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

An electron accelerated through a potential difference $V_1$ has a de-Broglie wavelength of $\lambda$. When the potential is changed to $V_2$, its de-Broglie wavelength increases to $2\lambda$. The value of $(V_1/V_2)$ is equal to

The wavelength of the radiation emitted is $\lambda_0$ when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be $(20\lambda_0/x)$. The value of $x$ is