# Electromagnetic Mode Theory for Optical Propagation MCQ

1. Which equations are best suited for the study of electromagnetic wave propagation?

1. Maxwell’s equations
2. Allen-Cahn equations
3. Avrami equations
4. Boltzmann’s equations

Explanation:

In his formulation of electromagnetism, Maxwell described light as a propagating wave of electric and magnetic fields. More generally, he predicted the existence of electromagnetic radiation: coupled electric and magnetic fields traveling as waves at a speed equal to the known speed of light.

Electromagnetic mode theory finds its basis in electromagnetic waves. Electromagnetic waves are always represented in terms of electric field E, magnetic field H, electric flux density D, and magnetic flux density B. These sets of equations are provided by Maxwell’s equations.

2. The phenomenon which occurs when an incident wave strikes an interface at an angle greater than the critical angle with respect to the normal to the surface is called as _______

1. Refraction
2. Partial internal reflection
3. Total internal reflection
4. Limiting case of refraction

Explanation:

Total internal Reflection of light If the angle of incidence in the denser medium is greater than the critical angle C, then the ray is reflected back into the first rarer medium, this phenomenon is called total internal reflection. The critical angle is an angle beyond which no propagation takes place in an optical fiber. In a desert, the phenomenon of mirage occurs due to total internal reflection.

Example of Total Internal Reflection

i. Sparkling of the diamond.

ii. Mirage and looming.

iii. Shining of air bubble in water.

iv. Increase in duration of sun’s visibility.

v. Shining of a smoked ball or a metal ball on which lamp stool deposited when dipped in water.

vi. Optical Fibre.

3. When λ is the optical wavelength in a vacuum, k is given by k=2π/λ. What does k stand for in the above equation?

1. Phase propagation constant
2. Dielectric constant
3. Boltzmann’s constant
4. Free-space constant

Explanation:

k = 2π/λ also termed as the wave equation, k gives us the direction of propagation and also the rate of change of phase with distance. The wave vector k counts the wavenumber (number of nodes) in a particular direction. Hence it is termed as phase propagation constant.

4. What is refraction?

1. Bending of light waves
2. Reflection of light waves
3. Diffusion of light waves
4. Refraction of light waves

Explanation:

When a ray of light propagating in a medium enters the other medium, it deviates from its path. This phenomenon of change in the direction of propagation of light at the boundary, when it passes from one medium to another medium, is called the refraction of light.

Example of Refraction

1. Bending of a linear object when it is partially dipped in a liquid inclined to the surface of the liquid.
2. Twinkling of stars.
3. The oval shape of the sun in the morning and evening.
4. An object in a denser medium, when seen from a rarer medium, appears to be at a smaller distance.
5. Due to refraction, rivers appear shallow, coin in a beaker filled with water appears raised, pencil in the beaker appears broken.
6. At sunset and sunrise, due to refraction, the sun appears above the horizon while it is actually below the horizon. The duration of the day appears to be increased by nearly 4 minutes to atmospheric refraction.
7. Writing on a paper appears lifted when a glass slab is placed over the paper.

5. Constructive interference occurs when total phase change after two successive reflections at upper and lower interfaces is equal to? (Where m is an integer)

1. πm
2. 2πm
3. πm/4
4. πm/6

Explanation:

Constructive interference occurs where the lines (representing peaks), cross over each other. In other words, when two waves are in phase, they interfere constructively. Destructive interference occurs where two waves are completely out of phase (a peak lies at the midpoint of two waves.

When measuring the reflectivity of a thin film on a substrate, we obtain constructive interference for 2δ = 2πm,

Where δ = Phase Shift

The component of phase waves which is in the x-direction is reflected in the interference between the higher and lower refractive index media. It is assumed that such an interference forms the lowest order standing wave, where the electric field is maximum at the center of the guide, decaying towards zero.

