A plane wavefront of width ' $x$ ' is incident on an air-water interface and the corresponding refracted wavefront has a width ' y ' as shown in figure. The refractive index of air with respect to water in terms of distances ' $w$ ' and ' $z$ ' is $(\mathrm{AD}=\mathrm{w}, \mathrm{CB}=\mathrm{z})$

The intermediate image formed by an objective lens of a compound microscope is
A solid sphere and a ring have equal mass and equal radius of gyration. If sphere is rotating about its diameter and ring about an axis passing through centre and perpendicular to its plane, then the ratio of radius of sphere to that of ring is $\sqrt{\frac{x}{2}}$ then the value of ' $x$ ' is
The third overtone of a closed pipe of length ' $\mathrm{L}_{\mathrm{c}}$ ' has the same frequency as the third overtone of an open pipe of length ' $L_0$ '. The ratio ' $\mathrm{L}_{\mathrm{c}}$ ': ' $\mathrm{L}_0$ ' is equal to (Neglecting end correction)