UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Describe the working principle of a three level solid state laser giving the transitions involved in the laser action.

Write a short note on Holography.

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?

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?

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.

Show that for forced oscillations amplitude resonance and energy resonance do not occur at the same frequency.

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)

A body of mass m supported by a spiral spring causes an extension of d is the spring. The body is set in vertical oscillations of small amplitude. Find an expression for the periodic time of the oscillations.

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}.

Obtain the intensity pattern due to Fraunhofer diffraction at two parallel slits. Each slit has a width ‘a’ and the separation between the slits is d. How many interference fringes will appear in the central diffraction maximum, it d = 4a?

In a biprism experiment the fringe-width with lightly of wavelength \lambda = 5900\text{ \AA} is 0.43\text{ mm}. On introducing a mica sheet in the path of one of the interfering rays the central fringe shifts by 1.89\text{ mm}. If refractive index of mica is 1.59, calculate the thickness of the sheet.

Write a short note on Fourier transformation.

State Fourier's theorem. Discuss the conditions which a complex periodic curve must satisfy if it is to be analysed by this theorem. Show how the diffraction of waves at a single slit is related with a Fourier transform.

Briefly discuss the feasibility of a laser, emitting monochromatic Fermions, such as electrons.

The light (\lambda = 6000\text{\AA}) from a laser of sectional diameter 1.0 cm and power 0.02 watt is loosed by a lens of focal length 10 cm. Determine the area at the image and intensity in it in watt/cm{}^2.