Dispersive methods of measuring oscillator strengths are widely used because they have a wide dynamic range and are independent of any assumptions about the spectral line shape. They are not, however, very sensitive. The advantages may be retained and the sensitivity improved by a factor of 102 if the dispersing vapour contained in one arm of a Mach-Zender interferometer is illuminated by a tunable dye laser and the shift in the interference fringes is observed directly. The method is described in detail and its sensitivity demonstrated by measurement of the ratio of oscillator strengths for the 62S1/2-72P1/2,3/2 transitions of caesium.