A magnetic field vector in an electromagnetic wave is represented by $\vec{B}=B_0 \sin \left(2 \pi v t-\frac{2 \pi x}{\lambda}\right) \hat{j}$. Its associated electric field vector is $\_\_\_\_$ .

A convex lens is made from glass material having refractive index of 1.4 with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is $\_\_\_\_$ .

An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at $30^{\circ}$ and $90^{\circ}$, respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at $60^{\circ}$ with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is $\_\_\_\_$ .

In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because

A. The size of gold nucleus is very small as compared to the size of gold atom.

B. Alpha particle and gold nucleus have equal charge.

C. The impact parameter is minimum for a few alpha particles.

D. A few alpha particles have very high kinetic energy.

E. Only a few alpha particles undergo head-on collision with the nuclei.

Choose the correct answer from the options given below :