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Author – Saurabh Salvi

One of my favourite scene from ‘3 idiots’ movie is when Rancho is asked the definition of ‘Machine’ by his Professor. And we all know what he answers and we all love that explanation but professor didn’t seem to like that simplified version of his. Instead, he was much impressed by the definition given by Chatur and most of us (actually, all of us) just skipped that definition part.

Ofcourse, it’s not a great idea to mug up things without understanding (we have already discussed this point in Understanding Projectile Motion), but the definition of machine which he gives is also quite impressive. It goes something like this :

Definition :

“Machines are any combination of bodies so connected that their relative motions are constrained and by which means, force and motion may be transmitted and modified as a screw and its nut, or a lever arranged to turn about a fulcrum or a pulley about its pivot, etc. especially, a construction, more or less complex consisting of a combination of moving parts, or simple mechanical elements as wheels, levers, cams etc.”

In today’s blog, we will be breaking this definition down with the help of a very simple example which most of us (from PCM or PCB background) have studied i.e. Atwood machine – the simplest pulley-block system

Let’s divide the definition in parts and try to get this thing sorted out quickly :

1st part – “Machines are any combination of bodies so connected that their relative motions are constrained“

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2nd part – “and by which means, force and motion may be transmitted“

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3rd part – “as a screw and its nut, or a lever arranged to turn about a fulcrum or a pulley about its pivot, etc.“

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4th part – “especially, a construction, more or less complex consisting of a combination of moving parts, or simple mechanical elements as wheels, levers, cams etc.“

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This was a short and fun kind of post just to make sure that all of the 3 idiots movie lovers can now breakdown this definition the next time they watch the movie! My aim was to explain this thing in the simplest way possible.

Also, I would like to add that just memorizing blindly doesn’t make any sense but understanding the definition would really help us to make our grip on the concepts much more better. I would also be quite impressed if Chatur had the understanding of this beautiful definition. But sadly, the character ‘Chatur’ doesn’t seem to be interested in all this 🙁

Keep Learning!

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Physics & Electronics

Projectile Motion is one of the basic thing we encounter in our daily life. Studying it becomes important because the ‘understanding’ (not mugging up Formulae) which we take here comes handy while analyzing complex concepts and experiments 

“Formulae give you Marks but Derivations give you Understanding !

We already do have a video on our Channel about such a experiment on our channel where knowledge of Projectile is needed for the Analysis part :

• Calculating e/m Ratio – https://www.youtube.com/watch?v=rxL8DkdYCTw 

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Equation of Trajectory

We all have played ‘catch-catch’ and we know how the motion of a ball when thrown looks like. But how do you describe that curve mathematically. What’s the equation of that curve ?

Most Important Tip that fixes everything related to Projectile !

Divide this whole 2-D situation into separate 1-D problems (X and Y)

• Note down all quantities in X separately. This will be your separate problem
• Note down all quantities in Y separately. This will be your another separate problem
• At last, combine them to get results for 2-D motion

Following the Tip :

Starting from origin (point where ball is throwed) till point P (x,y) :

The Projectile Trajectory is a Parabola !

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Finding Range Expression

Range is basically the ‘horizontal’ distance which the ball covers (from origin to the point where it lands). It means that, we need to find R in the figure

• This can be easily found since x = 0 and x = R are the two roots of the parabola.
• To calculate the roots, simply put y = 0 in our Equation of Trajectory

Calculations :

Substituting y = 0 and taking ‘x’ common on RHS of Equation of Trajectory, we get : 

* In the simplifying process, you need to use sin2theta trigonometric identity

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Finding Time of Flight Expression

Let’s find out for how much time does the body stay in the projectile motion.

Note that :

• On landing, after completing the motion, the displacement in Y direction is zero (Pause and observe !), since it again came to the same Y-level (y = 0 here)
• The time taken for this displacement in Y to become 0 is nothing but the Time of Flight (T)

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Finding Maximum Height Covered :

If we look at the Equation of Continuity, in this case (simple throwing); the trajectory resembles downward parabola since a<0

Hence visualizing it graphically, 

Finishing the Calculations,

So, this is how, we get the expression for the Maximum Height reached, denoted by ‘H’

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Conclusion

So, this is how we derive the expressions for Time of Flight, Range, Maximum Height and Equation of Trajectory. Note that – With this same approach, we can solve almost any kind of problem related to Projectile Motion. And, Why is that the case?