One of the best examples of constructive interference that may be observed in our day-to-day life is two speakers playing the same music while facing each other. At this time, music will appear louder and more powerful as compared to music played by a single speaker.

6. Destructive interference occurs when the maxima of two waves are _______ out of phase.

1. 45 Degrees
2. 90 Degrees
3. 180 Degrees
4. 120 Degrees

Explanation:

Destructive interference occurs when the maxima of two waves are 180 degrees out of phase: a positive displacement of one wave is canceled exactly by a negative displacement of the other wave. The amplitude of the resulting wave is zero.

An example of destructive interference can be seen in. When the waves have opposite amplitudes at the point they meet they can destructively interfere, resulting in no amplitude at that point. For example, this is how noise-canceling headphones work.

7. When measuring the reflectivity of a thin film on a substrate  destructive interference occurs when

1. δ = (2m + 1)π
2. 2πm
3. 2δ = (2m)π
4. 2δ = (2m + 1)π

Answer: 4. 2δ = (2m + 1)π

Explanation:

Destructive interference occurs when the maxima of two waves are 180 degrees out of phase: a positive displacement of one wave is canceled exactly by a negative displacement of the other wave. The amplitude of the resulting wave is zero.

When measuring the reflectivity of a thin film on a substrate  destructive interference occurs when 2δ = (2m + 1)π

Where

δ = Phase Shift

m = integer

An example of destructive interference can be seen in. When the waves have opposite amplitudes at the point they meet they can destructively interfere, resulting in no amplitude at that point. For example, this is how noise-canceling headphones work.

8.  When light is described as an electromagnetic wave, it consists of a periodically varying electric E and magnetic field H which are oriented at an angle?

1. 90 degrees to each other
2. Less than 90 degree
3. Greater than 90 degree
4. 180 degree apart

Answer:1. 90 degrees to each other

Explanation:

• When light is described as an electromagnetic wave, it consists of a periodically varying electric field E and magnetic field H that are oriented at right angles(90 degrees) to each other.
• The traverse modes illustrate the case when the electric field is perpendicular to the direction of propagation and hence Ez = 0, but a corresponding component of the magnetic field H is in the direction of propagation.
• In this instance, the modes are said to be transverse electric (TE). • Alternatively, when a component of the E field is in the direction of propagation, but Hz = 0, the modes formed are called transverse magnetic TM0.
• In the case of electromagnetic waves which occur only in presence of both electric and magnetic fields, a particular change in the magnetic field will result in a proportional change in electric field and vice versa. These changes result in the formation of electromagnetic waves and for electromagnetic waves to occur both fields should be perpendicular to each other in direction of the wave travel.

9. A monochromatic wave propagates along a waveguide in the z-direction. These points of constant phase travel in constant phase travel at a phase velocity Vp is given by?

1. Vp=ω/c
2. Vp=ω/β
3. Vp=C/N
4. Vp=mass/acceleration

Explanation:

The phase velocity of light is the velocity with which phase fronts propagate in a medium. It is related to the wavenumber k and the (angular) optical frequency ω

Velocity is a function of displacement. Phase velocity Vp can be concluded by keeping the phase constant. Phase velocity Vp is a measure of angular velocity and it is given as

Vp=ω/β

where

ω = angular frequency of the wave

β = propagation constant

10. Which is the most important velocity in the study of transmission characteristics of optical fiber?

1. Phase velocity
2. Group velocity
3. Normalized velocity
4. Average velocity

Explanation:

The group velocity of a wave is the velocity with which the overall envelope shape of the wave’s amplitudes known as the modulation or envelope of the wave propagates through space.

The wave packet does not travel at the phase velocity of the individual waves but is observed to move at a group velocity vg given by:

vg = δω/δβ

where

ω = angular frequency of the wave

β = propagation constant

The group velocity is of greatest importance in the study of the transmission characteristics of optical fibers as it relates to the propagation characteristics of observable wave groups or packets of light.

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