To investigate the distribution of dust in Sb and Sc galaxies we have analyzed near-infrared and optical surface photometry for an unbiased sample of 37 galaxies. Since light in the K-band is very little affected by extinction by dust, the B - K colour is a good indicator of the amount of extinction, and using the colour-inclination relation we can statistically determine the extinction for an average Sb/Sc galaxy. We find in general a considerable amount of extinction in spiral galaxies in the central regions, all the way out to their effective radii. In the outer parts, at D_K,21_, or at 3 times the typical exponential scale lengths of the stellar distribution , we find a maximum optical depth of 0.5 in B for a face-on galaxy. If we impose the condition that the dust is distributed in the same way as the stars, this upper limit would go down to 0.1.