An apparatus for measuring the height of a work held by a chuck table provided in a machining apparatus, including: a white light source for emitting a white beam of light; a chromatic aberration lens for condensing the white beam emitted from the white light source; a beam splitter which is disposed between the white light source and the chromatic aberration lens and by which a reflected beam of the white beam irradiating the work therewith is split; a first condenser lens for condensing the reflected beam split by the beam splitter; a diffraction grating by which the reflected beam condensed by the first condenser lens is converted into a diffracted beam; a second condenser lens for condensing the diffracted beam diffracted by the diffraction grating; and a wavelength detecting unit for detecting the wavelength of the diffracted beam condensed by the second condenser lens.