A transparent film of glass of refractive index 1\cdot 5 is introduced normally in the path of one of the interfering beams of Michelson interferometer which is illuminated with light of wavelength 5893\text{ \AA}. This causes 500 dark fringes to shift across the field. Determine the thickness of the film.
What are beats ? A tuning fork gives 6 beats per second with 25\cdot 4\text{ cm} length of stretched sonameter wire. The same 6 beats are heard per second when the length of the same wire is reduced to 24\cdot 6\text{ cm}. Calculate the frequency of the tuning fork.
Two glasses have dispersive powers in the ratio 2 : 3. These glasses are used in the manufacture of an achromatic contact objective of focal length 50\text{ cm}. What are the focal lengths of the lenses ?
What is holography ? Briefly discuss the applications of holography.
What is the principle of propagation in optical fibers ? Explain with the help of neat diagram, the ray propagation in Step index and Parabolic index optical fibers. How can pulse dispersion be minimized using Parabolic index optical fibers ?
A comet of mass m moves towards the Sun with initial velocity v_0. The mass of the sun is M and its radius is R. Find the total cross-section \sigma for striking the Sun. Take the Sun to be at rest and ignore all other bodies.
(i) Define the angular velocity \omega of a rigid body rotating about some axis.
(ii) Then derive the relation \vec{v} = \vec{\omega} \times \vec{r} for the velocity of a point in the body with position vector \vec{r} relative to an origin on the axis. Draw a diagram explaining all the vectors.
On a space-time diagram after the Lorentz transformation with given v we get new tilted axis ct' and x'. For a point on the ct' axis which is at the (geometrical) distance \delta on the diagram measured from the origin, find the values of t' and t.
During take-off, an aircraft accelerates horizontally in a straight line at a rate A. A small bob of mass m is suspended on a string attached to the roof of the cabin, and a hydrogen balloon (total mass m) is tethered to the floor by a string. For each, determine the tension in the string and the equilibrium angle \theta between string and vertical. Draw a neat diagram to explain your answer.
A block of mass m is sliding on a wedge of mass M as shown in the figure below. The wedge can slide on the horizontal table. Find the equation of motion.
A rigid body is rotating under the influence of an external torque (N) acting on it. If T is the kinetic energy and \omega is the angular velocity, show that \dfrac{dT}{dt} = N \cdot \omega in the principal axes system.
A pion at rest decays into a muon and a neutrino.
(i) Find the energy of the outgoing muon in terms of the two masses m_\pi and m_\mu (assuming m_\nu = 0). (ii) Find the velocity of muon.
Obtain the Lorentz transformations for the components of momentum-energy four vector.
Describe the basic segments of a microprocessor and briefly mention their functions. Mention the name of widely used 8-bit microprocessors.
Describe briefly the construction of an n-channel JFET. Define the pinch-off voltage and pinch-off current. Give the relationship between the pinch-off voltage, the saturation voltage and gate-source voltage.
What is Meissner Effect ? Explain the validity of Meissner Effect in Type I and Type II superconductors.
What is Josephson Effect ? Give an account of applications of superconductivity.
Verify the following Boolean identities : (i) A + \bar{A} B = A + B (ii) \overline{\bar{A} + B} + \overline{\bar{A} + \bar{B}} = A
A transistor operating in the CE mode draws a constant base current \text{I}_{\text{B}} of 30\ \mu\text{A}. The collector current \text{I}_{\text{C}} is found to change from 3\cdot 5\text{ mA} to 3\cdot 7\text{ mA} when the collector-emitter voltage \text{V}_{\text{CE}} changes from 7\cdot 5\text{ V} to 12\cdot 5\text{ V}. Calculate the output resistance and \beta at \text{V}_{\text{CE}} = 12\cdot 5\text{ V}. What is the value of \alpha ?
Consider atoms as hard, uniform spheres and packed closely together so that they fold touch one another. Calculate the number of atoms per cubic unit cell and fraction of volume occupied for simple cubic, body-centred and face-centred cubic structures.
