What happens to the direction of bullet penetrating water surface? If I fire a bullet (for simplicity, let's assume its shape is spherical) from outside a water tank on the surface making a nonzero angle $\theta$ from the normal. As the bullet penetrates the water whether it will follow the same path or it will change its direction and bent towards normal.
I want to know whether the bullet behaves like a light ray refracting under the water. Some of its momentum is lost along the surface of water as the penetrating bullets generates ripples on the surface of water. To counter this momentum lost from the ripple, it should bent towards the normal just like light rays reflects.
This is just my thought, I am not sure whether my thought is in the right direction. If anyone is aware of such experiment I would appreciate if you could share me the insight of it.
 A: Upon entry, the projectile will experience high forces that are not co-linear with its trajectory, thus bending it. The added mass force will be the main component of the resistance at the expected speeds in the initial stages of its entry into the fluid medium.
The added mass coefficient is a non dimensional constant of proportionality that relates the acceleration of the body in a quiescent fluid to the resistance force that it experiments due to acceleration of the fluid immediately surrounding the body. Conceptually, it represents the proportion of the mass of the body made up by the mass of fluid that one has to mobilise to accelerate the submerged body. And while this constant will actually depend on the direction and shape of the body (and will be evolving as the projectile enters the fluid), it is a quantity that for relatively bulky bodies (like a sphere) will be close to one in order-of-magnitude terms. So one could attempt to derive a rough estimate of the effect that it will have on the projectile assuming an order-1 value and obtain a sort of 'Snell's law' for the bullet.
However, it turns out that this strategy would not work, since the nonlinearity of the problem results in the following situation (see Miloh and Shukron (1991)):


*

*For trajectories that have a not-too-small incidence angle the projectile will barely bend, so it will go straight into the water.

*For trajectories with an angle close to the critical angle (that at which the projectile will actually bounce back and emerge from the water), the trajectory will be very sensitive to the incidence angle.

*Neither the critical angle, nor the sensitivity with respect to variations of the incidence angle around it are very sensitive to the relative density of the projectile.

*The trajectory will be curved after entry, so that too broken straight lines will not represent a good approximation of the motion of the projectile.


In a nutshell, the behaviour will not resemble that of a light ray, although the projectile will surely bend, if a small enough incidence angle is considered.
