Why a light ray does not refract when it is incident normally to the surface? I had read that when light enters a glass( or any other medium) its speed changes which lead to the bending of its path. But why doesn't light bend when it is incident normal to the surface. It is still entering a new medium and likewise, its speed will change but why doesn't it refract then?
I just can't understand it!
 A: Gilbert's answer is great, but if you want a different approach just look at Snell's law: $$n_1sin(\theta _1)=n_2sin(\theta _2)=$$
Where $n_i$ is the index of refraction for medium $i$, and $\theta _i$ is the angle the light ray makes with respect to the normal in each medium.
If light enters from medium $1$ to $2$ perpendicular to the boundary between the two media, then $\theta _1=0$. This means than $sin(\theta _2)=0$. The only values $\theta _2$ can have are then $0$ or $\pi$, but an angle of $\pi$ wouldhave the light ray not in medium $2$. Hence it must be that $\theta _2=0$.
A: According to Maxwell’s equations, the in-plane component of the light wave vector must be conserved across the interface.  This is one of the ways to think about refraction: it occurs to conserve the in-plane wave vector.  When light is at normal incidence, the in-plane wave vector is zero, so there’s no need for refraction.
Also, if light did refract from normal incidence, which way would it go?  Due to the symmetry of the system, there’s nothing to distinguish between left and right relative to the surface. 
A: The reason that the light is not refracting is that it will take the path that will take the shortest time from through the medium. This is essentially what snell's law gives us. Since, we are looking at light at normal incidence there is no path that will take shorter time than to continue straight forward in the same medium.
You can think of it as a life guard who is trying to save a person drowning in a river. If the river is flowing and the life guard will run towards the person at an angle(on land) and he takes the current into account as he is faster on land than in the water. Thus, having different angles on land and in the water. If the water is still and the person needing help is straight out from the shore the life guard will run in a straight line to the shore and then swim straight out to rescue the person in the water.
Snell's law can be derived from Fermat's Principle which is the statement that the light will take the path that uses the least time. See the wikipedia article Snell's law for the derivation of the formula.
as mentioned by Aaron since the $\theta_1$ is zero, thus $\sin(\theta_1)=0$, $\theta_2$ needs to be zero for Snell's law to be satisfied. Below is snell's law:
$$n_1\sin(\theta _1)=n_2\sin(\theta _2)$$
It is also possible to derive this directly form Maxwell's equations but that would be a boring and time consuming task.
Also note that if we are going from a medium with higher refractive index to a medium with lower refractive index we can get a situation where we will need $sin(\theta_2)$ to be greater than 1, this will result in a total internal reflection where no light will pass trough the interface.
A: It does change speed. Only it bends to the same angle. Remember Snell's law.
$$ \sin(\theta_1) \mu_1 = \sin(\theta_2) \mu_2 $$
The $\theta$'s are the angle away form perpendicular. So at perpendicular they are zero. And $\sin()$ of zero is zero.
But it does change speed. And you can demonstrate this by using an object with a back that is not parallel to its front. When the light gets to the back it will then refract as usual when it exits. 
A: The premise is only true for substances that can be described with a single refractive index: isotropic substances or cubic crystals. 
It is not true for uniaxial crystals etcetera like quartz or calcite. Those are birefringent. There will be two rays, with different polarizations. At normal incidence, the extraordinary ray is bent. The  ordinary ray follows Snell's law with the ordinary refractive index and is not bent at normal incidence.
Huygens explained this in Traité de la Lumière, using Huygens construction and elliptical wavefronts. 

