Let n₁ be the refractive index of air and n₂ be of water.
You already know that n₂>n₁ because light is bent towards normal in case of denser medium.
Speed of light in air(v₁) = c/n₁................ c = ultimate speed limit of the universe which is speed of light in vacuum.
Speed of light in water(v₂) = c/n₂
Dividing both the relations,
v₁ c/n₁ n₂
--- = ------- = ---
v₂ c/n₂ n₁
v₁/v₂ = n₂/n₁
∴ v₂ = v₁n₁/n₂
As n₂>n₁,
v₂<v₁
So the speed of light slows down!
