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The reason is due to the difference in refractive indices bwteen air and water.
Short-sight is due to elongation of the eye-ball such that distance objects form images in front of the retina, giving a blur vision to the individual. It is corrected by wearing spectalces made of concave lenses so as to bring the image back to the position of the retina.
See diagrams on the following web-page
http://www.patient.co.uk/health/Short-Sight-Myopia.htm
When a short-sighted individual is swimming under water, the refractive index of water (~1.33) is higher than that of air. The difference in refractive indices between water and the eye-lens, and between air and the eye-lense thus reduces. This makes the light rays less convergent after passing through the eye-lens if the individual is under water. The image so formed, which originally is in front of the retina because of short-sight, would then be moved backward toward the retina. That is to say, the distance between the image and the retina is reduced when a short-sighted person is under water than he is in air. A short-sighted person would thus find himself seeing objects clearer in water, even without the help of eye-glasses, than in air.
Hence, to bring the image back to the retina, the focal length of the concave lens that the person wears can be longer (i.e. less divergent) than that used in air.
Swimming goggles are used under water. Therefore, concave lens of longer focal length (i.e. of less power) in the goggles would be sufficient to bring the image back to reach the retina.