Light of wavelength $580$ nm is incident normally on a slit of width '$a$'. The distance between slit and screen is $2.5$ m and the distance of the second order maximum from the centre of the screen is $14.5$ mm in a diffraction pattern. The value of '$a$' is

In an interference experiment, the $m^{th}$ bright fringe for light of wavelength $\lambda_1$ coincides with the $n^{th}$ dark fringe for light of wavelength $\lambda_2$ . The ratio $\dfrac{\lambda_2}{\lambda_1}$ is

In a biprism experiment, the distance between $4^{th}$ and $13^{th}$ bright band on the same side is '$y$' when light of wavelength $6000$ Å is used. For a light of wavelength '$\lambda$' the distance between $6^{th}$ and $16^{th}$ bright band on the same side is again '$y$'. The value of '$\lambda$' in Å units is

The proton and $\alpha$ - particle are accelerated through same potential difference. Then the ratio of the de-Broglie wavelength of proton and $\alpha$ - particle is (mass of $\alpha$-particle is $4$ times mass of proton, charge of $\alpha$-particle is $2$ times charge of proton)