Certain string has a linear mass density of 0.25\text{ kgm}^{-1} and stretched with a tension of 25 N. One end is given a sinusoidal motion, its frequency 5 Hz and amplitude 0.01 metre. If at t = 0, the end has zero displacement and is moving along the positive Y direction, derive the wave speed, the wavelength and the wave equation of the wave in the string.

Why does one get polarised light from a Nicol's prism? How should one adjust the polariser and analyser, so that an intensity of the incident light is reduced by a factor of 0.25?

A parallel laser beam is incident perpendicularly on a photographic plate. An object is placed at a distance a in front of the photographic plate. Discuss the recording from the plate. If the plate is illuminated by the same light, what is expected and why?

Parallel rays fall on circular aperture of diameter 1 mm. At a certain position of the screen one gets a dark spot on an axial point. When the screen is moved by 12.5 cm, one again gets a dark spot. Determine \gamma (wavelength).

Monochromatic light from a distance source of wavelength \lambda falls on a double slit. A glass plate of thickness t is inserted between one slit and the screen. Calculate the intensity at the central point as the function of thickness t.

When fixed at both ends, a wire under tension of 900\text{ N} and having a linear density 10^{-2}\text{ kg/m} is resonant at the frequency of 420\text{ Hz}. The next higher frequency at which it resonates is 490\text{ Hz}. What is the length of the wire.

The case of a Simple Harmonic Progressive Wave traversing through a medium is expressed as y = 4 \times 10^{-5} \sin(600\ \pi t + \varphi) Determine

(i) amplitude of vibration of the particles.

(ii) wavelength of the sound wave and

(iii) the phase difference between the particles situated at a distance of 22\text{ cm}. (The sound velocity in the medium is 3.4 \times 10^4\text{ cm/s}).

Show that Simple Harmonic Motion can he described as the projection on its diameter of a uniform circular motion.

A book sits on a horizontal board that is undergoing simple harmonic motion with amplitude of 1\text{ m}. The coefficient of friction between the book and the board is \mu = 0.5. Find the frequency of the motion of the board at which the book is about to slip.

Explain in detail how one can obtain fringes with the Michelson Interferometer using incandescent lamps.

How does the resolving power of a microscope differ from that of a telescope ? Find the resolving power of an electron microscope that uses 15\text{ Key} electrons, assuming that this is equal to the electron wavelength.

Write a short note on Holography.

Four perfect polarizing plates are stacked so that the axis of each is turned 30 clockwise with respect to the preceding plate: the last plate is crossed with the first. How much of the intensity of an incident unpolarized light is transmitted by the stack ?

The maximum pressure variation P that the human ear can tolerate in loud sounds is about 28\text{ nt/m}^2. Normal atmospheric pressure is about 100,000\text{ nt/m}^2. Find the corresponding maximum displacement for a soundwave in air having a frequency of 100\text{ cycles/second}. (Take velocity of sound in air as 331\text{ m/sec.} arid density of air = 1.22\text{ kg/m}^3)

Write a short note on Forced oscillations.

What are damped oscillations ? Obtain the differential equation for damped oscillations and write its possible solution. Explain with corresponding sketches, when there can be very heavy damping, critical damping and weak damping.

The equation of a one-dimensional propagating harmonic transverse wave is given by: y = 8 \sin 30\pi \left(t - \frac{x}{240}\right) \text{meter} Find the resultant wave formed by the superposition of the incident and the reflected waves from a rigid end. Also determine the amplitude of stationary waves formed at x = 2\text{ meter}. What will be the distance between consecutive nodes ?

Write a short note on Holography.

A short-focus lens is used to focus a laser beam of wavelength 6328 \AA. If the beam width is comparable to the focal length of the lens, calculate the area of cross-section of the region of focus.

Explain why a two-level system is not adequate for laser operation. Draw the essential parts of a ruby laser and explain the working principle with the help of an energy level diagram.