Optics and Modern Physics

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

https://www.youtube.com/watch?v=rxL8DkdYCTw

*Note : (Prefer Desktop for better Experience)

Calculation of charge-to-mass ratio is of great importance when it comes to the subject of Modern Physics. Understanding the procedure behind this experiment is equivalent to revising the following topics as well :

• Moving charge in Magnetic Field
• Behaviour of Charge in Electric Field
• Projectile Motion

Sections :

• Importance of calculating e/m ratio
• Setup of the experiment
• Procedure (*Imp) 
• Final Data & Conclusion

1. Importance of e/m Ratio

Ok, so you have a value called e/m ratio ! But why is it important to caluculate this value? Is there any applications of it ?

• In simple words, the charge-to-mass ratio of a charge helps us to predict the behaviour of the particle under electric and magnetic fields. This ability to predict the particles behaviour enables us to have an idea of adjusting the setup in order to have so and so outcomes.

We can see it’s application in : 

Electron Microscopes :

• Electron Microscopes are known for their ability to magnify the images to a very high resolution & this is done with the help of a beam of electrons
• Knowing the e/m ratio enables the scientists to control the movement of electrons and a result, they produce the required resolution of the image

Particle Accelerometers :

• These are used in order to accelerate the charged particles.
• By knowing the charge-to-mass ratios, we can actually control the trajectories of the particles.

2. Setup of the Experiment

The Setup mainly consists of the following things :

• Filament F
• Battery V
• Pump
• 2 parallel plates, across which another battery has been connected 
• Current carrying coil wire (not shown in setup)
• Screen S

                                                                                              Fig. Setup for the Experiement

Purpose :

• Filament F : The filament is inclusive of that battery (not V) shown in figure.

• Voltage V : 

       –   The plate attached to the positive terminal is used as anode to attract the electron cloud. This is done to make the electrons                         accelerate.

       –   Each electron has different energies when they come out from atoms. And when they are accelerated due to potential                                   difference of V, then they all end having different set of velocities. 

• Pump : To create vacuum inside the tube

•  The parallel plates kept facing each other + battery setup,  is used to create a uniform electric field E in the region between the two plates. Direction will be from positive plate to negative plate

• Current carrying coil wire : This is done in order to setup a steady magnetic field B (going into the plane)

• Screen S : Whenever an electron strikes the screen S; it creates a spot on the screen which helps us to detect and hence analyze the trajectory/path taken by the electron.

Note that : The E and B vectors are perpendicular to each other

3. Procedure

Step-1 :

As discussed, the anode attracts the electron cloud which makes them to accelerate towards the screen S. But well before they reach the screen, the electrons are made to pass through a region R where, for now, only Electric field is applied (B is turned off).

The current setup for Step-1 looks like : 

As the electrons pass through ‘Region R‘ , they undergo deflection ‘y’ due to the electric field and follow a trajectory as shown (green) . We zoom into the Region R to get a better understanding of what’s happening

Zoomed picture of Region R :

We need the expression for deflection ‘y’.

Important : Note that the deflection is going to be measured from axis

Some of the Projectile comes into picture now !

• This ‘y’ is measured during the experiment

Step-2 :

Now, our aim is to find the velocity ‘v’ of the electron. Recall that the ‘y’ is the deflection –> BUT Deflection from which path ? The answer is ‘the axis’ . We need to find the deflection caused in electron’s trajectory due to the electric field E because otherwise in the absence of E, it would just follow the straight path along axis.

• For getting the speed (v) of the electrons which go undeflected, we introduce B now in addition to E in order to make zero deflection. This is equivalent to saying that there was none of the fields present in region R

We have to balance the forces (to get zero deflection). Remember it’s a negative charge.

We then adjust the values of E and B until the magnitudes of forces are same. This allows us to build a ‘velocity selector‘

Velocity Selector :

As discussed in Section 2 of this article, all the electrons come with different set of velocities. But, for continuing our experiment, we need only the electrons of specific velocity to be focused on. So, how to exactly distinguish those electrons ?

We can clearly see the relation of E and B with velocity. This means that controlling the values of E and B allows us to select the electrons which have their velocities as E/B. The electrons possessing this specific velocity will go through the region undeflected and hence we can separate them. 

Step-3 :

Calculating the e/m ratio with the expressions and equations we got till now :

Substituting v = E/B in the expression of y obtained in step-1, we get  :

4. Final Data

Conclusion

•  This completes our e/m calculation experiment performed by Sir J.J. Thomson.  

• The article or the whole experiment procedure itself has a lot of concepts involved in it which makes it even more important to understand, both as an Experiment as well as an good multi-concept level problem

Keep Learning !