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 by $50\%$. The value of $\left(\frac{V_1}{V_2}\right)$ is equal to :

If a source of electromagnetic radiation having power $15 \mathrm{kW}$ produces ${10}^{16}$ photons per second, the radiation belongs to a part of spectrum is :

(Take Planck constant $h = 6\times {10}^{-34} \mathrm{J} \mathrm{s})$

As shown in the figure, in Young's double slit experiment, a thin plate of thickness $t=10 \mathrm{\mu m}$ and refractive index $\mu =1.2$ is inserted infront of slit $S_1$. The experiment is conducted in air ($\mu =1$) and uses a monochromatic light of wavelength $\lambda =500 \mathrm{nm}$. Due to the insertion of the plate, central maxima is shifted by a distance of $x{\beta }_0$. ${\beta }_0$ is the fringe-width before the insertion of the plate. The value of the $x$ is ______.