UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Consider a bare fiber having n_1 = 1\cdot 48 and n_2 = 1\text{ (air)}. Find out the NA. What is the maximum incident angle up to which light can be guided through the fiber?

(i) What is birefringence? Indicate how it can be used to obtain plane and circularly polarized light.

(ii) A left circularly polarized beam of light having \lambda_0 = 5893\text{ \AA} is incident on a calcite crystal with its optic axis cut parallel to the surface. The crystal has thickness d = 0\cdot 005141\text{ mm}, n_o = 1\cdot 65836 and n_e = 1\cdot 48641 at this \lambda_0. What will be the state of polarization of the incident beam?

With a suitable diagram, deduce an expression for numerical aperture (NA) for an optical fiber having refractive indices of core and cladding n_1 and n_2, respectively and being placed in a medium of index n_0.

What do you mean by underfilled and overfilled conditions with reference to numerical aperture in exciting light in fiber?

Why is the NA of the single-mode optical fiber low as compared to multimode fiber?

Show that two convex lenses of the same material kept separated by a distance a, which is equal to the average of two focal lengths, may be used as an achromat, that is, a=\frac{1}{2}(f_1+f_2).

In the propagation of longitudinal waves in a fluid contained in an infinitely long tube of cross-section A, show that \rho=\rho_0\left(1-\frac{\partial\xi}{\partial x}\right) where, \rho_0 = equilibrium density \rho = density of the fluid in the disturbed state \frac{\partial\xi}{\partial x}=\text{volume strain}\quad\left(\left|\frac{\partial\xi}{\partial x}\right|\ll1\right)

What is the significance of the null result of Michelson-Morley experiment? Does it disprove the existence of ether? Justify.

When a sphere of radius r falls down a homogeneous viscous fluid of unlimited extent with the terminal velocity v, the retarding viscous force acting on the sphere depends on the coefficient of viscosity \eta, the radius r and its velocity v. Show how Stokes' law was arrived at connecting these quantities from the dimensional considerations.

What are Eulerian angles? A body with rotational symmetry about an axis is rotating under gravity about a point on the axis without friction. What are the quantities remaining constant during the motion? Find them in terms of suitable Eulerian angles. Explain 'precession' and 'nutation' of such a body.

Establish the relation between the angular momentum and torque of a particle. Show that this relation leads one to the principle of conservation of angular momentum.

How can one introduce the constraints of motion through the concept of generalized coordinate systems? Write down the set of transformation equations for a system of N particles relating the generalized coordinates with the real coordinates.

(ii) Which term in the above equation represents the Coriolis force?

A uniform solid sphere of radius R having moment of inertia I about its diameter is melted to form a uniform disc of thickness t and radius r. The moment of inertia of the disc about an axis passing through its edge and perpendicular to the plane is also equal to I. Show that the radius r of the disc is given by r=\dfrac{2R}{\sqrt{15}}.

(iii) Discuss the important role of Coriolis forces in the circulation pattern of winds.

A planet revolves around the Sun in an elliptic orbit of eccentricity e. If T is the time period of the planet, find the time spent by the planet between the ends of the minor axis close to the Sun.

(ii) At what velocity, the electron momentum will be m_0 c?

(i) An electron of rest mass m_0 moves with a velocity v such that its total energy is double of its rest mass energy. What is the electron velocity?

(i) For a particle of mass m moving with velocities \vec{v}_s and \vec{v}_r relative to the space and rotating axis, respectively, show that the equation of motion is obtained as \vec{F}-2m(\vec{\omega}\times\vec{v}_r)-m\vec{\omega}\times(\vec{\omega}\times\vec{r}) = m\vec{a}_r with \vec{\omega} and \vec{a}_r being the angular velocity and acceleration in rotating coordinates.