An oscillator of mass 0\cdot 01\text{ kg} draws maximum power at a frequency of 96\text{ Hz} with half power points at 93\text{ Hz} and 99\text{ Hz}. If the amplitude of driving force is 3\cdot 88\text{ N}, calculate (i) quality factor, (ii) the damping factors and amplitude of the oscillator at resonance.
Write down the equation of motion of a weakly damped harmonic oscillator driven by a harmonic force. Obtain an expression for the maximum amplitude of oscillation under steady-state conditions.
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.
When two tuning forks were sounded together, 24 beats were produced in 6\text{ seconds}. After loading one tuning fork with wax, they produced 30 beats in 6\text{ seconds}. If the unloaded fork frequency is 512, what is the frequency of the other ?
Explain mathematically the phenomenon of beats. How does it differ from that of interference ?
An optical waveguide has core and cladding of refractive indices 1\cdot 46 and 1\cdot 45 respectively. (i) Calculate the maximum number of modes with wavelength \lambda = 900\text{ nm} that can travel if it is a planar waveguide of core thickness 10\ \mu\text{m}. (ii) What is the number of modes if it is a cylindrical fiber of diameter 10\ \mu\text{m} ?
A step-index silica fiber consists of core of refractive index 1\cdot 450 and diameter 90\ \mu\text{m}. If the numerical aperture of the fiber is 0\cdot 16, calculate : (i) the acceptance angle of the fiber, (ii) refractive index of the cladding, and (iii) if the fiber is immersed in water of refractive index 1\cdot 33, how does the acceptance angle change ?
Explain the Fraunhofer diffraction at a single slit and obtain the condition for minima. Derive the expression for resolving power of a grating.
Two lenses of focal lengths 8\text{ cm} and 4\text{ cm} are placed at a certain distance apart. Calculate the distance between the lenses if they form an achromatic combination.
What are Einstein's A and B coefficients ? Establish a relation between them.
A body describing simple harmonic motion (SHM) has a maximum acceleration of 8\ \pi\text{m/sec}^2 and a maximum speed of 1\cdot 6\text{ m/sec}. Find the time period (T) and the amplitude (A) of SHM.
In a double slit experiment the slits are 2\text{ mm} apart and are illuminated with a mixture of two wavelengths, \lambda = 750\text{ nm} and \lambda' = 900\text{ nm}. At what minimum distance from the common central bright fringe on a screen 2\text{ m} distant from the slits will a bright fringe from one interference pattern coincide with a bright fringe from the other ?
Explain the diffraction at straight edge with the help of Cornu's spiral.
Distinguish between the intensity patterns due to diffraction from a narrow slit and a straight edge.
Consider a Gaussian pulse propagating in pure silica, at \lambda_0 = 0\cdot 85\\ \mu\text{m}, along z-direction. As the pulse propagates, it gets broadened according to the formula \tau^2(z) = \tau_0^2 \left( 1 + \frac{4 \alpha^2 z^2}{\tau_0^4} \right), \quad \alpha = \left. \frac{d^2 k}{d \omega^2} \right|_{\omega=\omega_0} where \tau(z) is the pulse width after propagation through a distance z and \tau_0 is the pulse width at z = 0. Given that \alpha = 3 \times 10^{-26}\\ \frac{\text{S}^2}{\text{m}} at \lambda_0 = 0\cdot 85\\ \mu\text{m}. Calculate the distance at which \tau(z) = \sqrt{2} \cdot \tau_0.
In the steady state forced vibration of the damped harmonic oscillator, show that the amplitude of the driven system is maximum when p = \sqrt{\omega^2 - 2b^2} and further the value of the maximum amplitude is \frac{f}{2b \sqrt{\omega^2 - b^2}}, where the symbols have their usual significance. (Here you start from the steady state solution)
A light spring of relaxed length 'a_0' is suspended from a point. It carries a mass 'm' at its lower free end, which stretches it through a distance l. Show that the vertical oscillation of the system is simple harmonic in nature and has time period T = 2\pi \sqrt{l / g}, where g is the acceleration due to gravity.
A plano-convex lens of crown glass is connected to a concavo-convex lens of flint glass so that the convex surface of the first and the concave surface of the second fit exactly. If the combination is achromatic and the combined focal length is -50\text{ cm}, determine the radii of curvature of the faces of the flint glass lens. The dispersive power of the crown glass is one-half of that of the flint glass and the refractive indices for yellow light are respectively 1\cdot 500 and 1\cdot 625 respectively.
What is Fermat's principle ? Derive the laws of reflection and refraction with the help of this principle, when the light is incident on a curved surface.