Because, whatever we discussed in this blog/article is not a trick or something, it’s a complete concept with complete understanding. This makes us equipped to solve any kind of problem (Throwing from a cliff, projectile on incline or just anything…)

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Diodes are one of the very important components used in electronic circuits. These are one which help to safeguard your circuits. 

• For now, we will ignore about what happens inside these diodes (e.g. p-n junction, holes, etc) which makes them to work like they do. Let’s keep it for upcoming articles but making it’s use in our project circuits is what we need and that’s what we will be covering in this article.

Table of Content :

• Unlike Resistors, Diodes have Polarity !
• Using Rectifier Diode
• AC to DC & Process of Rectification 

1. Diodes have Polarity !

As we have already discussed about Resistors in our previous articles (Dealing with Resistors : Part 1 & Combining Resistors : Part 2 ), we know that Resistors don’t care in what way you are connecting them in circuits. 

• BUT for Diodes, it’s not the same ! The way you connect the diodes in our circuit does matter. Hence we have the terminologies of cathode and anode for a Diode

2. Using Rectifier Diode

There are many types of diode but the most basic one is rectifier diode. Diodes mainly behave like one-way valves. One way valves only allow fluid to flow in one direction. If it flows in one, it can’t come or flow back in opposite direction. 

• This is just a common analogy. You can say that the diode offers very less resistance to current in one direction while it offers a very high resistance in other direction; making the current difficult to flow in other direction

Understanding the below flowchart will help :

The below circuits show the Forward Bias and Reverse Bias Configuration for Diode :

For connecting the Diode in Forward Biased Configuration :

• Connect the anode of diode to higher voltage and cathode to lower voltage

And for Reversed Biased Configuration :

• Connect the anode of diode to lower voltage and cathode to higher voltage

Diodes have a ‘constant’ voltage drop :

We know that voltage drop across a Resistor depends on the current passing through it. 

• Unlike Resistors, Diodes have a fixed voltage drop which doesn’t change on the amount of current passing through it.
• Generally it is around 0.5V but depends on diode to diode. Checking datasheet before calculations always helps !

By applying Kirchhoff’s Law in the circuit loop above, we get the voltage drop across Resistor R1 to be 8.5V. From this information, we can calculate current in the circuit ‘i’ :

3. Conversion & Process of Rectification

Diodes can also help to convert AC Voltage to DC Voltage. Recall that AC has both a positive component and a negative component. If a diode allows one part to go through (say positive), the negative part won’t be allowed. 

• A picture will help in better understanding : 

The Voltage source finally does have just a positive part left (unidirectional like DC), but still it’s not constant. It does have some fluctuations. To smoothen this out and obtain a near constant voltage :

• Connect a Capacitor in parallel to a Resistor across the voltage source

BUT how does this combination of Resistor and Capacitor help to smoothen out the given voltage signal ?

Answer :

The capacitor smoothens out the fluctuations by charging and discharging in response to the ‘changing input voltage’. 

• When the input voltage starts rising, the capacitor charges up to store energy and matches the input voltage very fast
• When the input voltage begins to fall, the voltage across the capacitor doesn’t decrease rapidly even if input voltage falls at a faster rate. The capacitor discharges very slowly; releasing its stored energy.

Hence, this process helps to decrease the fluctuations and hence obtain a near DC like voltage signal

Refer to the Following Sections of the Articles for more :

• Learning about Capacitors (Section 2 and 3)
• Low and High Pass Filter Circuits 

‘Stress‘ and ‘Strain‘ are the most encountered terms when it comes to studying Elasticity. Though, it might not have such a huge weightage in competitive exams like JEE/NEET, but trust me ladies and gentlemen : “There’s no Mechanical Engineering without these 2 terms” – Being a student pursuing my UG degree in Mechanical, I can confirm this. And if there’s no Mechanical, there are no cars, bridges, buildings, etc.

Through this article, We are going to find out which one of the two comes first – is it Stress or is it Strain ?

Table of Content :

• Introduction to Stress
• Introduction to Strain
• Final Decision

1. Introduction to Stress :

Stress is defined as the Internal Restoring Force acting per unit area.

