An a.c. source is applied to a series LR circuit with $X_L = 3R$ and power factor is $X_1$. Now a capacitor with $X_c = R$ is added in series to LR circuit and power factor is $X_2$. The ratio $X_1$ to $X_2$ is

In an a.c. circuit, a resistance R is connected in series with an inductance 'L'. If phase angle between voltage and current is $45^\circ$, the value of inductive reactance will be
($\sin 45^\circ = \dfrac{1}{\sqrt{2}} = \cos 45^\circ$)

A simple microscope is a combination of two lenses in contact. Their powers are $+20\text{D}$ and $-4\text{D}$. The distance of distinct vision is $25\ \text{cm}$. When seen through the microscope, the size of the image of an object $3\ \text{mm}$ high is

When a glass plate of refractive index $1.44$ is introduced in the path of one of the interfering beams, the fringes are displaced by a distance '$y$'. If this plate is replaced by another plate of same thickness but of refractive index $1.66$, the fringes will be displaced by a distance