A solenoid has a core made of material with relative permeability 400 . The magnetic field produced in the interior of solenoid is 1.0 T . The magnetic intensity in SI units is $\alpha \times 10^5$. The value of $\alpha$ is $\_\_\_\_$ .

(Free space permeability $\mu_0=4 \pi \times 10^{-7}$ SI units.)

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 $\_\_\_\_$ .