A prism is an optical medium bounded by three refracting plane surfaces. A ray of light suffers successive refractions on passing through its two surfaces and deviates by a certain angle from its original path. The refractive index of the material of the prism is given by $\mu=\sin \left(\frac{A+\delta_m}{2}\right) / \sin \frac{A}{2}$. If the angle of incidence on the second surface is greater than an angle called critical angle, the ray will not be refracted from the second surface and is totally internally reflected.

(i) The critical angle for glass is $\theta_1$ and that for water is $\theta_2$. The critical angle for glass-water surface would be (given ${ }_a \mu_g=1.5,{ }_a \mu_w=1.33$ )

(A) less than $\theta_2$

(B) between $\theta_1$ and $\theta_2$

(C) greater than $\theta_2$

(D) less than $\theta_1$

(ii) When a ray of light of wavelength $\lambda$ and frequency $v$ is refracted into a denser medium

(A) $\lambda$ and $v$ both increase.

(B) $\lambda$ increases but $v$ is unchanged.

(C) $\lambda$ decreases but $v$ is unchanged.

(D) $\lambda$ and $v$ both decrease.

(iii) (a) The critical angle for a ray of light passing from glass to water is minimum for

(A) red colour

(B) blue colour

(C) yellow colour

(D) violet colour

OR

(b) Three beams of red, yellow and violet colours are passed through a prism, one by one under the same condition. When the prism is in the position of minimum deviation, the angles of refraction from the second surface are $r_{\mathrm{R}}, r_Y$ and $r_{\mathrm{V}}$ respectively. Then

(A) $r_V< r_Y

(B) $r_Y< r_R

(C) $r_R< r_Y

(D) $r_{\mathrm{R}}=r_{\mathrm{Y}}=r_{\mathrm{V}}$

(iv) A ray of light is incident normally on a prism ABC of refractive index $\sqrt{ } 2$, as shown in figure. After it strikes face AC, it will

(A) go straight undeviated

(B) just graze along the face AC

(C) refract and go out of the prism

(D) undergo total internal reflection

(a) (i) Draw equipotential surfaces for an electric dipole.

(ii) Two point charges $q_1$ and $q_2$ are located at $\overrightarrow{r_1}$ and $\vec{r}_2$ respectively in an external electric field $\vec{E}$. Obtain an expression for the potential energy of the system.

(iii) The dipole moment of a molecule is $10^{-30} \mathrm{Cm}$. It is placed in an electric field $\vec{E}$ of $10^5 \mathrm{~V} / \mathrm{m}$ such that its axis is along the electric field. The direction of $\vec{E}$ is suddenly changed by $60^{\circ}$ at an instant. Find the change in the potential energy of the dipole, at that instant.

OR

(b) (i) A thin spherical shell of radius R has a uniform surface charge density $\sigma$. Using Gauss' law, deduce an expression for electric field (i) outside and (ii) inside the shell.

(ii) Two long straight thin wires AB and CD have linear charge densities $10 \mu \mathrm{C} / \mathrm{m}$ and $-20 \mu \mathrm{C} / \mathrm{m}$, respectively. They are kept parallel to each other at a distance 1 m . Find magnitude and direction of the net electric field at a point midway between them.

(a) (i) You are given three circuit elements $\mathrm{X}, \mathrm{Y}$ and $Z$. They are connected one by one across a given ac source. It is found that V and I are in phase for element $X$. V leads I by $\left(\frac{\pi}{4}\right)$ for element $Y$ while I leads $V$ by $\left(\frac{\pi}{4}\right)$ for element $Z$. Identify elements X, Y and $Z$.

(ii) Establish the expression for impedance of circuit when elements $X, Y$ and $Z$ are connected in series to an ac source. Show the variation of current in the circuit with the frequency of the applied ac source.

(iii) In a series LCR circuit, obtain the conditions under which (i) impedance is minimum and (ii) wattless current flows in the circuit.

OR

(b) (i) Describe the construction and working of a transformer and hence obtain the relation for $\left(\frac{v_s}{v_p}\right)$ in terms of number of turns of primary and secondary.

(ii) Discuss four main causes of energy loss in a real transformer.

(a) (i) A plane light wave propagating from a rarer into a denser medium, is incident at an angle $i$ on the surface separating two media. Using Huygen's principle, draw the refracted wave and hence verify Snell's law of refraction.

(ii) In a Young's double slit experiment, the slits are separated by 0.30 mm and the screen is kept 1.5 m away. The wavelength of light used is 600 nm . Calculate the distance between the central bright fringe and the $4^{\text {th }}$ dark fringe.

OR

(b) (i) Discuss briefly diffraction of light from a single slit and draw the shape of the diffraction pattern.

(ii) An object is placed between the pole and the focus of a concave mirror. Using mirror formula, prove mathematically that it produces a virtual and an enlarged image.