Now, What is this Internal Restoring Force ? Let’s understand the process to know what happens inside the material

The atoms inside the solid are arranged in a spring-ball system. So, when a load (external force) is applied, it disturbs the equilibrium state by making the springs deformed. This deformation is responsible for the Internal restoring force and we call it as Restoring, because it tends to bring the system back to its equilibrium.

The following flow-chart explains the process :

2. Introduction to Strain :

Strain is defined as ‘Change in Dimensions / Original Dimensions’

Again, there are types of strain :

• Longitudinal Strain – Change happens in the length
• Shear Strain – There is a shift which leads to an angle change
• Volumetric Strain – Change happens in the Volume

Important Note :
A careful observation of the Flowchart above would tell that : There is ‘Strain’ coming into the picture at the second step since on applying load, there is a deformation happening. This is exactly what we discuss in Strain

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3. Final Decision

Now, It’s very much clear from the above discussion that : it’s the Strain which comes first ! All of this because of the Definition of Stress. Most of the times, we just memorize the formula of Stress as ‘Force/Area’ which is not complete.

• Complete Answer is : Stress = Restoring Force/Area

Misconception : Friction always opposes motion

Corrected Version : Friction always opposes ‘relative‘ motion. Relative is the word which most of the people miss and this creates the whole confusion. 

But, how can we explain this concept in a much clearer manner ? – We are going to do this in today’s short but important article

Explanation :

Analogy for better understanding :

You can imagine this scenario as a teacher controlling a small group of students on a picnic. The teacher strictly instructs that “No student should try going forward and no one should be left behind. Stay Together”

• In physics terms, what she means is : There should be no relative motion between any student i.e. all should move as a unit

Having an idea of this, we are in a postition to answer the following question below :

Case 1 : if  (v1 > v2)

Then the direction of friction on the block will be forward while that on the surface will be backward. This is because :

• As the surface moves faster, the block will say to surface, “Hey, be with me…you are too fast”. Hence it tries to oppose surface 
• While, as the block moves slower relatively, the surface will say to block, “Hey, be with me…you are too slow…I will support you”. Hence, friction gets applied in forward direction for the block

Case 2 : if  (v1 < v2)

Then the direction of friction on the block will be backward while that on the surface will be forward.

Case 3 : if  (v1 = v2)

There is no friction between the block and the surface as there is no relative motion between the two

In the last article, we got to know a very useful theorem called ‘Parallel Axis Theorem’. But as well know, it can be applied only when the 2 axes under consideration are parallel to each other. 

But what if we want to know MOI about an axis which is not the plane ? Perpendicular Axis Theorem comes to our rescue*

Topics Covered :

• Perpendicular Axis Theorem
• Example
• Miscellaneous Activity (Parallel + Perpendicular)

1. Perpendicular Axis Theorem

Conditions :

•  Applicable to only planar 2-D bodies
• 3 axes to be considered
• 2 axes in plane of the body and 3rd should be perpendicular to both
• All 3 axes needs to be concurrent

Descriptive Statement :

‘The moment pf inertia of the planar body about an axis perpendicular to the plane is equal to the sum of moment of inertias of two perpendicular axis concurrent with perpendicular axis and lying in the plane of the body’

(Observe that all the points have been covered in ‘Conditions’ section above)

Mathematical Expression :

2. Example

Question : Find the moment of inertia Ip passing through center of mass C of the square plate having mass M and side length L.

Solution :

Would there be any difference in the answer you get in Figure 1 and Figure 2 ? (Remember, it’s a square plate)

The answer is : NO ! This is because of the beautiful symmetry that this square plate holds about axis shown in both the cases. There is the same mass distribution about the axis in both the case. That’s the reason, you can’t really make out the difference !

Step-1 : Remember, we need 3 axes : 2 in plane and 1 perpendicular to them and concurrent. In this we already got 2 planar axis (Combine figure 1 and figure 2). These will be our Ix and Iy. Hence, Ix = Iy = Ip. We get

Step-2 : Now, we also know the standard MOI for square plate about an axis passing through C and perpendicular to plane of square plate. i.e. ML^2/6. This is our Iz

Step-3 : Applying perpendicular axis theorem

Solve it yourself !

