In Young's double slit experiment, an electron beam is used to produce interference fringes of width $\beta_1$. Now the electron beam is replaced by a beam of protons with the same experimental set-up and same speed. The fringe width obtained is $\beta_2$. The correct relation between $\beta_1$ and $\beta_2$ is

When light propagates through a given homogeneous medium, the velocities of

An unpolarised light of intensity $$I$$ is passed through two polaroids kept one after the other with their planes parallel to each other. The intensity of light emerging from second polaroid is $$\frac{I}{4}$$. The angle between the pass axes of the polaroids is

In the Young's double slit experiment, the intensity of light passing through each of the two double slits is $$2 \times 10^{-2} \mathrm{~Wm}^{-2}$$. The screen-slit distance is very large in comparison with slit-slit distance. The fringe width is $$\beta$$. The distance between the central maximum and a point $$P$$ on the screen is $$x=\frac{\beta}{3}$$. Then, the total light intensity at the point is