A printer and an ink tank for the printer capable of precisely detecting that ink has run out in a foam type ink tank. The ink chamber and an ink passage are formed in this order between the foam containing portion and the ink outlet of a foam-type ink tank. A first filter is installed between the foam containing portion and the ink passage and used to pass bubbles therethrough, whereas a second filter having a pore diameter smaller than the pore diameter of the first filter is installed between the ink chamber and the ink passage. A rectangular prism for detecting an ink end is formed on the side of the ink chamber. When the reflective surface of the rectangular prism is exposed from an ink liquid level as bubbles are gathered in the ink chamber with ink that is running short, light is reflected from the reflective surfaces and is detected by a reflection type optical sensor on the ink-jet printer side, so that the ink end can be determined. In a case where the capacity of the ink chamber is set sufficiently smaller, the ink end is detectable at a point of time when the ink has substantially run out.