Discuss Rayleigh’s criterion for resolving power of an optical instrument. Obtain an expression for resolving power of a microscope.
See Answer →A plane light wave of wavelength falls on a long narrow slit of width
. (i) Calculate the angles of diffraction for the first two minima. (ii) How are these angles influenced if the width of slit is changed to
? (iii) If a convex lens of focal length
is now placed after the slit, calculate the separation between the second minima on either side of the central maximum.
A plano-convex lens of radius is placed on an optically flat glass plate and is illuminated by an extended monochromatic source. Assume that the point of contact is perfect. The diameters of the
and
dark rings in the reflected light are
and
. Next, the space between the lens and the glass plate is filled with a liquid. The diameter of the
ring changes to
. Calculate the refractive index of the liquid when the ring is (i) dark, and (ii) bright, if the wavelength of light is
.
Obtain the expression for shift in fringes when a thin transparent sheet is introduced in the path of one of the waves in a double slit interference experiment.
See Answer →Obtain an expression for elliptically polarised light resulting due to superposition of two orthogonal linearly polarised light waves. Show that plane polarised light and circularly polarised light are special cases of elliptically polarised light.
See Answer →Obtain expressions for reflection and transmission amplitude coefficients when electric vector associated with a plane monochromatic electromagnetic wave is in the plane of incidence.
See Answer →Depict spatial evolution of Fresnel diffraction pattern.
See Answer →Discuss the concept of missing orders with reference to double slit diffraction pattern.
See Answer →Describe polarisation of light by reflection. How does degree of polarisation vary with angle of incidence of light?
See Answer →The sodium lamp used in a physics laboratory gives out light uniformly. Suppose that the lamp uses 40 W. Calculate the magnitude of electric field.
See Answer →wo tritium () nuclei fuse to release 11.3 MeV energy. Calculate the total energy released in the fusion of 1 kg tritium.
From the semi-empirical mass formula, calculate the value of the atomic number (Z) for the most stable nucleus at a given mass number A. Calculate Z0 for .
Calculate the kinetic energy of the alpha particle emitted in the alpha decay of the Radium isotope (
). It is given that
,
and
.
The half-life of is known to be 5730 years. Calculate the decay constant (in
). Also, calculate the rate of disintegration for 1 g of
.
An electron with a energy of 8.0 eV strikes a potential barrier of energy 12.0 eV. If the tunnelling probability is 4.0 percent, determine the width of the barrier.
See Answer →Explain whether the eigen functions of the following Hamiltonian for a particle of mass m will have a definite parity: .
Calculate the probability current density of the incident and reflected waves for the quantum mechanical particle incident on a step potential$
when E < V0.
The eigenfunction of a particle confined in a box of length L () is
$
i) Show that is not an eigenfunction of the momentum operator.
ii) Calculate the expectation value of the kinetic energy.
The normalized wave function for a particle is given by$
Determine
i) the value of x at which the probability density function is maximum, and
iii) the probability of finding the particle between and
.
The average decay life time of an elementary particle is . Calculate the minimum uncertainty in the measurement of its energy. Also, calculate the minimum uncertainty in the measurement of its mass using the mass-energy equivalence.