What do you understand by attenuation in optical fibers? What are the factors responsible for the attenuation?

Consider a 10\text{ mW} laser beam passing through a 50\text{ km} fiber link of attenuation 0.5\text{ dB/km}. Calculate the power of the laser at the end of the link.

The diameter of central zone of a zone plate is 2.4\text{ mm}. If a point source of light of wavelength 600\text{ nm} is placed at a distance of 5.0\text{ m} from the zone plate, calculate the position of the first image.

Consider a damped harmonic oscillator given by the equation \ddot{x} + 2\mu \dot{x} + \omega_0^2 x = 0. Obtain the displacements for (i) overdamped, (ii) underdamped and, (iii) critically damped motion.

Calculate the group and phase velocities for the wave packet corresponding to a relativistic particle.

A three-level laser system emits laser light at a wavelength of 550\text{ nm}. If the population of the upper level exceeds that of the lower level by 25\%, determine the negative temperature characterizing the system.

Explain the phenomenon of double refraction. What are positive and negative crystals? Give their examples.

Draw the energy level diagram of He-Ne laser. The metastable state of ruby laser is at 1.786\text{ eV}. Calculate the wavelength of the light emitted.

Write down the system matrix for a combination of two thin lenses in paraxial approximation. Hence obtain the focal length of the combination and the positions of unit planes.

(i) Distinguish between interference fringe pattern and diffraction fringe pattern. (ii) In an experiment using Newton's rings, the diameter of 5^{\text{th}} and 15^{\text{th}} rings were found to be 33.6 \times 10^{-4}\text{ m} and 59 \times 10^{-4}\text{ m} respectively. Calculate the radius of curvature of the plano-convex lens if the source of light is sodium light (\lambda = 589.0\text{ nm}). Mention any other applications of Newton's ring experiment.

A weakly damped harmonic oscillator consisting of spring-mass system has the following parameters : Mass m = 0.25\text{ kg}, Spring constant k = 100\text{ N m}^{-1}, Damping coefficient \gamma = 1\text{ N s m}^{-1} A periodic force F = 5 \cos \omega t (newton) is applied to the system. Determine (i) the amplitude of the oscillator at resonance and (ii) the Q-value of the oscillator.

What are the special features of step-index fibre ? The step-index fibre has core glass and cladding glass with refractive indices 1.68 and 1.5 respectively. Calculate the numerical aperture. Find the critical angle and acceptance angle for entrance of light if the fibre is placed in air.

Consider a thin lens combination of two convex lenses of focal lengths f_1 = +10\text{ cm} and f_2 = +20\text{ cm}, respectively, separated by 25\text{ cm}. Determine the focal length of the combination and the positions of unit planes.

A telescope has an objective lens of diameter 10\text{ cm}. Determine whether this telescope can resolve two stars having an angular separation of 2\cdot 4 seconds of arc. (Assume the wavelength of starlight as 550\text{ nm})

(i) What are the similarities and dissimilarities between a zone plate and a convex lens ? (ii) A monochromatic light of wavelength 5860 \times 10^{-8}\text{ cm} is incident normally on a 2\text{ cm} wide grating. The first order spectrum is produced at an angle of 20^\circ with respect to the normal. Determine the total number of lines on the grating. How does the resolving power of grating depend on the number of rulings on the grating ?

What do you understand by optical activity? A linearly polarized light is propagating along the optic axis of a quartz crystal of thickness 0.2\text{ cm}. If the difference in the refractive indices corresponding to right circularly polarized and left circularly polarized beams is 7 \times 10^{-5} and the wavelength of the light is 0.5\text{ }\mu\text{m}, calculate the angle of polarization.

The intensity at the central maximum observed on a screen in a double-slit experiment is 2 \times 10^{-3}\text{ W/m}^2. If the path difference between interfering waves reaching a point on the screen is \frac{\lambda}{6}, where \lambda is the wavelength of the light used in the experiment, determine the intensity at that point.

Explain the phenomenon of double-refraction in calcite crystal with special reference to Ordinary Ray (OR), Extraordinary Ray (ER) and uniaxial negative crystal.

Define generalized coordinates. How many generalized coordinates are required to describe the dynamics of (i) a free rigid body in 3 dimension ? (ii) a solid cylinder rolling in an inclined plane without slipping ?

Show that the angular momentum of a rigid body consisting of n particles of masses m_i, i = 1, 2, 3, \dots, n, rotating with an instantaneous angular velocity \mathbf{\omega} about an axis passing through the origin O of the coordinate system OXYZ is given by \mathbf{L} = \mathbf{I} \cdot \mathbf{\omega}, where \mathbf{I} is known as the inertia tensor.