The figure shows surface XY separating two transparent media, medium -1 and medium -2 . The lines ab and cd represent wavefronts of a light wave traveling in medium -1 and incident on X Y. The lines ef and gh represent wavefronts of the light wave in medium -2 after refraction.
The phases of the light wave at $$c, d, e$$ and $$f$$ are $$\phi_c, \phi_d, \phi_{e}$$ and $$\phi_{f}$$ respectively.
It is given that $$\phi_{c} \neq \phi_{f}$$.
The figure shows surface XY separating two transparent media, medium -1 and medium -2 . The lines ab and cd represent wavefronts of a light wave traveling in medium -1 and incident on X Y. The lines ef and gh represent wavefronts of the light wave in medium -2 after refraction.
Speed of the light is
Column I describe some situations in which a small object moves. Column II describes some characteristics of these motions. Match the situation in Column I with the characteristics in Column II and indicate your answer by darkening appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.
| Column I | Column II | ||
|---|---|---|---|
| (A) | The object moves on the x-axis under a conservative force in such a way that its "speed" and "position" satisfy $$v = {c_1}\sqrt {{c_2} - {x^2}} $$, where $$c_1$$ and $$c_2$$ are positive constants. | (P) | The object executes a simple harmonic motion. |
| (B) | The object moves on the x-axis in such a way that its velocity and its displacement from the origin satisfy $$v=-kx$$, where $$k$$ is a positive constant. | (Q) | The object does not change its direction. |
| (C) | The object is attached to one end of a massless spring of a given spring constant. The other end of the spring is attached to the ceiling of an elevator. Initially everything is at rest. The elevator starts going upwards with a constant acceleration a. The motion of the object is observed from the elevator during the period it maintains this acceleration. | (R) | The kinetic energy of the object keeps on decreasing |
| (D) | The object is projected from the earth's surface vertically upwards with a speed $$2\sqrt {GMe/{\mathop{\rm Re}\nolimits} } $$, where, M$$_e$$ is the mass of the earth and R$$_e$$ is the radius of the earth. Neglect forces from objects other than the earth. | (S) | The object can change its direction only once. |
Two wires each carrying a steady current I are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.
| Column I | Column II | ||
|---|---|---|---|
| (A) | Point P is situated midway between the wires. |
(P) | The magnetic fields (B) at P due to the currents in the wire are in same direction. |
| (B) | Point P is situated at the mid-point of the line joining the centers of the circular wires, which have same radii. |
(Q) | The magnetic fields (B) at P due to the currents in the wires are in opposite directions. |
| (C) | Point P is situated at the mid-point of the line joining the centers of the circular wires, which have same radii. |
(R) | There is no magnetic field at P. |
| (D) | Point P is situated at the common center of the wires. |
(S) | The wires repel each other. |