As shown in the figure, a plane mirror is fixed at a height of $$50 \mathrm{~cm}$$ from the bottom of tank containing water $$\left(\mu=\frac{4}{3}\right)$$. The height of water in the tank is $$8 \mathrm{~cm}$$. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed by mirror from the bottom of the tank is ___________ $$\mathrm{cm}$$.

The radius of curvature of each surface of a convex lens having refractive index 1.8 is $$20 \mathrm{~cm}$$. The lens is now immersed in a liquid of refractive index 1.5 . The ratio of power of lens in air to its power in the liquid will be $$x: 1$$. The value of $$x$$ is _________.

A point object, 'O' is placed in front of two thin symmetrical coaxial convex lenses $$\mathrm{L}_{1}$$ and $$\mathrm{L}_{2}$$ with focal length $$24 \mathrm{~cm}$$ and $$9 \mathrm{~cm}$$ respectively. The distance between two lenses is $$10 \mathrm{~cm}$$ and the object is placed $$6 \mathrm{~cm}$$ away from lens $$\mathrm{L}_{1}$$ as shown in the figure. The distance between the object and the image formed by the system of two lenses is __________ $$\mathrm{cm}$$.

Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature $$30 \mathrm{~cm}$$. The centre of curvature of surface is towards denser medium and a point object is placed on the principle axis in rarer medium at a distance of $$15 \mathrm{~cm}$$ from the pole of the surface. The distance of image from the pole of the surface is ____________ $$\mathrm{cm}$$.