-1 s^-1.

Coefficient of Viscosity Unit and Dimension

Since, the formula for coefficient of viscosity is given by,

η  = F . d/ A .ⅴ  =  MLT⁻² . L / L² . LT ⁻¹

On solving  we get,

The Viscosity of Water in SI Units

The coefficient of viscosity of water can be determined by using Poiseuille’s law.

Poiseuille’s equation for the flow of liquid determines the volume of the liquid flowing through a capillary tube in a unit of time.

Poiseuille’s formula is given by,

Here, the rate of flow of the viscous liquid through a tube of length ‘l’ and radius ‘໗’ is proportional to the applied pressure P. 

The rate of flow of the viscous liquid is proportional to the fourth power of the inner radius of the tube and inversely proportional to the viscosity of the liquid and the length of the tube. 

The formula for the coefficient of viscosity of water is given by,

Here, Ⅴ  is the rate of flow of the volume of liquid.

P is the pressure that would be applied to the liquid.

໗ is the inner radius of the capillary tube.

l is the length of the capillary tube.

SI unit of viscosity of water is Ns.m^-2 or Pa.s.

Do You know?

The dynamic viscosity of water at room temperature  25⁰C are having various values mentioned below:

In the SI unit, the value of viscosity is 8.90 × 10^{– 4} Pa·s.

In CGS unit, the value of viscosity is 8.
90 × 10^{– 3} dyn·s/cm² or  0.890 cP.

Therefore, water has a viscosity of 0.0091 poise

Viscosity and density are two different terms where viscosity is the thickness of fluid and density refers to the space between its particles.

Benefits of Referring the Study Materials From

• The topic will be holistically covered with all the sub-topics thus providing the students with a one-stop solution for all their problems.

• Study materials are prepared with utmost care ensuring credibility and quality notes.

• Use of easy language and diagrams while explaining the concept thus making it more adaptable for the students.

• Every concept is explained with the help of several examples giving students an experience to solve practical problems.

• Important facts about the topics are provided to make students learn some extra knowledge on the topic.

• Along with the knowledge reading these study materials with utmost sincerity will help you excel in the exams without much difficulty.

• Related videos on the topics to add to your learning experience.

• Free PDF notes exercise papers, past year solved papers are compiled in one place to boost your level of preparation.

• Quick response to all the valid questions of the students on the live page or through live chats on the website.

A mirror can be termed as a highly polished and smooth reflecting surface. The most common types of mirrors that are used are plane mirrors. The spherical mirror is part of the spherical reflecting surface. There are two categories of spherical mirrors – concave mirrors and convex mirrors.

Concave mirror: 

Concave mirror has a reflecting surface that caves inwards. The concave mirrors essentially converge light to only one prime focus point. This is why they are also known as converging mirrors. These mirrors are used for focusing light and the image that is formed by the concave mirror differs in size based on object position with respect to the mirror. The image exists either in virtual or real form. Erect or magnified and inverted, of the same size as that of the object or diminished, and it all depends on the position of the object. 

Convex mirror: 

The convex mirror is the curved mirror where the reflective surface bulges out towards the position of the light source. The convex mirrors tend to reflect light in the outwards direction, diverging light rays, and hence they are not used for focusing light. The image is erect, virtual, and smaller than the object, however gets larger as the object comes closer to the mirror. These mirrors are also referred to as diverging mirrors. 

Mirrors and the reflection laws

When we have a look at ourselves in the flat mirror, we appear to be of the same size as we actually are and our distance appears to be as behind the mirror as we actually are standing in front of the mirror. This is due to how reflection happens and it is known as the laws of reflection. According to the 1st law of reflection, the light, which hits a mirror would essentially bounce back at the same angle. If the specific mirror is flat, then it would lead to the image appearing as life-size. The image type that is created by the flat mirror, is known as the virtual image since it appears behind the mirror. The reflection laws are valid and hold true for any type of surface or mirror. 

The different terms that are used in spherical mirrors are pole, a centre of curvature, a radius of curvature, principal axis, aperture, focus, focal length. The pole is the midpoint of the mirror while the centre of curvature is the centre of the sphere, which is part of the image formed by the mirror. The radius of curvature refers to the distance between the centre of curvature and the pole. Its focal length is twice the length of the mirror. 

The principal axis is essentially the imaginary line that passes via the pole and centre of curvature of a spherical mirror. Aperture is used for denoting the mirror size. The focus is the point on the principal axis, where light rays that are parallel to the principal axis will appear to diverge from (for convex mirror) or converge ( for concave mirror) after reflecting from the mirror. The focal length is the distance between the focus of the mirror and the pole.

More on the Topic

A mirror is a part of a smooth and highly polished reflecting surface. Most commonly used mirrors are plane mirrors. A spherical mirror is a part of a spherical reflecting surface. There are two types of spherical mirrors – convex mirror and concave mirror.

