Geometrical theory of diffraction (GTD) is an alternative model of diffraction propounded first by Thomas Young in 1802. GTD has a long history of nearly 150 years over which many eminent people enriched this model which has now become an accepted tool in the calculation of diffraction patterns. In the conventional Helmholtz-Kirchhoff theory the diffracted field is obtained by computing the net effect of the waves emitted by all points within the area of the aperture. But GTD reduces this problem to one of computing the net effect of waves from a few points on the boundary of the aperture or obstacle, thus simplifying considerably the labour involved in computations. Also the theory can easily be modified to include polarization effects. This has been done specifically by Keller (1962) who exploited the Sommerfeld solution of diffraction of electromagnetic waves at a half plane, making the theory more versatile than the Kirchhoff scalar wave theory. Interestingly the geometry of difffracted rays is predictable from a generalized Fermat principle. According to this the total path chosen by light from the source to the point of observation via the diffracting boundary is an extremum. Historically it should be stated that many of the salient features of GTD were established by a school led by Raman which was active from 1919–1945. Later when Keller (1962) revived GTD independently, he and others who followed him rediscovered many of the results of the Raman school. We have stressed wherever necessary the contributions of the Indian School. We have also discussed certain geometries where GTD can be effectively used. We get some new and interesting results, which can be easily understood on GTD, but are difficult to interpret on the conventional theory of diffraction.

The isochoric temperature derivative of sound velocity, Beyer’s nonlinearity parameter, the isothermal volume derivatives of thermodynamic Grüneisen parameter and isochoric heat capacity and the repulsive exponent of intermolecular potential are shown to be related to the molecular constant representing the ratio of internal pressure to cohesive pressure of liquids. The calculated values are reasonably satisfactory and explain the experimental results on sound propagation data of liquids. The results have been used to develop further understanding of the significance of molecular constant, fractional free volume and repulsive exponent of intermolecular potential in describing various thermoacoustic and nonlinear properties and the anharmonic behaviour with regard to molecular order and intermolecular interactions in liquids.

The ultrasonic velocities of binary liquid mixtures of 1,1,2,2-tetrachloroethane with benzene, toluene,p-xylene, acetone and cyclohexane have been evaluated at 298.15 and 308.15 K using Schaaff’s collision factor theory (CFT), Jacobson’s free length theory (FLT), Nomoto’s relation and Van Dael ideal mixing relation. The ideal mixing relation gives the minimum deviation for all the systems except with acetone. The intermolecular free length has also been evaluated using ultrasonic and thermodynamic methods and the limitations of both the methods have been discussed. The deviations in ultrasonic velocity and intermolecular free length are discussed in terms of weak interaction between unlike molecules.

In the present paper, we report a theoretical calculation of temperature variation of the ultrasonic absorption coefficient of PbF₂. The absorption can be explained by the TLS model, with parameters which simultaneously reproduce the specific heat, thermal expansion, bulk modulus and ionic conductivity. Our results agree well with recent experimental reports of ultrasonic attenuation in PbF₂.

The Bloch enhancement factor α(k_f) of the electric field gradient has been evaluated for the half-filledd-core Fe host metal and completely filledd-core Cu host metal in single orthogonalized plane wave (OPW) approximation. For this purpose the radially-dependent antishielding factors,γ(r) have been calculated in non-orthogonal Hartree-Fock perturbation theory (NHFPT). The results show that the contributions of antishielding to α(k_f) from the plane wave-plane wave part and the core part of the OPW state are individually large but opposite in sign and thereby lead to partial cancellation. The net effect of antishielding on α(k_f) is found to be − 5.6% in Fe and 14% in Cu.

A comparison has been made of irreversibility temperature determined by four different methods in few specimens of lead (type-I) and niobium (type-II). The merger ofM_ZFC(T) andM_FC(T) curves giveT_r(H) values lower than those evident from vanishing the hysteresis in isothermal DC magnetization. The identification of peak temperature inx″_H(T) data withT_r(H) is appropriate only if the contribution from changes in the normal state electrodynamics can be isolated and the peak is narrow. The appearance of differential paramagnetic effect inx′_H(T) data is adequate to imply reversibility, however, its efficacy to precisely locate irreversibility line remains to be established.

A new technique has been developed to measure isotope shifts of high-lying atomic levels using multi-step photoionization. This technique has been demonstrated with the measurement of isotope shift between²³⁵U and²³⁸U isotopes in the energy level at 34372.992 cm⁻¹. The value of isotope shift thus measured matches well with the value reported in literature.