Underwater cameras have a flat piece of glass between the lens and the water – essentially the same as underwater goggles (you can also see clearly underwater when wearing goggles).
However, it is possible to see clearly underwater when the rounded lens touches the water directly, but it requires a much more rounded lens shape. For example, fish can see perfectly fine without a flat surface between the lens and the water. Note that the lenses of a fish are much more rounded than ours. If our eye muscles could pull our lens into such a round shape, we could also see clearly underwater.
Fun fact: there are fish that hunt by spitting water at low-flying insects. Their lenses are split horizontally, with two different curvatures: the top half can see clearly in air, while the bottom half can see clearly underwater.
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