Why does object look larger in water relative to air?

In physics, refraction is normally the change in the path of a wave moving from one medium to a different or from a progressive change in the medium. Refraction of light may be the most commonly observed trend, but other waves for example sound waves and water waves also experience refraction. Just how much the wave is generally refracted is dependent upon the actual shift in wave speed and also the preliminary path associated with wave propagation relative to the path associated with alter in speed.

Light refraction follows Snell's law, which says that, for a given set of media, the ratio of the sines of the angle of incidence θ1 as well as angle of refraction θ2 is equivalent to the ratio of phase velocities (v1 / v2) in both media, or, the ratio of the indices of refraction (n2 / n1) of the two media. The refractive index or index of refraction of the material is a dimensionless quantity in optics that describes how fast light propagates within the material. The index of refraction indicates just how much the path of light is bent, or refracted, whenever entering a material.

Since air possesses a refractive index of essentially 1 and water comes with an index of refraction of just 1.33 the angle that the rays of light reach your eyes is bigger than the angle they might in air. This causes the angular size much larger for your eyes which makes the item appears larger compared to that they would likely appear in the air.