In a series LR circuit with $X_L = R$. Power factor is $P_1$. If a capacitor of capacitance $C$ with $X_c = X_L$ is added to the circuit the power factor becomes $P_2$. The ratio of $P_1$ to $P_2$ will be :

When a beam of white light is allowed to pass through convex lens parallel to principle axis, the different colors of light converge at different point on the principle axis after refraction. This is called

In Young's double slit experiment, following figure shows that $Q$ is the position of second bright fringe on the right side of point $O$. $P$ is the eleventh bright fringe on the other side measured from point $Q$. If the wavelength of light used is $6000$ Å, then what will be the value of $S_1 B$?

'n' polarizing sheets are arranged such that each makes an angle $45^\circ$ with the preceding sheet. An unpolarized light of intensity $I$ is incident into this arrangement. The output intensity is found to be $I/64$. The value of $n$ will be