Convex Mirror:

Convex mirror is a curved mirror for which the reflective surface bulges out towards the light source. Convex mirrors reflect light outwards (diverging light rays) and therefore they are not used to focus light. The image is virtual, erect and smaller in size than the object, but gets larger (maximum upto the size of the object) as the object comes towards the mirror. Such mirrors are also called diverging mirrors.

Concave Mirror:

A concave mirror has the reflecting surface that caves inwards. Concave mirrors converge light to one prime focus point. Therefore, they are also called converging mirrors. They are used to focus light. The image formed by a concave mirror varies in size depending on the position of the object with respect to the mirror. The image can be real or virtual, erect or inverted and magnified, diminished or of the same size as that of the object, all depending on the position of the object.

 

Real images can be brought onto a screen and they are always inverted.

Mirrors and reflection Laws of Reflection:

When we look at ourselves in a flat mirror, we will appear in the same size as we are and will appear to be just as far behind the mirror as we will be actually standing in front of the mirror.

This is because of how reflection takes place. This is concluded as the laws of reflection. The first law of reflection says that the light that hits a mirror would bounce back at the same angle. If the mirror is flat that would cause the image to appear life-size. 

The type of image created by a flat mirror is called the virtual image as it will appear behind the mirror. 

Laws of reflection are valid for any type or mirror or surface. 

Terms Used in Spherical Mirrors:

• Pole (P): It is the midpoint of a mirror.

• Centre of Curvature (C): It is the centre of the sphere of which the mirror forms a part.

• The Radius of Curvature (R): It is the distance between the pole and the centre of the curvature. It is twice the focal length of the mirror.

• Principal Axis: An imaginary line that is passing through the pole and the centre of curvature of the spherical mirror.

• Aperture: It is used to denote the size of the mirror.

• Focus: It is the point on the principal axis, where the light rays parallel to the principal axis will converge (in the case of a concave mirror) or appear to diverge from (in the case of a convex mirror) after reflection from the mirror.

• Focal Length: The distance between the pole and the focus of the mirror.

Properties of the Images Formed by a Convex Mirror:

Whatever be the position of the object in front of the convex mirror, the images is always smaller than the object, erect, virtual and also formed within the focus. 

Why is that a Convex Mirror Never Forms a Real Image?

A real image occurs where rays converge, whereas virtual image occurs when rays diverge and only appear to come from a point. The real images cannot be produced by a convex mirror as it diverges the rays. 

Real Image:

The real image is formed as a result of the actual convergence of the reflected light rays. It can be received on a screen and it is always inverted.

Do Concave Mirrors Always Form Real Images?

The concave mirror forms an image and that depends on the two parameters: the object distance and the focal length of the mirror.

If the object is placed between the pole and the focus of a concave mirror, a magnified and erect virtual is found to be formed.

Difference Between Convex and Concave Mirrors:

Image Formation by Concave and Convex Mirrors:

Convex Mirror Ray Diagram:

• When an object is placed at a finite distance from the mirror, the virtual image will be formed between the pole and focus. The size of the image is smaller as compared to the object.

Concave Mirror Ray Diagram:

• A real image will be formed between the focus and centre of curvature, when the object is placed beyond the centre of curvature. The size will be small as compared to the object.

• When an object or thing is set at the centre of curvature, the real image gets formed at the centre of the curvature. The size of the image is the same as that of the object.

• When an object/thing is set between the curvature and focus, the real image will be formed beyond the centre of curvature. The size will be larger as compared to the object.

• When an object is placed at the focus, the real image will be formed at infinity. The size of the image is much larger as compared to the object that is placed at the focus.

()

Uses of Convex Mirrors:

The convex mirror is used as a side-view/rear – view mirror of a vehicle because it forms an erect and smaller image. Convex mirror gives a wide rear view.

The convex mirror is suitable for convenient shops and big supermarkets and any other corner for a wide observation.

They can be used as street light reflectors because they can spread the light over a bigger area.

They are put on the corners of roads so that the drivers can see any vehicles and avoid collisions by taking due measures.

Uses of Concave Mirrors:

The concave mirror is a converging mirror, so it is used for many purposes. 

• It is used in a torch, automobile headlamps, lighthouses etc to reflect the light and make a fine beam.

• It is used in the aircraft landing at the airports to guide the airplane.

• It is used in the shaving process where you can get an enlarged and erect image of the face.

• It is used in solar ovens also. It collects a large amount of solar energy and focuses to a point where the vessel containing water or item to be cooked is placed.

• Concave mirrors are used in satellite dishes, they are also used by dentists and ENT doctors use them to obtain a larger image.

• Concave mirrors are used in electronic microscope, astronomical telescopes, visual bomb detectors etc.