The radius of curvature of a concave mirror is 24 cm and the image is magnified by 1.5 times. The object distance is

A point source of light is kept at a depth of h in water of refractive index 4/3. The radius of the circle at the surface of water through which light emits is

Two convex lens $$(\mathrm{L}_1$$ and $$\mathrm{L}_2)$$ of equal focal length $$\mathrm{f}$$ are placed at a distance $$\frac{\mathrm{f}}{2}$$ apart. An object is placed at a distance $$4 \mathrm{f}$$ in the left of $$\mathrm{L_1}$$ as shown in figure. The final image is at

If $$\hat{n}_1, \hat{n}_2$$ and $$\hat{\mathrm{t}}$$ represent, unit vectors along the incident ray, reflected ray and normal to the surface respectively, then