Now that we have learnt about Parallel and Perpendicular Axis theorem, we are in a good state to apply this to a problem which requires both these theorems. (This itself is a good hint)

Question : Find the moment of inertia Ip for the uniform disc of mass M and radius R

To calculate moment of inertia about an unknown axis, we often take help of 2 Theorems namely :

• Parallel Axis Theorem
• Perpendicular Axis Theorem

There’s one thing common in both : which is you need to know atleast one moment of inertia about an axis. This will act as a reference for you while calculating the unknown MOI

Topics Covered :

• Parallel Axis Theorem
• Important Observation
• Example

1. Parallel Axis Theorem

1.1 Conditions to apply

• Applicable on all types of bodies
• Axis through COM || Axis about which MOI is to be found out

This is an Alert !
There are infinite axes passing through center of mass C. Don’t just choose any axis passing through C. Choose only that axis passing through C which is parallel to required axis

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1.2 Theorem

The mathematical equation for this theorem can be given as :

Where,

Ip is the MOI about the required axis

Icom is the MOI about the axis passing through COM

h is the distance between the parallel axes

M is the mass of the body

1.3 Important Observation

Hence, we can say that among all the parallel axes in the plane (shown in Figure 1), the moment of inertia of the body about the axis passing through COM is the least. We also know the expression for torque :

Therefore, we can say that, for rotations in a given plane, choosing an axis through the center of mass gives the greatest angular acceleration for a given torque

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Proof for the statement (1)

2. Example

Question : Find the moment of inertia of the rod about the axis passing through P. The rod has mass M and length L

Solution :

Step-1 : Choose an axis parallel to the required one and it must be passing through COM of the body

Step-2 : Apply Parallel axis theorem

• And we are already aware of standard MOI about axis passing through COM for rod
• h = L/2

We all have seen engine oil can somewhere, and most commonly at the mechanics shop. How you ever wondered about what’s this 5W-30 written on it ? Well, that’s what we are going to find out through this article

Topics Covered :

• Short Introduction to viscosity
• Temperature effect on viscosity
• Need for Multigrade Oil

1. Short Introduction to viscosity

Let’s say you have water flowing over a flat plate. For sure, it’s not going to move freely. But, why do we say that ? The answer to this is : Viscosity. In simpler words, there is a kind of internal friction among the moving layers of the fluid. This resistance doesn’t let the fluid flow freely over the plate.

You can say that : ‘Friction loves keeping all the layers together’. In technical terms, we say : “Friction opposes relative motion”. Having this understanding, consider layer number 2. 

• Layer 3 moves at a faster speed (v+dv) than 2. Hence, viscous force on lower layer of 3 acts in such a way that it gets slowed down. 
• Layer 1 moves at slower speed (v-dv) than 2. Hence, viscous force on upper layer of 1 acts in such a way that it gets faster.

This fluid property of trying to keep and move the fluid ‘together’ is known as Viscosity.

The thing which separates the low viscous fluid from the highly viscous fluid is the amount of ‘strictness’ that the fluid shows for keeping them together.

• For example, water is less viscous than honey because water doesn’t care much about keeping the layers moving together. While, Honey is like a much ‘strict master’ who wants all of this layers to be united/together

Technical Definition for Viscosity –
The measure of resistance to relative motion within the fluid is called viscosity

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2. Temperature effect on Viscosity

Temperature does have an effect on viscosity of the fluid.

• In case of a liquid, the molecules are bonded by a weak chemical bonds. 
• On increasing temperature, you are actually providing enough thermal energy to the molecules that they break the bonds and become free. This causes the viscosity of fluid to decrease as there is no more dependency of fluid layers on one another because of moving apart. We say, the fluid becomes thinner.
• While, at much lower temperatures, the fluid tends to become thicker.

3. Need for Multigrade Oil

Engine Oil is mostly used in order to ensure that there is proper lubrication among the contact parts i.e. with engine oil, we ensure there is no wear and tear among the interacting parts. 

3.1 What happens if oil is too thin or too thick ?

• If the oil you use is too thin, it will just flow out of the surfaces very quickly and hence won’t be of any help

• If the oil is too thick, a lot of power would go into just moving the parts through your ‘thick’ oil

3.2 Effect of Temperature on motor oil ?

So, knowing this, we choose a motor oil with some given viscosity. Now, consider 2 cases :

• Case 1 : I use this oil in peak summer days
• Case 2 : I use this oil in peak winters

We have already discussed about the effect of temperature on the viscosity. An oil with given viscosity would becomes thinner in peak summer and thicker on peak winters.

