In interference experiment the path difference between two interfering waves at a point $A$ on the screen is $\lambda / 3$, where $\lambda$ is the wavelength of these waves, and at another point $B$ the path difference is $\lambda / 6$. The ratio of intensities at points $A$ and $B$ is $\_\_\_\_$ .

The maximum intensity in a Young's double slit experiment is $I_0$. Distance between the slits $(d)$ is $5 \lambda$, where $\lambda$ is the wavelength of light used. The intensity of the fringe, exactly opposite to one of the slits on the screen, placed at $D=10 d$ is $\_\_\_\_$ .

In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is $2.4 \mu \mathrm{~m}$. If the experiment is carried out in another medium having refractive index 1.2 , the fringe width will be $\_\_\_\_$ $\mu \mathrm{m}$.

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 $\_\_\_\_$ .