Using the scalar theory of diffraction, obtain the expression for Fresnel diffraction integral.
See Answer →Determine the collisional width for laser operating at a gas pressure of
and gas temperature of
. Obtain the ratio of spontaneous and stimulated emission if the wavelength is
.
What is Jones vector? Determine the Jones matrix for a linear polariser which makes an angle of with the x-axis.
Derive the wave equation for the electric field in anisotropic non-conducting medium starting from Maxwell's equations.
Differentiate between isotropic and anisotropic media for electromagnetic wave propagation. Give one example of each.
See Answer →What would be the maximum possible period of this random number sequence?
See Answer → Using the linear congruential random number generator determine the first five random numbers given that: ,
,
, and
. Transform these random numbers to lie between 0 and
Derive the Runge-Kutta 2nd Order formula for the differential equation
Use this to determine the value of y at given that
, using a step size
.
The spacing between of
molecule in Raman spectrum is
. Calculate the bond length of the molecule.
Evaluate the integral using the 2-point Gaussian Quadrature Rule with the following values:
| Points | Weights | Arguments |
| 1 | 1.0 | 0.577 |
| 2 | 1.0 |
|
i) The fundamental vibrational frequency of a molecule occurs at . Determine the position of Raman line if the molecule is excited with a laser of wavelength
.
Calculate the first derivative of the function at
using the forward divided difference, backward divided difference and central divided difference methods with a step size of
rad. Also calculate the absolute true error in each case.
A population of single-celled organisms was grown in a Petri dish over a period of 24 hours. The number of organisms at a given time is recorded in the table below. Fit the data in the table below to an exponential model :
| x (time in hours) | 0 | 4 | 8 | 12 | 16 | 20 | 24 |
| y | 25 | 36 | 52 | 68 | 85 | 104 | 142 |
The rotational constant for the excited electronic state of a particular molecule is 20% smaller as compared to the rotational constant of its ground electronic state. Determine the values for the first 15 lines of the R-branch. Discuss the variation of the separation between successive transition lines of this branch.
See Answer →The HCl molecule shows its first and second overtone transitions at and
, respectively. Assuming anharmonic oscillator model, determine the anharmonicity constant, the equilibrium vibrational frequency, zero point energy, and the force constant of this molecule.
What are the advantages and drawbacks of the Secant method when compared to the Bisection Method and the Newton-Raphson Method?
See Answer →Write the Hamiltonian of a multi-electron atom. Obtain an expression for the effective potential experienced by an electron of this atom under the central field approximation.
See Answer → Use the Secant method with initial guesses of and
to calculate the root/s of the equation
up to three iterations. Calculate the absolute relative approximate error at each stage.