In Young's double slit experiment, following figure shows that $Q$ is the position of second bright fringe on the right side of point $O$. $P$ is the eleventh bright fringe on the other side measured from point $Q$. If the wavelength of light used is $6000$ Å, then what will be the value of $S_1 B$?

'n' polarizing sheets are arranged such that each makes an angle $45^\circ$ with the preceding sheet. An unpolarized light of intensity $I$ is incident into this arrangement. The output intensity is found to be $I/64$. The value of $n$ will be

In Young's double slit experiment, two slits $S_1$ and $S_2$ are 'd' distance apart and the separation from slits to screen is $D$. Now if two transparent slabs of equal thickness $0.1$ mm but refractive index $1.51$ and $1.55$ are introduced in the path of beam ($\lambda = 4000$ Å) from $S_1$ and $S_2$ respectively. The central bright fringe spot will shift by ___ number of fringes.

The threshold frequency of metal is $f_0$. When the light of frequency $2f_0$ is incident on the metal plate, the maximum velocity of photoelectron is $v_1$. When the frequency of incident radiation is increased to $5f_0$ the maximum velocity of photoelectrons emitted is $v_2$. The ratio $v_1$ to $v_2$ is