SOLUTION :
To overcome this, earlier people used a 30-weight motor oil (already thicker) in summers, so that, it thins out and reach required value because of high temperature WHILE they used 5-weight motor oil (already thin) in winters, so that, it thickens to reach the required value in peak winters due to low temperature.

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BUT Now, we have come up with something even better, known as ‘Multigrade Oil‘. 

The speciality of this oil being that it can maintain a constant value of viscosity over a wide range of temperatures. Hence, we no longer have to change our oil from season to season. 

• The key feature of multigrade oils is their ability to remain fluid when cold and provide adequate viscosity at higher temperatures.

Rating :

5W-30 means 5 weight in winter and 30 weight in summer. Hence, viscous nature remains maintained. Now, you know the reason behind 5W-30. Similarly, we also have 10W-40 and many more…

More Articles to Read :

How to write Coefficient of Restitution expression ? – Part 1

How to write Coefficient of Restitution expression ? – Part 1

physicsandelectronics.com
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29 August 2024
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Writing expression of Coefficient of Restitution (COR) can be a bit confusing. Also COR is one of the important concepts when it comes to designing sports equipments like racquets and balls

What is Total Internal Reflection ? – Geometrical Optics

What is Total Internal Reflection ? – Geometrical Optics

physicsandelectronics.com
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24 August 2024
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Total Internal Reflection, shortly known as TIR is one of the useful phenomenon in Geometrical or Ray Optics which has applications in lot of areas. In this Article, we discuss this topic in detail

Problem 7 : Red or Blue ?

Problem 7 : Red or Blue ?

physicsandelectronics.com
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14 August 2024
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Physics Problem 7 – It mixes up Physics and Electronics. But not only that, the physics part itself consists of multiple concepts

Charge Induction in Metals and Non-metals

Charge Induction in Metals and Non-metals

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21 July 2024
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Charge Induction is a topic under Electrostatics. The article describes the process of how actually charges get induced onto the surface of conducting and non-conducting bodies

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Topic Under Chapter – Center of Mass and Collisions

Coefficient of Restitution also called in short as COR is one of the important concepts to be taken into consideration when it comes 

in designing sports equipments like badminton racquet, tennis racquet, several types of balls like baseball, basketball, cricket

ball ,etc. 

• This is mainly because of the fact that these sports like basketball, badminton, tennis, etc involve collisions which makes terms like collision energy and rebound energy come into picture. To relate how good the bounce will happen, we have a ratio known as ‘Coefficient of Restitution’. As simple as that !

1. Rules to Remember

There are 2 cases :

• Before collision (Deals with the Approach of the bodies)
• After Collision (Deals with the Separation of the bodies)

Remember This !
For Before Collision (Vapp) : The velocity component which supports the approach i.e. that component feels as if bodies should approach each other, is positive

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Remember This !
For After Collision (Vsep) : The velocity component which supports the separation i.e. that component feels as if bodies should get separated from each other, is positive

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2. Examples (Different Cases for COR) :

We have 2 bodies (body 1 and body 2) undergoing collision. We will be trying to write the Coefficient of Restitution for each case.

Case 1 :

Writing Velocity of approach (Vapp) first :

• Both u1 and u2 want the approach of the bodies to happen. So both will be positive. Hence Vapp is ‘u1+u2’

Writing Velocity of separation (Vsep) :

• v1 and v2, both want separation to happen. So, +v1 and +v2. Hence Vsep will be ‘v1 + v2’

Case 2 :

Writing Velocity of approach (Vapp) first :

• u1 wants approach but u2 doesn’t want that. So, +u1 but -u2. Hence Vapp is ‘u1-u2’

Writing Velocity of separation (Vsep) first :

• v1 wants to separate but v2 doesn’t want that. So, +v1 but -v2. Hence Vsep is ‘v1-v2’

Case 3 :

Writing Velocity of approach (Vapp) first :

• Both u1 and u2 want the approach of the bodies to happen. So both will be positive. Hence Vapp is ‘u1+u2’

Writing Velocity of separation (Vsep) first :

• v2 wants to separate but v1 doesn’t want that. So, -v1 but +v2. Hence Vsep is ‘-v1+v2’

Case 4 :

Writing Velocity of approach (Vapp) first :

• u1 wants approach but u2 doesn’t want that. So, +u1 but -u2. Hence Vapp is ‘u1-u2’

Writing Velocity of separation (Vsep) first :

• v1 and v2, both want separation to happen. So, +v1 and +v2. Hence Vsep will be ‘v1 + v2’

FAQ section :

What is Coefficient of Restitution ?

