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.
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.
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.
What do you understand by attenuation in optical fibers? What are the factors responsible for the attenuation?
Explain the phenomenon of double refraction. What are positive and negative crystals? Give their examples.
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.
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.
Write conditions for working of a step-index optical fiber. In a step-index fiber, the core and cladding materials have refractive indices 1\cdot50 and 1\cdot43, respectively. Find the following : (i) Critical propagation angle (ii) Acceptance angle (iii) Total time delay in 1\text{ km} length of the fiber (iv) Total dispersion in 50\text{ km} length of the fiber
Write equation for damped harmonic oscillations and obtain expression for logarithmic decrement. In a damped harmonic motion, the first amplitude is 10\text{ cm}, which reduces to 2\text{ cm} after 50 oscillations, each of period 4\text{ seconds}. Determine the logarithmic decrement. Also, calculate the number of oscillations in which the amplitude decreases to 25\%.
Consider the interaction of an electromagnetic wave at the interface of two dielectric media. If electric field \vec{E} is parallel to the plane of incidence, obtain Fresnel's equations and Brewster's law of polarization.
(i) What is the difference between Fresnel diffraction and Fraunhofer diffraction ? (ii) What is resolving power of a telescope ? Why is the resolving power of microscope more with UV light than with visible light ?
Using Huygens' principle for a plane wave travelling from rarer medium 1 to a denser medium 2, show that \frac{\sin i}{\sin r} = \frac{v_1}{v_2} = \frac{\mu_2}{\mu_1}, where i and r are the angles of incidence and refraction, respectively. v_1, \mu_1 and v_2, \mu_2 are the velocities and refractive indices in media 1 and 2, respectively.
Obtain condition for achromatism of two thin lenses separated by a finite distance. If the dispersive powers of the materials of the two lenses are 0\cdot020 and 0\cdot028, their focal lengths are 10\text{ cm} and 5\text{ cm}, respectively. Calculate the separation between them in order to form achromatic combination.
(i) What are the requisite conditions for observation of interference pattern on a screen ? (ii) Derive the expression for fringe width and intensity at a point on the screen in a double slit experiment.
What are three and four level pumping schemes ? Explain the lasing action in these with schematic diagrams.
Show that the mean kinetic and potential energies of non-dissipative simple harmonic vibrating systems are equal.
Obtain the system matrix for a thick lens and derive the thin lens formula.
Newton's rings are observed between a spherical surface of radius of curvature 100 cm and a plane glass plate. The diameters of 4th and 15th bright rings are 0.314 cm and 0.574 cm, respectively. Calculate the diameters of 24th and 36th bright rings and also the wavelength of light used.
In He-Ne laser, what is the function of He gas? Explain the answer with the help of energy level diagram for He – Ne laser.
Discuss the phenomenon of Fraunhofer diffraction at a single slit and show that the intensities of successive maxima are nearly in the ratio 1 : \frac{4}{9\pi^2} : \frac{4}{25\pi^2} : \frac{4}{49\pi^2}.
