What is a quarter plate? A phase retardation plate of quartz has a thickness 0.1436\text{ mm}. Calculate the wavelength in visible region for which this plate will act as a quarter for plate. The refraction indices of quartz for ordinary and extraordinary rays are 1.5443 and 1.5533 respectively.
The amplitude of damped oscillator of frequency 300\text{ Hz} reduces one-tenth of its initial amplitude after 3000 oscillations. Calculate the damping constant and the time in which its energy will reduce to one-tenth of its initial energy.
Give the concept of Fresnel's half period zones. Describe the salient features of Fresnel's diffraction pattern due to a straight edge, showing the intensity distribution. How are these features explained?
A plane transmission grating has 6000 lines per cm. Determine the angular separation between the two lines of sodium of wavelengths 5896\text{ \AA} and 5890\text{ \AA} in the second order spectrum. If the width of the grating is 2.5\text{ cm}, will these lines be resolved?
In a hydrogen atom for the 2\text{p} \to 1\text{ s} transition the probability per unit time is 6 \times 10^8\text{ s}^{-1}. Calculate the angular frequency of the emitted photons and the order of Einstein's coefficient \text{B}_{21}.
Why does a soap film appear coloured when is viewed by reflected white light? A thin film is illuminated by sodium light of wavelength 5900\text{\AA}. Its refractive index is 1.42. Calculate its minimum thickness so that it appears dark in reflected light.
What is spatial coherence ? Considering Young's two slit experiment, prove that the distance between the slits must be sufficiently less than (\lambda/\theta) for obtaining fringes of good contrast. \lambda is the wavelength of light used and \theta is the angle subtended by the source at the slits.
Write a short note on Holography.
What is a quarter wave plate? Explain its use in the production and detection of circularly polarized light. For calcite for \lambda = 5472 \text{\AA}, \mu_O = 1.658 and \mu_E = 1.486. If the minimum thickness of a plate that can be cut from calcite is 30 \mu\text{ m}, what should be the minimum thickness for preparing a quarter wave plate?
A fine slit is illuminate by monochromatic light of wave-length 6000 Å. A thin wire is placed parallel to the slit and the diffraction pattern is observed on a screen at a distance of 1 m from the wire. In the shadow of the wire equidistant fringes of thickness 1.5 mm are observed. How do you explain this observation ? Calculate he diameter of the wire also.
The angular separation between two distant stars is 1 arc-second. If the effective wavelength of light is 5500 Å; what should be the diameter of the objective of a telescope so that the stars are just resolved?
Show that the interference fringes obtained in Young's two slit experiment are hyperbolic in shape. Under what conditions these are expected to appear straight?
What is meant by temporal and spatial coherence ? Show that the coherence length L = \lambda Q, where \lambda is the mean wavelength and Q represents the purity of a spectral line.
The potential energy for the interaction between two gas molecules can be represented by the function. \phi(r) = -\phi_0 \left[ 2 \left(\frac{r_0}{r}\right)^6 - \left(\frac{r_0}{r}\right)^{12} \right] Where \phi_0 and r_0 are constant. Prove that for small oscillations the frequency is given by \omega = \left( \frac{144 \phi_0}{m r_0^2} \right)^{1/2} Where m is mass of each molecule.
Write a short note on Fourier transformation.
Write the equation of motion for an oscillator driven by a simple harmonically varying force. Obtain the condition for maximum energy transfer to the oscillator.
Describe the working principle of a three level solid state laser giving the transitions involved in the laser action.
Obtain an expression for the ratio of the probabilities of stimulated and spontaneous emissions. What do you infer from this relation? How is population inversion interpreted thermodynamically?
A left circularly polarized beam of light (\lambda = 6000\text{ \AA}) is incident on a quartz crystal (Optic axis parallel to the surface). Find the state of polarisation of the emergent beam. (Thickness of quartz crystal = 2.3 \times 10^{-5}\text{ m}, \mu_e = 1.5538, \mu_o = 1.5444)
Discuss the working principle of He-Ne laser indicating the transitions involved in the process. Determine the power output of a laser in which a 3.0\text{ J} pulse is delivered in 1.0\text{ ns}.
