Discuss the phenomenon of birefringence in a crystal. What do you understand by positive and negative crystals ? If the refractive indices of a calcite crystal for E-ray and O-ray are 1\cdot 488 and 1\cdot 658, respectively, then calculate the thickness of the crystal for which it can work as
(i) quarter wave plate,
(ii) half wave plate. (Wavelength of the light is 5890\text{ \AA})
The coherence length and the bandwidth of a light source is 3\text{ km} and 1 \times 10^{-5}\text{ nm}, respectively. Determine its wavelength and the pulse duration.
A transmission hologram is recorded in a medium of refractive index 1\cdot 15. If the spacing between the two consecutive maxima is 557\text{ nm} and the angle of incidence of reference and object waves from the reference axis (say z-direction) is 30^\circ, find the wavelength of the light source.
What is forced oscillation ? Write its equation of motion and obtain the general solution. Discuss the condition for the resonance.
A tuning fork A produces 6 beats per second with another tuning fork B of frequency 508\text{ Hz}. When the prongs of A are loaded with a little wax, number of beats heard are 4 per second. Find the frequency of A before it was loaded with wax.
State Fermat's principle. Using this principle, establish the Snell's law of refraction.
In a Newton's ring experiment, explain the following :
(i) Why are the fringes circular ?
(ii) Why is the central spot dark as seen by reflection ?
(iii) How can one obtain Newton's ring with bright centre ?
What do you understand by missing orders in a double-slit diffraction pattern ? Obtain condition for missing orders in a double-slit Fraunhofer diffraction pattern, if the slit width and the separation between the slits are equal. In a double-slit diffraction experiment, if the slit widths are 0\cdot 20\text{ mm} and they are 0\cdot 10\text{ mm} apart, find the missing orders.
Obtain the system matrix for a thick lens and derive the thin lens formula.
Show that the mean kinetic and potential energies of non-dissipative simple harmonic vibrating systems are equal.
Newton's rings are observed between a spherical surface of radius of curvature 100 cm and a plane glass plate. The diameters of 4th and 15th bright rings are 0.314 cm and 0.574 cm, respectively. Calculate the diameters of 24th and 36th bright rings and also the wavelength of light used.
A phase retardation plate of quartz has thickness 0.1436\,\mathrm{mm}. For what wavelength in the visible region will it act as quarter-wave plate? Given that \mu_{O}=1.5443 and \mu_{E}=1.5533.
In He-Ne laser, what is the function of He gas? Explain the answer with the help of energy level diagram for He – Ne laser.
Discuss the phenomenon of Fraunhofer diffraction at a single slit and show that the intensities of successive maxima are nearly in the ratio 1 : \frac{4}{9\pi^2} : \frac{4}{25\pi^2} : \frac{4}{49\pi^2}.
A mass m is suspended by two springs having force constants k_1 and k_2 as shown in the figure. The mass m is displaced vertically downward and then released. If at any instant t, the displacement of the mass m is x, then show that the motion of the mass is simple harmonic motion having frequency f=\frac{1}{2\pi}\sqrt{\frac{1}{m}\left(\frac{k_1k_2}{k_1+k_2}\right)}
What is damped harmonic oscillation? Write the equation of motion and obtain the general solution for this oscillation. Discuss the cases of dead beat, critical damping and oscillatory motion based on the general solution. What would be the logarithmic decrement of the damped vibrating system, if it has an initial amplitude 30\,\mathrm{cm}, which reduces to 3\,\mathrm{cm} after 20 complete oscillations?
What is achromatism ? Obtain the condition for achromatism of two thin lenses separated by a distance of x metres.
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 ?
A thin film of petrol of thickness 9 \times 10^{-6}\,\mathrm{cm} is viewed at an angle 30^\circ to the normal. Find the wavelength(s) of light in visible spectrum which can be viewed in the reflected light. The refractive index of the film \mu = 1.35.
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.
