For a multimode step index optical fibre, the core refractive index is 1.5 and fractional index difference is 0.001. Calculate the pulse broadening for 1\,\mathrm{km} length of the fibre. Over a length of 2\,\mathrm{km} of the fibre, calculate the minimum pulse separation that can be transmitted without overlap.
In a certain engine, a piston undergoes vertical SHM with an amplitude of 10\,\mathrm{cm}. A washer rests on the top of the piston. As the motor is slowly speeded up, at what frequency will the washer no longer stay in contact with the piston?
What are the step index and graded index optical fibers ? What are the conventional optical windows for light propagation through optical fibers ?
Explain the working principle of a 3-level laser with a specific example. Comment on why the third level is needed.
Draw a neat diagram to show how light propagates through a graded index optical fiber from the entrance to the fiber end and explain.
How does the population inversion in an active medium lead to the amplification of light in a laser ? Explain in details.
Starting with the rate equations for matter-radiation interaction, show that the ratio of the Einstein's A and B coefficients is proportional to the third power of the frequency of radiation.
Show that the group velocity is equal to particle velocity. Also prove that the group velocity of the photons is equal to c, the velocity of light.
If the system matrix for a thin lens of focal length f is given by : S = \begin{bmatrix} 1 & -1/f \\ 0 & 1 \end{bmatrix} , show that the system matrix for a combination of two thin lenses of focal lengths f_1 and f_2 separated by a distance d can be obtained as S_{12} = \begin{bmatrix} 1 - d/f_2 & -(1/f_1 + 1/f_2 - d/f_1 f_2) \\ d & 1 - d/f_1 \end{bmatrix}
Explain how you can construct a zone plate from Fresnel's half period zone. Show that a zone plate has multiple foci.
Write down the mathematical representation of Fermat's principle and explain all the notations used. With the help of a neat diagram, show that this principle can be used to obtain the law of refraction : n_1 \sin \theta_1 = n_2 \sin \theta_2 , where n_1 and n_2 are the refractive indices of the two media while \theta_1 and \theta_2 are the angles of incidence and refraction of the light beam.
A left circularly polarized beam (\lambda = 5893^\circ\text{A}) is incident normally on a calcite crystal (with its optic axis cut parallel to the surface) of thickness 0.005141\text{ mm}. What will be the state of polarization of the emergent beam ? Justify your answer. Here the refractive indices for the ordinary and the extraordinary rays are 1.65836 and 1.48641 respectively.
Explain the lasing action of \text{He}-\text{Ne} laser using energy level diagram and describe the operation of \text{He}-\text{Ne} laser experimental set-up.
Discuss the applications of lasers in communication and medicine.
The displacement associated with a three-dimensional plane wave is given by \Psi(x,y,z,t) = a\cos\left[\frac{\sqrt{3}}{2}kx + \frac{1}{2}ky - \omega t\right]. Calculate the angles made by the propagating wave with the x, y and z-axes.
Discuss spatial evolution of Fresnel diffraction into Fraunhofer diffraction.
Classify fibers based on the number of modes that can propagate through them. Depict step-index and graded-index multimode fibers pictorially.
If a thin sheet of glass of thickness t and refractive index \mu is placed in the path of one of the interfering waves, show that the distance through which a fringe is displaced is a function of t.
In a tungsten filament lamp, thermionic emission takes place at 1.2\times10^3\ \mathrm{K}. Calculate the ratio of spontaneous emission to stimulated emission for non-degenerate energy levels. Interpret your result physically. Take \lambda=550\ \mathrm{nm}, k_B=1.38\times10^{-2}\ \mathrm{J\,K^{-1}}, h=6.67\times10^{-34}\ \mathrm{J\,s} and c=3\times10^8\ \mathrm{m\,s^{-1}}.
In a double slit interference experiment, show that the fringe shape is a hyperbola.
