The velocity of light changes all the time. If the velocity of light were constant, eveyrtything would be perfectly transparent and you couldn't see anything. So let me list down when, where and how the velocity of light changes.

1. Reflection.

Let us choose a convinient orthonormal coordinate system where the reflector is sitting in the $xy$-plane and the $z$-direction is normal (orthogonal, perpendicular) to the reflector. Then, the $y$-direction, let us say, is redundant, so discard it. For convenience, also let the point where the the light ray hits the reflector be the origin of the coordinate system. Now, clearly, then, the $x$ component of the light ray's velocity is negated while the $z$ component remains the same.

2. Refraction

The speed and direction are both changed. Let us say the light ray is hitting the refracvtive medium from a vacuum. Then, it will change its speed as $v=r^{-1}c_0$ and its angle will also be affected as $\theta_f=\arcsin\left(r\sin\theta_1\right)$.

3. Deflection

Here, light appears to bend due to gravity as per the Geodesic Equation, which can be shown using the Euler-Lagrange Equations. $$\frac{\mbox{d}^2x_\lambda}{\mbox{d}\tau^2}=-\Gamma_{\mu\nu}^\lambda\frac{\mbox{d}x^\mu}{\mbox{d}\tau}\frac{\mbox{d}x^\nu}{\mbox{d}\tau}$$ Of course, switching your coordinate system back to a curved one (using the inverse of the Christoffel symbols $\mathbf{\Gamma}$), the light is still following its geodesic in curved spacetime.

Luckily, photons are uncharged (electromagnetically) and thus are not deflected by electromagnetism.

For these reasons, light almost NEVER goes at a constant direction (in a straight line) or at a constant speed. Since there is gravity, opaque objects, non-vacuum media, etc. Also, in case you are talking about a constant being applied to light's direction, then there' is one more.:

4. Light is emmitted in different directions, and if it were only one, then that would single out a prefered direction,.

There are two questions here -- is the velocity of light constant, and is it invariant?

The direction/velocity of light changes whenever it interacts with something. This includes gravitational deflection, since things have to change direction in curved spacetime in one sense or another. The velocity isn't constant.

Is it invariant under Lorentz boosts in perpendiculal directions? No. The speed is invariant, but the velocity isn't. This should be fairly clear, but you can prove it with brute force --

We need to apply a boost to light's four-velocity, but the four-velocity of light is actually infinite -- it's (infinity, infinity, 0, 0), except the infinities satisfy a certain relation in the sense of being related through a limit. So we consider an object traveling at speed $w$ in the $x$-direction, boost $v$ in the $y$-direction and let $w\to c$. The four-velocity transforms under this boost as:

$$\left[ {\begin{array}{*{20}{c}}{\gamma (w)}\\{w\gamma (w)}\\0\\0\end{array}} \right] \to \left[ {\begin{array}{*{20}{c}}{\gamma (v)\gamma (w)}\\{w\gamma (w)}\\{ - v\gamma (v)\gamma (w)}\\0\end{array}} \right]$$

The conventional 3-velocity can be extracted here by considering $dx/dt$, $dy/dt$:

$$\frac{{dx}}{{dt}} = \frac{{dx/d\tau }}{{dt/d\tau }} = \frac{{w\gamma (w)}}{{\gamma (v)\gamma (w)}} = \frac{w}{{\gamma (v)}}$$ $$\frac{{dy}}{{dt}} = \frac{{dy/d\tau }}{{dt/d\tau }} = \frac{{ - v\gamma (v)\gamma (w)}}{{\gamma (v)\gamma (w)}} = - v$$

Taking the limit as $w\to 1$, you get a 3-velocity of $(1/\gamma(v),-v, 0)$ -- one may confirm that this is not equivalent to the original three-velocity that was $(1,0,0)$, but nonetheless has the same magnitude (speed is invariant).

The velocity of light changes all the time. If the velocity of light were constant, eveyrtything would be perfectly transparent and you couldn't see anything. So let me list down when, where and how the velocity of light changes.

1. Reflection.

Let us choose a convinient orthonormal coordinate system where the reflector is sitting in the $xy$-plane and the $z$-direction is normal (orthogonal, perpendicular) to the reflector. Then, the $y$-direction, let us say, is redundant, so discard it. For convenience, also let the point where the the light ray hits the reflector be the origin of the coordinate system. Now, clearly, then, the $x$ component of the light ray's velocity is negated while the $z$ component remains the same.

2. Refraction

The speed and direction are both changed. Let us say the light ray is hitting the refracvtive medium from a vacuum. Then, it will change its speed as $v=r^{-1}c_0$ and its angle will also be affected as $\theta_f=\arcsin\left(r\sin\theta_1\right)$.

3. Deflection

Here, light appears to bend due to gravity as per the Geodesic Equation, which can be shown using the Euler-Lagrange Equations. $$\frac{\mbox{d}^2x_\lambda}{\mbox{d}\tau^2}=-\Gamma_{\mu\nu}^\lambda\frac{\mbox{d}x^\mu}{\mbox{d}\tau}\frac{\mbox{d}x^\nu}{\mbox{d}\tau}$$ Of course, switching your coordinate system back to a curved one (using the inverse of the Christoffel symbols $\mathbf{\Gamma}$), the light is still following its geodesic in curved spacetime.

Luckily, photons are uncharged (electromagnetically) and thus are not deflected by electromagnetism.

For these reasons, light almost NEVER goes at a constant direction (in a straight line) or at a constant speed. Since there is gravity, opaque objects, non-vacuum media, etc. Also, in case you are talking about a constant being applied to light's direction, then there' is one more.:

4. Light is emmitted in different directions, and if it were only one, then that would single out a prefered direction,.

The velocity of light changes all the time. If the velocity of light were constant, eveyrtything would be perfectly transparent and you couldn't see anything. So let me list down when, where and how the velocity of light changes.

1. Reflection.

Let us choose a convinient orthonormal coordinate system where the reflector is sitting in the $xy$-plane and the $z$-direction is normal (orthogonal, perpendicular) to the reflector. Then, the $y$-direction, let us say, is redundant, so discard it. For convenience, also let the point where the the light ray hits the reflector be the origin of the coordinate system. Now, clearly, then, the $x$ component of the light ray's velocity is negated while the $z$ component remains the same.

2. Refraction

The speed and direction are both changed. Let us say the light ray is hitting the refracvtive medium from a vacuum. Then, it will change its speed as $v=r^{-1}c_0$ and its angle will also be affected as $\theta_f=\arcsin\left(r\sin\theta_1\right)$.

3. Deflection

Here, light appears to bend due to gravity as per the Geodesic Equation, which can be shown using the Euler-Lagrange Equations. $$\frac{\mbox{d}^2x_\lambda}{\mbox{d}\tau^2}=-\Gamma_{\mu\nu}^\lambda\frac{\mbox{d}x^\mu}{\mbox{d}\tau}\frac{\mbox{d}x^\nu}{\mbox{d}\tau}$$ Of course, switching your coordinate system back to a curved one (using the inverse of the Christoffel symbols $\mathbf{\Gamma}$), the light is still following its geodesic in curved spacetime.

Luckily, photons are uncharged (electromagnetically) and thus are not deflected by electromagnetism.

For these reasons, light almost NEVER goes at a constant direction (in a straight line) or at a constant speed. Since there is gravity, opaque objects, non-vacuum media, etc. Also, in case you are talking about a constant being applied to light's direction, then there' is one more.:

4. Light is emmitted in different directions, and if it were only one, then that would single out a prefered direction,.