Light from a point source in air falls on a convex curved surface of radius $$20 \mathrm{~cm}$$ and refractive index 1.5. If the source is located at $$100 \mathrm{~cm}$$ from the convex surface, the image will be formed at ________ $$\mathrm{cm}$$ from the object.

In an experiment to measure the focal length $$(f)$$ of a convex lens, the magnitude of object distance $$(x)$$ and the image distance $$(y)$$ are measured with reference to the focal point of the lens. The $$y$$-$$x$$ plot is shown in figure.

The focal length of the lens is ________ $$\mathrm{cm}$$.

The distance between object and its two times magnified real image as produced by a convex lens is $$45 \mathrm{~cm}$$. The focal length of the lens used is _______ cm.