Coefficient of Restitution or COR is the Ratio of the Rebound speed (velocity of separation) to Collision Speed (velocity of approach). It helps in determining the intensity/type of collision that can take place

How is elastic and inelastic collision determined by COR ?

If value of Coefficient of Restitution (COR) is 1, it implies that the collision is elastic in nature i.e. no kinetic energy will be lost during collision. If the COR is <1, it implies partially elastic while if COR is 0, then collision is called ‘perfectly inelastic’

Introduction :

Total Internal Reflection also known as TIR is one of the useful phenomenon which has applications in lot of areas. One such example is of Optical Fiber Cables. In this Article, we will be discussing about TIR : What is it ? Under what conditions does it happen ? What is the difference between ‘normal reflection’ and ‘total internal reflection’ ? 

Topics Covered :

• What is meant by reflection ?
• How does TIR happen ?
• Difference between normal reflection and TIR

1. What is meant by reflection ?

In simple words, Reflection is nothing but bouncing back of light into the ‘same medium’ once it gets hit onto a polished hard surface (usually mirror).

2. How does Total Internal Reflection happen ?

When a light travels from one medium to another, it bends. But does it bend toward the normal or away from the normal depends on the fact that from which medium to which medium it is going.

• Rarer to Denser – bends towards the normal
• Denser to Rarer – bends away from the normal

Now, this specific case of Total Internal Reflection (TIR) happens when the light travels from denser medium to rarer medium.

From the figure, as we keep increasing the angle of incidence, the angle of refraction also increases until the critical angle is reached.

Critical Angle :
For each medium interface, we have a special angle defined, known as critical angle. In simple words, it is the angle of incidence at which the refracted ray grazes along the medium-separating interface (the angle of refraction becomes 90 deg).

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TIR Condition :
When the angle of incidence goes beyond this critical angle, the ray gets ‘reflected back’ into the ‘same medium’. This phenomena is called ‘Total Internal Reflection’

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3. Difference between Normal Reflection and TIR :

Normal Reflection :

• The intensity of the incident ray is much greater than the intensity of reflected ray. This is because during normal reflection, a part of the light gets absorbed by the material of which it hits and some of it gets transmitted further. 

Total Internal Reflection :

• In this case of the incident ray intensity is retained 100 % by the reflected ray. This is the major differnce between Normal Reflection and Total Internal reflection

A small Question (JEE Advance PYQ) :

Question : 

A light ray travelling in glass medium is incident on glass-air interface at an angle of incidence. The reflected (R) and transmitted (T) intensities, both as function of theta, are plotted. The correct sketch is : 

Answer : (C) option

• At angle of incidence = 0 deg : Most of the light (not 100%) is transmitted.
• At angle of incidence > critical angle : 100 % of light is reflected and hence 0% transmission of light

FAQ section :

What is Total Internal Reflection (TIR) ?

TIR is the phenomenon in which the incident light travelling from denser medium to rarer medium gets reflected back into the denser medium retaining its full intensity (100%).

What is a grazing ray ?

We call an refracted ray as a grazing ray when it passes along the interface separating two mediums

What is meant by critical angle in TIR ?

For each medium interface, we have a special angle defined, known as critical angle. In simple words, it is the angle of incidence at which the refracted ray grazes along the medium-separating interface (the angle of refraction becomes 90 deg).

Who can read this article ?

Students from class 10, class 11, class 12 preparing for boards or competitive exams like JEE, NEET, etc. or someone just having interest in Physics can refer to this article

Under which chapter, does this topic come ?

This topic of Total Internal Reflection or TIR comes under the ‘Ray Optics’ Chapter, also known as ‘Geometrical Optics’ 

What are the main concepts needed to study this ?

Reflection and Refraction (applying Snell’s Law) are the two important concepts needed