The equation of simple harmonic progressive wave is given by $y=A \sin (100 \pi t-4 x)$. The distance between two particles having a phase difference of $\left(\frac{\pi}{4}\right)^c$ is
A photon and an electron have an equal energy ' E '. The ratio of wavelength ' $\lambda_{\mathrm{p}}$ ' of photon to that of electron ' $\lambda_{\mathrm{e}}$ ' is proportional to
The height at which the acceleration due to gravity becomes $\frac{g}{4}$ in terms of $R$ is $[R=$ the radius of the earth $]$
In a biprism experiment, fifth dark fringe is obtained at a point. A thin transparent film of refractive index ' $\mu$ ' is placed in one of the interfering paths. Now $7^{\text {th }}$ bright fringe is obtained at the same point. If ' $\lambda$ ' is the wavelength of light used, the thickness of film is equal to