Three polaroid sheets are co-axially placed as indicated in the diagram. Pass axes of the polaroids 2 and 3 make $30^{\circ}$ and $90^{\circ}$ with pass axis of polaroid sheet 1 . If $I_0$ is the intensity of the incident unpolarised light entering sheet 1 , the intensity of the emergent light through sheet 3 is

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